Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#51 2015-12-20 15:29:53

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

38. Nikola Tesla

Nikola Tesla (10 July 1856 – 7 January 1943) was a Serbian American inventor, electrical engineer, mechanical engineer, physicist, and futurist best known for his contributions to the design of the modern alternating current (AC) electricity supply system.

Tesla gained experience in telephony and electrical engineering before emigrating to the United States in 1884 to work for Thomas Edison in New York City. He soon struck out on his own with financial backers, setting up laboratories and companies to develop a range of electrical devices. His patented AC induction motor and transformer were licensed by George Westinghouse, who also hired Tesla for a short time as a consultant. His work in the formative years of electric power development was involved in a corporate alternating current/direct current "War of Currents" as well as various patent battles.

Tesla went on to pursue his ideas of wireless lighting and electricity distribution in his high-voltage, high-frequency power experiments in New York and Colorado Springs, and made early (1893) pronouncements on the possibility of wireless communication with his devices. He tried to put these ideas to practical use in his ill-fated attempt at intercontinental wireless transmission, which was his unfinished Wardenclyffe Tower project. In his lab he also conducted a range of experiments with mechanical oscillators/generators, electrical discharge tubes, and early X-ray imaging. He also built a wireless controlled boat, one of the first ever exhibited.

Tesla was renowned for his achievements and showmanship, eventually earning him a reputation in popular culture as an archetypal "mad scientist". His patents earned him a considerable amount of money, much of which was used to finance his own projects with varying degrees of success. He lived most of his life in a series of New York hotels, through his retirement. He died on 7 January 1943. His work fell into relative obscurity after his death, but in 1960 the General Conference on Weights and Measures named the SI unit of magnetic flux density the tesla in his honor. There has been a resurgence in interest in Tesla in popular culture since the 1990s.

znameniti-srbi.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#52 2015-12-21 14:35:48

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

39. Werner Heisenberg

Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 he published his uncertainty principle, upon which he built his philosophy and for which he is best known. Heisenberg was awarded the Nobel Prize in Physics for 1932 "for the creation of quantum mechanics". He also made important contributions to the theories of the hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles, and he was instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in Munich, in 1957.


Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics, which soon thereafter was renamed the Max Planck Institute for Physics. He was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics.

Heisenberg was also president of the German Research Council, chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation.

heisenberg-werner-quantum-1.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#53 2015-12-21 20:21:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: crème de la crème

An interesting fellow that Tesla.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#54 2015-12-22 10:03:21

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: crème de la crème

Do you take requests? P:
I would add John von Neumann, and John Nash, even if bobbym thinks game theory is boring xD

Offline

#55 2015-12-22 13:58:46

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

Thanks, bobbym! Certainly, Relentless...I shall add these soon!

Benjamin Franklin

40. Benjamin Franklin (January 17, 1706 – April 17, 1790) was one of the Founding Fathers of the United States. A renowned polymath, Franklin was a leading author, printer, political theorist, politician, freemason, postmaster, scientist, inventor, civic activist, statesman, and diplomat. As a scientist, he was a major figure in the American Enlightenment and the history of physics for his discoveries and theories regarding electricity. As an inventor, he is known for the lightning rod, bifocals, and the Franklin stove, among other inventions. He facilitated many civic organizations, including Philadelphia's fire department and a university.

Franklin earned the title of "The First American" for his early and indefatigable campaigning for colonial unity, first as an author and spokesman in London for several colonies. As the first United States Ambassador to France, he exemplified the emerging American nation. Franklin was foundational in defining the American ethos as a marriage of the practical values of thrift, hard work, education, community spirit, self-governing institutions, and opposition to authoritarianism both political and religious, with the scientific and tolerant values of the Enlightenment. In the words of historian Henry Steele Commager, "In a Franklin could be merged the virtues of Puritanism without its defects, the illumination of the Enlightenment without its heat." To Walter Isaacson, this makes Franklin "the most accomplished American of his age and the most influential in inventing the type of society America would become."

Franklin became a successful newspaper editor and printer in Philadelphia, the leading city in the colonies. With two partners he published the Pennsylvania Chronicle, a newspaper that was known for its revolutionary sentiments and criticisms of the British policies. He became wealthy publishing Poor Richard's Almanack and The Pennsylvania Gazette.

He played a major role in establishing the University of Pennsylvania and was elected the first president of the American Philosophical Society. Franklin became a national hero in America when as agent for several colonies he spearheaded the effort to have Parliament in London repeal the unpopular Stamp Act. An accomplished diplomat, he was widely admired among the French as American minister to Paris and was a major figure in the development of positive Franco-American relations. His efforts to secure support for the American Revolution by shipments of crucial munitions proved vital for the American war effort.

For many years he was the British postmaster for the colonies, which enabled him to set up the first national communications network. He was active in community affairs, colonial and state politics, as well as national and international affairs. From 1785 to 1788, he served as governor of Pennsylvania. Toward the end of his life, he freed his own slaves and became one of the most prominent abolitionists.

His colorful life and legacy of scientific and political achievement, and status as one of America's most influential Founding Fathers, have seen Franklin honored on coinage and the $100 bill; warships; the names of many towns; counties; educational institutions; corporations; and, more than two centuries after his death, countless cultural references.

benjamin-franklin-520.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#56 2015-12-22 14:12:10

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: crème de la crème

That's good! I think von Neumann is quite underappreciated.

I once played around with various lists of names for a bit of fun, in order to create an amateur scale of "revolutionary genius".
From memory, the top five names in order were:
Isaac Newton
Albert Einstein
Euclid
Aristotle
Galileo Galilei

Offline

#57 2015-12-23 14:55:41

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

41. Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Christian philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.

In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and fifty prototypes, he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following ten years, establishing him as one of the first two inventors of the mechanical calculator.

Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646, he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.

In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. His father died in 1651. Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids.

Pascal had poor health, especially after his 18th year, and his death came just two months after his 39th birthday.

Blaise-Pascal1.jpg

Last edited by Jai Ganesh (2015-12-23 14:57:42)


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#58 2015-12-25 15:01:04

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

42. Ferdinand Magellan

Born: 1480 - Oporto, Portugal
Died: April 27, 1521 - Cebu, Philippines

Portuguese explorer

While in the service of Spain, the Portuguese explorer Ferdinand Magellan led the first European voyage of discovery to circumnavigate (travel around) the globe. His voyage provided clear proof that the Earth is round.

Early life and travels

Ferdinand Magellan was born in Oporto, Portugal, in 1480. His parents were members of the Portuguese nobility, and the young Magellan found himself in the service of royalty at an early age. He was only twelve when he began serving the queen of Portugal as a page, a position of employment for youths in royal courts. As a young member of Queen Leonora's School of Pages in Lisbon (the Portuguese capital) Magellan was encouraged to learn subjects that would aid him greatly later, such as cartography (mapmaking), astronomy, and celestial navigation (learning how to steer a ship based on the positions of the stars).

Magellan joined the Portuguese service to sail with the fleet in 1505. He went to East Africa and later was at the battle of Diu, in which the Portuguese destroyed the Egyptian fleet's dominance in the Arabian Sea. He went twice to Malacca, located in present-day Malaysia, and participated in that port's conquest (the act of conquering) by the Portuguese. It is possible that he also went on a mission to explore the Moluccas (islands in Indonesia, then called the Spice Islands). Trading in spices brought great wealth to European nations at this time, and there was much competition among them to claim territories that were rich in spices, especially in Southeast Asia, called the East Indies. The Moluccas were the original source of some of the world's most valuable spices at that time, including cloves and nutmeg.

In 1513 Magellan was wounded in a battle in North Africa. But all of his services to Portugal brought him little favor from the Portuguese king, and in 1517 he went to Seville, Spain, to offer his services to the Spanish court.

Exploring for Spain

Spain and Portugal were both great powers at this time. They were in great competition over the rights to claim and settle the newly "discovered" regions of the Americas and the East. In 1494 the Treaty of Tordesillas divided the overseas world of the "discoveries" between the two powers, essentially splitting the globe in half from pole to pole. Portugal acquired everything from Brazil eastward to the East Indies, while the Spanish hemisphere (half-globe) of discovery and conquest ran westward from Brazil to an area near the Cape Verde Islands. The parts of this area that lay furthest east of Spain had not yet been explored by the Spaniards, and they assumed that some of the Spice Islands might lie within their half of the globe. They were wrong, but Magellan's scheme was to test that assumption. He decided that the best way to reach these islands was to sail in a westward direction from Europe, thus traveling around the globe.

Other explorers had paved the way for Magellan by making key mistakes and discoveries. Christopher Columbus (1451–1506) had badly underestimated the distance between Europe and the East Indies, sailing westward from the European coast and "discovering" North America and the Caribbean islands (West Indies). Vasco Núñez de Balboa's (1475–1517) march across the Panamanian isthmus had revealed the existence of the Pacific Ocean, which he had claimed for Spain. Thereafter, explorers eagerly sought northern and southern all-water passages across the Americas to reach the spice-rich East. Magellan also sought such a passage.

Magellan's great voyage

King Charles V (1500–1558) of Spain approved Magellan's proposal, and on September 20, 1519, Magellan led a fleet of five ships out into the Atlantic. Unfortunately, the ships—the San Antonio, Trinidad, Concepción, Victoria, and Santiago —were barely adequate to sail, and the crew were not all firmly loyal to their leader. With Magellan went his brother-in-law, Duarte Barbosa, and the loyal and able commander of the Santiago, João Serrão. Arriving at Brazil, the fleet sailed down the South American coast to the San Julián bay in the region called Patagonia. They stayed there from March to August 1520. During this time an attempted mutiny was put down, with only the top leaders being punished. Afterwards, however, the Santiago was wrecked, and its crew had to be taken aboard the other vessels.

Leaving San Julián, the fleet sailed southward. On October 21, 1520, it entered what is now called the Strait of Magellan (the channel of water between the southern tip of South America and the island of Tierra del Fuego). The fleet proceeded cautiously, taking over a month to pass through the strait. During this time the master of the San Antonio deserted and sailed back to Spain, and so only three of the original five ships entered the Pacific on November 28. A long voyage northward through the Pacific followed, and it was only on March 6, 1521, that the fleet finally anchored at Guam.

Magellan then headed eastward to Cebu in the Philippines, where, in an effort to gain the favor of a local ruler, he became involved in a local war and was killed in battle on April 27, 1521. Barbosa and Serrão were killed soon afterwards. The remaining crew were forced to destroy the Concepción, and the great circumnavigation was completed by a courageous former mutineer, Juan Sebastián del Cano. Commanding the Victoria, he picked up a small cargo of spices in the Moluccas, crossed the Indian Ocean, and traveled around the Cape of Good Hope (at the southern tip of Africa) from the east. He finally reached Seville on September 8, 1522. In the meantime, the Trinidad had tried to head back across the Pacific to Panama but was finally forced back to the Moluccas. There its crew was jailed by the Portuguese, and only four men later returned to Spain.

Magellan's legacy

Magellan's project brought little in the way of material gain to Spain. The Portuguese were well established in the East. Their route to the east, by way of Africa, had proved to be the only practical way of getting by sea to India and the Spice Islands. Yet despite nearly destroying itself in the process, the Magellan fleet for the first time revealed in a practical fashion the full extent of the globe. As a scientific effort, it proved to be the greatest of all the "conquests" undertaken by the overseas adventurers of fifteenth-and sixteenth-century Europe.

1-Magellan.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#59 2015-12-26 14:05:44

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

43. Nicolaus Copernicus

Nicolaus Copernicus  (19 February 1473 – 24 May 1543) was a Renaissance mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe. The publication of this model in his book 'De revolutionibus orbium coelestium' (On the Revolutions of the Celestial Spheres) just before his death in 1543 is considered a major event in the history of science, triggering the Copernican Revolution and making an important contribution to the Scientific Revolution.

Copernicus was born and died in Royal Prussia, a region that had been a part of the Kingdom of Poland since 1466. He was a polyglot and polymath who obtained a doctorate in canon law and also practiced as a physician, classics scholar, translator, governor, diplomat, and economist. Like the rest of his family, he was a third order Dominican. In 1517 he derived a quantity theory of money – a key concept in economics – and in 1519 he formulated a version of what later became known as Gresham's law.

nicolaus-copernicus.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#60 2015-12-27 14:47:20

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

44. René Descartes (31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist. Dubbed the father of modern philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. He spent about 20 years of his life in the Dutch Republic.

Descartes's Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes's influence in mathematics is equally apparent; the Cartesian coordinate system — allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two- or three-dimensional coordinate system (and conversely, shapes to be described as equations) — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the scientific revolution.

Descartes refused to accept the authority of previous philosophers, and refused to trust his own senses. He frequently set his views apart from those of his predecessors. In the opening section of the Passions of the Soul, a treatise on the early modern version of what are now commonly called emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before". Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differs from the schools on two major points: First, he rejects the splitting of corporeal substance into matter and form; second, he rejects any appeal to final ends—divine or natural—in explaining natural phenomena. In his theology, he insists on the absolute freedom of God's act of creation.

Descartes laid the foundation for 17th-century continental rationalism, later advocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well.

His best known philosophical statement is "Cogito ergo sum" (French: Je pense, donc je suis; I think, therefore I am), found in part IV of Discourse on the Method (1637 – written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644 – written in Latin).

Descartes.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#61 2015-12-28 14:38:30

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

45. Dmitri Ivanovich Mendeleev,  8 February 1834 – 2 February 1907, Russian chemist. He is famous for his formulation (1869) of the periodic law and the invention of the periodic table, a classification of the elements; with Lothar Meyer, who had independently reached similar conclusions, he was awarded the Davy medal in 1882. From his remarkable table Mendeleev predicted the properties of elements then unknown; three of these (gallium, scandium, and germanium) were later discovered. He studied also the nature of solutions and the expansion of liquids. An outstanding teacher, he was professor at the Univ. of St. Petersburg (1868–90). He directed the bureau of weights and measures from 1893 and served as government adviser on the development of the petroleum industry. His Principles of Chemistry (2 vol., 1868–71; tr. 1905) was long a standard text. Various transliterations of his surname are common, among them Mendeleyev and Mendelejeff.


mendeleev.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#62 2015-12-29 18:39:44

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

46. Sir Joseph John Thomson  (18 December 1856 – 30 August 1940) was an English physicist. He was elected as a fellow of the Royal Society of London and appointed to the Cavendish Professorship of Experimental Physics at the Cambridge University's Cavendish Laboratory in 1884.

In 1897, Thomson showed that cathode rays were composed of previously unknown negatively charged particles, which he calculated must have bodies much smaller than atoms and a very large value for their charge-to-mass ratio. Thus he is credited with the discovery and identification of the electron; and with the discovery of the first subatomic particle. Thomson is also credited with finding the first evidence for isotopes of a stable (non-radioactive) element in 1913, as part of his exploration into the composition of canal rays (positive ions). His experiments to determine the nature of positively charged particles, with Francis William Aston, were the first use of mass spectrometry and led to the development of the mass spectrograph.

Thomson was awarded the 1906 Nobel Prize in Physics for the discovery of the electron and for his work on the conduction of electricity in gases. Seven of his students, and his son George Paget Thomson, also became Nobel Prize winners.

jj-tomson.jpg

Last edited by Jai Ganesh (2015-12-30 13:57:40)


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#63 2015-12-30 14:30:48

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

47.  Henry Cavendish was born in Nice, France, on October 10, 1731, the oldest son of Lord Charles Cavendish and Lady Anne Grey, who died a few years after Henry was born. As a youth he attended Dr. Newcomb's Academy in Hackney, England. He entered Peterhouse, Cambridge, in 1749, but left after three years without taking a degree.

Cavendish returned to London, England to live with his father. There, Cavendish built himself a laboratory and workshop. When his father died in 1783, Cavendish moved the laboratory to Clapham Common, where he also lived. He never married and was so reserved that there is little record of his having any social life except occasional meetings with scientific friends.

Contributions to chemistry

During his lifetime Cavendish made notable discoveries in chemistry, mainly between 1766 and 1788, and in electricity, between 1771 and 1788. In 1798 he published a single notable paper on the density of the earth. At the time Cavendish began his chemical work, chemists were just beginning to recognize that the "airs" that were evolved in many chemical reactions were clear parts and not just modifications of ordinary air. Cavendish reported his own work in "Three Papers Containing Experiments on Factitious Air" in 1766. These papers added greatly to knowledge of the formation of "inflammable air" (hydrogen) by the action of dilute acids (acids that have been weakened) on metals.

Cavendish's other great achievement in chemistry is his measuring of the density of hydrogen. Although his figure is only half what it should be, it is astonishing that he even found the right order. Not that his equipment was crude; where the techniques of his day allowed, his equipment was capable of precise results. Cavendish also investigated the products of fermentation, a chemical reaction that splits complex organic compounds into simple substances. He showed that the gas from the fermentation of sugar is nearly the same as the "fixed air" characterized by the compound of chalk and magnesia (both are, in modern language, carbon dioxide).

Another example of Cavendish's ability was "Experiments on Rathbone-Place Water"(1767), in which he set the highest possible standard of accuracy. "Experiments" is regarded as a classic of analytical chemistry (the branch of chemistry that deals with separating substances into the different chemicals they are made from). In it Cavendish also examined the phenomenon (a fact that can be observed) of the retention of "calcareous earth" (chalk, calcium carbonate) in solution (a mixture dissolved in water). In doing so, he discovered the reversible reaction between calcium carbonate and carbon dioxide to form calcium bicarbonate, the cause of temporary hardness of water. He also found out how to soften such water by adding lime (calcium hydroxide).

One of Cavendish's researches on the current problem of combustion (the process of burning) made an outstanding contribution to general theory. In 1784 Cavendish determined the composition (make up) of water, showing that it was a combination of oxygen and hydrogen. Joseph Priestley (1733–1804) had reported an experiment in which the explosion of the two gases had left moisture on the sides of a previously dry container. Cavendish studied this, prepared water in measurable amount, and got an approximate figure for its volume composition.

Electrical research

Cavendish published only a fraction of the experimental evidence he had available to support his theories, but his peers were convinced of the correctness of his conclusions. He was not the first to discuss an inverse-square law of electrostatic attraction (the attraction between opposite—positive and negative—electrical charges). Cavendish's idea, however, based in part on mathematical reasoning, was the most effective. He founded the study of the properties of dielectrics (nonconducting electricity) and also distinguished clearly between the amount of electricity and what is now called potential.

Cavendish had the ability to make a seemingly limited study give far-reaching results. An example is his study of the origin of the ability of some fish to give an electric shock. He made up imitation fish of leather and wood soaked in salt water, with pewter (tin) attachments representing the organs of the fish that produced the effect. By using Leyden jars (glass jars insulated with tinfoil) to charge the imitation organs, he was able to show that the results were entirely consistent with the fish's ability to produce electricity. This investigation was among the earliest in which the conductivity of aqueous (in water) solutions was studied.

Cavendish began to study heat with his father, then returned to the subject in 1773–1776 with a study of the Royal Society's meteorological instruments. (The Royal Society is the world's oldest and most distinguished scientific organization.) During these studies he worked out the most important corrections to be employed in accurate thermometry (the measuring of temperature). In 1783 he published a study of the means of determining the freezing point of mercury. In it he added a good deal to the general theory of fusion (melting together by heat) and freezing and the latent heat changes that accompany them (the amount of heat absorbed by the fused material).

Cavendish's most celebrated investigation was that on the density of the earth. He took part in a program to measure the length of a seconds pendulum close to a large mountain (Schiehallion). Variations from the period on the plain would show the attraction put out by the mountain, from which the density of its substance could be figured out. Cavendish also approached the subject in a more fundamental way by determining the force of attraction of a very large, heavy lead ball for a very small, light ball. The ratio between this force and the weight of the light ball would result in the density of the earth. His results went unquestioned for nearly a century.

Unpublished works

Had Cavendish published all of his work, his already great influence would undoubtedly have been greater. In fact, he left in manuscript form a vast amount of work that often anticipated the work of those who followed him. It came to light only bit by bit until the thorough study undertaken by James Maxwell (1831–1879) and by Edward Thorpe (1845–1925). In these notes is to be found such material as the detail of his experiments to examine the conductivity of metals, as well as many chemical questions such as a theory of chemical equivalents. He even had a theory of partial pressures before John Dalton (1766–1844).

However, the history of science is full of instances of unpublished works that might have influenced others but in fact did not. Whatever he did not reveal, Cavendish gave other scientists enough to help them on the road to modern ideas. Nothing he did has been rejected, and for this reason he is still, in a unique way, part of modern life.

henry-cavendish.png


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#64 2015-12-31 15:30:08

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

48. Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist. He developed the general theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics). Einstein's work is also known for its influence on the philosophy of science. Einstein is best known in popular culture for his mass–energy equivalence formula E = mc^2 (which has been dubbed "the world's most famous equation"). He received the 1921 Nobel Prize in Physics for his "services to theoretical physics", in particular his discovery of the law of the photoelectric effect, a pivotal step in the evolution of quantum theory.

Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to gravitational fields, and with his subsequent theory of gravitation in 1916, he published a paper on general relativity. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the general theory of relativity to model the large-scale structure of the universe.

He was visiting the United States when Adolf Hitler came to power in 1933 and, being Jewish, did not go back to Germany, where he had been a professor at the Berlin Academy of Sciences. He settled in the U.S., becoming an American citizen in 1940. On the eve of World War II, he endorsed a letter to President Franklin D. Roosevelt alerting him to the potential development of "extremely powerful bombs of a new type" and recommending that the U.S. begin similar research. This eventually led to what would become the Manhattan Project. Einstein supported defending the Allied forces, but largely denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, which highlighted the danger of nuclear weapons. Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955.

Einstein published more than 300 scientific papers along with over 150 non-scientific works. On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents. Einstein's intellectual achievements and originality have made the word "Einstein" synonymous with "genius".

Albert-Einstein-1879-1955-434x574.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#65 2016-01-01 15:31:48

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

49. Antonie Philips van Leeuwenhoek (October 24, 1632 – August 26, 1723) was a Dutch tradesman and scientist. He is commonly known as "the Father of Microbiology", and considered to be the first microbiologist. He is best known for his work on the improvement of the microscope and for his contributions towards the establishment of microbiology.

Raised in Delft, Netherlands, Van Leeuwenhoek worked as a draper in his youth, and founded his own shop in 1654. He made a name for himself in municipal politics, and eventually developed an interest in lensmaking. Using his handcrafted microscopes, he was the first to observe and describe microorganisms, which he originally referred to as animalcules. Most of the "animalcules" are now referred to as unicellular organisms though he observed multicellular organisms in pond water. He was also the first to document microscopic observations of muscle fibers, bacteria, spermatozoa, and blood flow in capillaries (small blood vessels). Van Leeuwenhoek did not author any books; his discoveries came to light through correspondence with the Royal Society, which published his letters.

Antoni-Van-Leeuwenhoek-2.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#66 2016-01-02 15:40:08

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

50.

Archimedes of Syracuse (c. 287 BC – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.

Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested to be placed on his tomb, representing his mathematical discoveries.

Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

Archimedes.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#67 2016-01-03 14:51:45

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

51.

Christiaan N. Barnard

The South African surgeon Christiaan N. Barnard (8 November 1922 – 2 September 2001) performed the world's first human heart transplant operation in 1967 and the first double-heart transplant in 1974.

Christiaan N. Barnard was born on November 8, 1922, in Beaufort West, South Africa. He received his early education in Beaufort West and then went on to the University of Cape Town, where he received an M.D. in 1953. Barnard worked for a short time as a general practitioner before joining the Cape Town Medical School staff as a research fellow in surgery. With the hope of pursuing his research interests and gaining new surgical skills and experiences, he enrolled at the University of Minnesota Medical School (1955). After two years of study with Dr. Owen H. Wangensteen he received his Ph.D. from Minnesota and returned to his native country to embark upon a career as a cardiothoracic surgeon.

Before he left for America (1953-1955), Barnard had gained recognition for research in gastrointestinal pathology. He proved that the fatal birth defect known as congenital intestinal atresia (a gap in the small intestines) was due to the fetus receiving an inadequate supply of blood during pregnancy and that it could be remedied by a surgical procedure.

Upon his return to South Africa, he introduced open-heart surgery to that country, designed artificial valves for the human heart, and experimented with the transplantation of the hearts of dogs. All of this served as preparation for his 1967 human heart transplant.

Although Barnard was a pioneering cardiac surgeon, his innovations were founded upon a half-century of experimental heart surgery that preceded them. Of crucial importance was the first use of hypothermia (artificial lowering of the body temperature) in 1952 and the introduction in the following year of an effective heart-lung machine. These advances, combined with other techniques perfected in the 1960s, enabled a surgeon for the first time to operate upon a heart that was motionless and free of blood.

After a decade of heart surgery, Barnard felt ready to accept the challenge posed by the transplantation of the human heart. In 1967 he encountered Louis Washkansky, a 54-year-old patient who suffered from extensive coronary artery disease and who agreed to undergo a heart transplant operation. On December 2, 1967, the heart of a young woman killed in an accident was removed while Washkansky was prepared to receive it. The donor heart was kept alive in a heart-lung machine circulating Washkansky's blood until the patient's diseased organ could be removed and replaced with the healthy one.

In order to suppress the body's defense mechanism that would normally reject a foreign organism, Barnard and his team of cardiac specialists gave the patient large doses of drugs, which allowed the patient's body to accept the new organ. However, Washkansky's body was not able to defend itself against infection, and he died on December 21, 1967 of double pneumonia. Despite Washkansky's death, Barnard was rightly hailed around the world for his surgical feat. Within a year (January 1968) Barnard replaced the diseased heart of Philip Blaiberg, 58-year-old retired dentist. This time the accompanying drug dosage was lowered, and Blaiberg lived for 20 months with his new heart.

Barnard's innovations in cardiac surgery brought him honors from a host of foreign medical societies, governments, universities, and philanthropic institutions. As he travelled abroad to receive these awards, he was criticized for readily accepting the role of a celebrity. Nevertheless, after Barnard's successful operations, surgeons in Europe and the United States began performing heart transplants, improving upon the procedures first used in South Africa. The first human heart transplantation in America took place on December 6, 1967, by Dr. Adrian Kantrowitz. But the patient, an infant, lived only 6 hours.

Seven years after his initial heart transplant, Barnard made medical history once again when he performed a "twin-heart" operation (November 25, 1974). This time he removed only the diseased portion of the heart of 58-year-old Ivan Taylor and replaced it with the heart of a 10-year-old child. The donor heart acted as a booster and back-up for the patient's disease-ravished organ. Although Barnard was optimistic about this new operation, which he believed was less radical than a total implantation, the patient died within four months.

Rheumatoid arthritis, which had plagued Barnard since the 1960s, limited his surgical experimentation in later years. As a result, he turned to writing novels as well as books on health, medicine, and South Africa, while serving as a scientist consultant. He has also been presented many honorary doctorates, foreign orders, and awards, including the Dag Hammarskjold International Prize and Peace Prize, the Kennedy Foundation Award, and the Milan International Prize for Science. Barnard was also featured in a BBC program about transplant surgery, "Knife to the Heart: The Man With the Golden Hands, " in early 1997.

F1.large_.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#68 2016-01-04 14:35:06

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

52. William Thomson, 1st Baron Kelvin (26 June 1824 – 17 December 1907) was an Irish mathematical physicist and engineer who was born in Belfast in 1824. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its modern form. He worked closely with mathematics professor Hugh Blackburn in his work. He also had a career as an electric telegraph engineer and inventor, which propelled him into the public eye and ensured his wealth, fame and honour. For his work on the transatlantic telegraph project he was knighted by Queen Victoria, becoming Sir William Thomson. He had extensive maritime interests and was most noted for his work on the mariner's compass, which had previously been limited in reliability.

Absolute temperatures are stated in units of kelvin in his honour. While the existence of a lower limit to temperature (absolute zero) was known prior to his work, Lord Kelvin is widely known for determining its correct value as approximately −273.15 degree Celsius or −459.67 degree Fahrenheit.

He was ennobled in 1892 in recognition of his achievements in thermodynamics, and of his opposition to Irish Home Rule, becoming Baron Kelvin, of Largs in the County of Ayr. He was the first British scientist to be elevated to the House of Lords. The title refers to the River Kelvin, which flows close by his laboratory at the University of Glasgow. His home was the imposing red sandstone mansion Netherhall, in Largs. Despite offers of elevated posts from several world-renowned universities Lord Kelvin refused to leave Glasgow, remaining Professor of Natural Philosophy for over 50 years, until his eventual retirement from that post. The Hunterian Museum at the University of Glasgow has a permanent exhibition on the work of Lord Kelvin including many of his original papers, instruments and other artefacts such as his smoking pipe.

Always active in industrial research and development, he was recruited around 1899 by George Eastman to serve as vice-chairman of the board of the British company Kodak Limited, affiliated with Eastman Kodak.

lord-kelvin-9.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#69 2016-01-05 15:55:47

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

53. Alessandro Giuseppe Antonio Anastasio Volta (18 February 1745 – 5 March 1827) was an Italian physicist, chemist, and a pioneer of electricity and power, who is credited as the inventor of the electrical battery and the discoverer of methane. He invented the Voltaic pile in 1799 and the results of which he reported in 1800 in a two-part letter to the President of the Royal Society. With this invention Volta proved that electricity could be generated chemically and debased the prevalent theory that electricity was generated solely by living beings. Volta's invention sparked a great amount of scientific excitement and led others to conduct similar experiments which eventually led to the development of the field of electrochemistry.

Alessandro Volta also drew admiration from Napoleon Bonaparte for his invention, and was invited to the Institute of France to demonstrate his invention to the members of the Institute. Volta enjoyed a certain amount of closeness with the Emperor throughout his life and he was conferred numerous honours by him. Alessandro Volta held the chair of experimental physics at the University of Pavia for nearly 40 years and was widely idolised by his students.

Despite his professional success Volta tended to be a person inclined towards domestic life and this was more apparent in his later years. At this time he tended to live secluded from public life and more for the sake of his family until his eventual death in 1827 from a series of illnesses which began in 1823. The SI unit of electric potential is named in his honour as the volt.

file.gif


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#70 2016-01-06 14:38:07

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

54.

Baron Jöns Jacob Berzelius  (20 August 1779 – 7 August 1848), named by himself and contemporary society as Jacob Berzelius, was a Swedish chemist. Berzelius is considered, along with Robert Boyle, John Dalton, and Antoine Lavoisier, to be one of the founders of modern chemistry.

Berzelius began his career as a physician but his researches in physical chemistry were of lasting significance in the development of the subject. He is especially noted for his determination of atomic weights; his experiments led to a more complete depiction of the principles of stoichiometry, or the field of chemical combining proportions. In 1803 Berzelius demonstrated the power of an electrochemical cell to decompose chemicals into pairs of electrically opposite constituents.

Berzelius's work with atomic weights and his theory of electrochemical dualism led to his development of a modern system of chemical formula notation that could portray the composition of any compound both qualitatively (by showing its electrochemically opposing ingredients) and quantitatively (by showing the proportions in which the ingredients were united). His system abbreviated the Latin names of the elements with one or two letters and applied superscripts to designate the number of atoms of each element present in both the acidic and basic ingredients.

Berzelius himself discovered and isolated several new elements, including cerium (1803) and thorium (1828). Berzelius’s interest in mineralogy also fostered his analysis and preparation of new compounds of these and other elements. He was a strict empiricist and insisted that any new theory be consistent with the sum of chemical knowledge. He developed classical analytical techniques, and investigated isomerism and catalysis, phenomena that owe their names to him. He became a member of the Royal Swedish Academy of Sciences in 1808 and served from 1818 as its principal functionary, the perpetual secretary. He is known in Sweden as "the Father of Swedish Chemistry". Berzelius Day is celebrated on 20 August in honour of him.

BerzeliusJons300px.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#71 2016-01-07 14:53:01

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

55. Alexander Graham Bell

Born: March 3, 1847 - Edinburgh, Scotland
Died: August 2, 1922
Baddeck, Nova Scotia -
Inventor and educator

Because of family tradition and upbringing, Alexander Graham Bell was, perhaps, destined to create one of the world's most commonly used inventions today: the telephone. He came from two generations of men who were students of speech and language and a hard-of-hearing mother who was a musician. These influences led him to dedicate his life to science and sound as well as to the education of the deaf.

"It is possible to connect every man's house, office or factory with a central station, so as to give him direct communication with his neighbors."

Teacher of the Deaf

Alexander Graham Bell was born on March 3, 1847, in Edinburgh, Scotland. He was the middle of three sons born to Alexander Melville Bell and Eliza Grace Symonds. Alexander Melville's father, Alexander Bell, had been an actor and later became a speech teacher. Alexander Melville followed in his footsteps and worked for many years as a teacher of elocution, which is the art of speaking correctly and effectively. He also studied the way a person uses his larynx, mouth, tongue, and lips to form sounds. After years of teaching and study, Bell invented Visible Speech, a set of symbols based on the position and action of the throat, tongue, and lips while making sounds. This technique would later be used in the education of the deaf.

Eliza Grace, the daughter of a surgeon in the Royal Navy, was an accomplished pianist despite the fact that she was hearing impaired. She was able to hear some sounds with the use of a speaking tube. She was Alexander Graham's first and most important teacher.

In 1865, the Bell family moved to London where Alexander Melville continued the work begun by his father who had recently died. In London, Alexander Graham became his father's assistant and studied anatomy and physiology at University College. He also began experimenting with the transmission of sounds using his family's piano and tuning forks. But his discoveries would soon be placed on hold. By 1870, both of his brothers had died of tuberculosis, and his father persuaded his family to move to Brantford, Ontario, Canada, where he considered the climate to be better for their health.

Alexander Melville had become well known for his work with Visible Speech, and when he was invited to introduce this technique to Sarah Fuller's School for the Deaf in Boston, he instead sent his partner and son, Alexander Graham. From then on, Alexander Graham Bell dedicated his life to teaching the deaf and developing new instruments for their use. He visited various schools for the deaf in the Boston area, and in 1873, he became professor of vocal physiology and the mechanics of speech. He presented lectures at Boston University and the University of Oxford.

When he was a teenager, Alexander Graham Bell and his older brother made a "speaking machine" that mechanically produced vocal sounds. A local butcher had given them a larynx from a lamb, and the boys made a model of the lamb's vocal organs. They attached levers that moved the organs. When they blew into a tube, it moved the levers which, in turn, made the organs produce sounds like human cries.

Bell also began to take private deaf students. From 1873 until 1876, Bell had the sole responsibility of educating the five-year-old, deaf son of Thomas Sanders in Haverhill, Massachusetts. Sanders would later become treasurer of the Bell Telephone Company. At the same time, Bell met another influential man, Gardiner G. Hubbard, who also had a deaf child and was dedicated to her education. Hubbard later became trustee of the Bell Telephone Company. On July 11, 1877, Bell, a slender, dark-haired young man, married Hubbard's eighteen-year-old daughter, Mabel, who had been deaf since early childhood.

A Man of Inventions

Thomas Sanders and Gardiner Hubbard were so impressed with Bell, they encouraged him to pursue his ideas and continue with his experiments. And they gave him the money to do it. At that time, Bell worked mostly on three kinds of equipment: a phonoautograph, a device that would help a deaf person see a sound; a multiple telegraph, a device that could transmit two or more messages over wire at the same time; and an electric speaking telegraph, or telephone.

All of the experiences he had prior to 1876, led Bell to one of the greatest inventions in history. He had a special ear for pitch and tones, thanks to music lessons with his mother; he had a mind for science like his father and grandfather; and he had knowledge gained from his experiments with the telegraph and other sound-producing devices. Bell developed a basic concept for the phone and worked diligently for over a year to get it to work. Finally, he discovered that he could reproduce the tone and overtones of the human voice through a wire.

Bell gave the plans to build the first telephone to his assistant, Thomas A. Watson (1854-1934), and on March 10, 1876, they used the phone to communicate for the first time. Two months later, Bell introduced the telephone to the scientific world at the Academy of Arts and Sciences in Boston. By July 1877, the Bell Telephone Company was formed and the first telephone was installed in a private home.

Bell continued experimenting with communication equipment and developed many noteworthy devices including the photophone, a device that transmits sound on a beam of light. The photophone was the predecessor of today's optical fiber systems. He also worked on an audiometer, an instrument used to measure how well a person hears, and the first successful phonograph record.

Beginning in 1895, Bell's scientific interests moved into the area of aviation. He worked with a friend, Samuel P. Langley, on things like gunpowder rockets and the rotating blades of helicopters. Bell eventually received five patents for aerial vehicles and four for a system called hydrodynamics, which propels a vehicle by skimming the surface of water.

After the Phone

Bell, his wife, and two daughters moved from Boston to Washington, D.C., in 1882, where he became a United States citizen. By this time, he had become a stout man with a full, gray beard, reminiscent of Santa Claus. And, just like Santa, his benevolent acts continued throughout his lifetime.

He was partly responsible for ensuring the advancement of science and Bell continued research to benefit the deaf. He helped develop the journal Science in 1880, became president of the American Association for the Promotion of the Teaching of Speech to the Deaf in 1890, joined the board of the Smithsonian Institution in 1898, served as president of the National Geographic Society from 1898 to 1903, succeeding his father-in-law, Gardiner Hubbard, who was founder of the society, and organized the Aerial Experiment Association in 1907.

During most of his later years, Bell and his family spent increasingly more time at a Baddeck, Nova Scotia, summer home they had purchased in 1886. Eventually they lived there year-round. Bell continued his work, often working and studying past midnight, enjoying the solitude of the quiet hours when everyone else was asleep. He died there at the age of seventy-five.

Alexander Graham Bell will always be remembered as the inventor of the telephone. But his life and works reached far beyond that. For his two daughters, nine grandchildren, and the countless numbers of deaf and hearing children who crossed his path, perhaps he was also remembered as a kind soul and a good teacher.

AlexanderGrahamBell250.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#72 2016-01-16 15:23:40

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

56. Hubble, Edwin Powell

(b. Marshfield, Missouri, 20 November 1889; d. San Marino, California, 28 September 1953)

observational astronomy, cosmology.

Hubble was the founder of modern extragalactic astronomy and the first to provide observational evidence for the expansion of the universe. The son of John Powell Hubble, a lawyer, and the former Virginia Lee James, he spent his early years in Kentucky and attended high school in Chicago, where his father was in the insurance business. At school he excelled both in his studies and in athletics. He won a scholarship to the University of Chicago, where he came under the influence of the eminent physicist R. A. Millikan and of the astronomer G. E. Hale, who inspired in him a love of astronomy. Hubble received a B.S. in mathematics and astronomy and also made his mark on the campus as a heavyweight boxer (he was six feet, two inches tall). A sports promoter wanted to train him to fight Jack Johnson, the world champion, but instead Hubble went to Queen’s College, Oxford, in 1910 as a Rhodes scholar from Illinois.

At Oxford, Hubble first thought of reading mathematics; but after studying some of the final examination papers, he concluded that they were too specialized for his liking and instead decided to read jurisprudence. He took his B.A. in that subject in 1912. Hubble had a great love of England and was interested in the common law of the country from which his ancestors had emigrated in the seventeenth century. While at Oxford he was awarded a blue for track events and boxed in an exhibition match with the French champion, Georges Carpentier.

In 1913 Hubble returned to the United States, was admitted to the bar, and opened a law office at Louisville, Kentucky. After a short while he abandoned this career and in 1914 went to the Yerkes Observatory of the University of Chicago, where he was an assistant and a graduate student under E. B. Frost. He was awarded the Ph.D. in 1917 for a thesis entitled “Photographic Investigations of Faint Nebulae,” in which he considered the classification of nebular types and concluded that planetary nebulae are probably within our sidereal system and the great spirals outside; but these questions, he said, could be decided only by instruments more powerful than those currently available.

Hubble’s powers as an observer attracted the attention of Hale during a visit to Yerkes; Hale offered him a post at the Mount Wilson Observatory, where the sixty-inch reflector was then in operation and the 100-inch under construction. Meanwhile the United States had entered World War I, and Hubble had immediately enlisted as a private in the infantry. He therefore telegraphed Hale that he would accept his offer as soon as he was demobilized. He served with the American Expeditionary Force in France and rose to the rank of major. After the Armistice he remained with the authmu of 1919. On his return to the United States in October, he joined Hale on Mount Wilson, as he had promised. At last, at the age of thirty, he settled down to the work that was to bring him fame.

Hubble’s earliest investigations at Mount Wilson were made with the sixty-inch telescope and concerned galactic nebulae. In one of his earliest papers, “A General Study of Diffuse Galactic Nebulae,” he suggested a classification system based upon fundamental differences between galactic and nongalacticnebulae. He discovered many new planetary nebulae and variable stars, but the most important result of his early researches concerned the origin of the radiation from diffuse galactic nebulae. Hubble showed that they were made luminous by certain stars assoiated with them, the nebulosity consisting of clouds of atoms and dust not hot enough to be selfluminous. He discovered a relation between the luminosity of a diffuse galactic nebula and the magnitudes of the associated stars and showed that the gases were excited and made luminous by neighboring blue stars of high surface temperature.

The Hooker 100-inch telescope came into operational use at about the time Hubble arrived on Mount Wilson. This was a most fortunate circumstance, for the crucial contributions made to cosmology by Hubble required the full light-gathering power and resolution of this instrument. From about 1922 he turned his attention more and more to objects that we now regard as lying beyond our own stellar system.

Hubble’s first great discovery was made when he recognized a Cepheid variable star in the outer regions of Messier 31, the great nebula in Andromeda in a plate that the he took on 5 October 1923. This proved to be the long-sought means of settling the problem of the status of the spiral nebulae that had puzzled astronomers for three-quarters of a century. The use of Cepheid variable stars as distance indicators had been suggested more than ten years earlier by Henrietta Leavitt of the Harvard College Observatory, and they had been used with great effect by Harlow Shapley to determine the distance and dimensions of the globular star clusters that surround the Milky Way. Hubble’s discovery was the first sure indication that the Andromeda nebula lies far outside our own stellar system.

Controversy on this question had previously culminated in the famous Shapley-Curtis debate held before the National Academy of Sciences on 26 April 1920, neither side convincing the other. Curtis had argued that “the spirals are not intragalactic objects but island universes, like our own galaxy, and that the spirals, as external galaxies, indicate to us a greater universe into which we may penetrate to distances of ten million to a hundred million light years.” Shapley rejected this conclusion. He maintained that there was no reason “for modifying the tentative hypothesis that the spirals are not composed of typical stars at all, but are truly nebulous objects,” The strongest argument for this view was evidence obtained by Adriaan van Maanen that Messier 101 rotated through 0.02 seconds of arc in a year and that Messier 33 and 81 rotated at comparable rates. These large angular velocities implied relativly small distances, of the order of a few thousand light-years. (The spurious nature of van Maanen’s measurements was finally established in 1935, when it was conclusively shown by Hubble that they arose from obscure systematic errors and did not indicate motion in the nebulae concerned.)

By the end of 1924 Hubble had found thirty-six variable stars in M 31, twelve of which were Cepheids. From the latter he derived a distance of the order of 285,000 parsecs, or about 900,000 lightyears, whereas the maximum diameter of the Milky Way stellar system was known to be in the order of 100,000 light-years. The public announcement of Hubble’s discovery was made at a meeting of the American Astronomical Society in Washington, D.C., at the end of December 1924. Hubble was not present; but Joel Stebbins recalled many years later that when Hubble’s paper had been read, the entire Society knew that the debate had come to an end, that the island-universe concept of the distribution of matter in space had been established, and that an era of enlightenment in cosmology had begun. Both Shapley and curtis were present.

The way was now open for a new attack on the cosmological problem which had hitherto been the concern of theoretical investigators. Two lines of research were possible for the observer to pursue, and Hubble was a pioneer in both. On the one hand, he studied the contents and general structure of galoxies. On the other, he investigated their distribution in space and their motion. Both approaches were strongly motivated by his belief that galaxies are the structural units of matter that together constitute the astronomical universe as a whole.

Hubble was the first to introduce a significant classification system for galaxies. He presented this at the meeting of the International Astronomical Union at Cambridge, England, in 1925 and it was published the next year in the Astrophysical Journal. This system is the basis of the classification still used. Hubble found that most galaxies showed evidence of rotational symmetry about a dominating central nucleus, although a minority, amounting to not more than 3 percent of those he studied, lacked both these features. He called the two types “regular” and “irregular,” respectively. He found that the regular galaxies fell into two main classes—“spirals” and “ellipticals”—and that each class contained a regular sequence of forms. One end of the elliptical sequence was found to be similar to one end of the spiral sequence. The spirals were subdivided into two parallel subsequences, normal and barred. The classification was essentially empirical and independent of any assumptions concerning the evolution of galaxies.

In addition to studying the shapes of galaxies, Hubble explored their contents and brightness patterns. In the nearer galaxies he discovered and studied almost every kind of intrisically bright object known in our own system: novae globular clusters, gaseous nebulae, super-giant blue stars, red long-period variables, Cepheids, and so on.

Despite the advance in knowledge in the last forty years, Hubble’s claim to have introduced order into the apparent confusion of nebular forms and to have shown that galaxies are closely related members of a singly family stands. It must be regarded as one of his most significant achievements.

During the late 1920’s Hubble’s main preoccupation was to determine a reliable extragalactic distance scale to the limits of observation. This was the essential preliminary to any serious investigation of the distribution of galaxies in space and its bearing on the cosmological problem. The philosophy underlying his approach to this problem had previously been summarized by him in his first detailed paper on an extragalatic system (NGC 6822), the distance of which was obtained by the Ceoheid criterion. Hubble’s use of the Cepheid period-luminosity law (which enabled him to regard these stars as distance indicators) was based on an appeal to the principle of the uniformity of nature. “This principle,” he wrote, “is the fundamental assumption in all extrapolations beyond the limits of known and observable data, and speculations which follow its guide are legitimate until they become self-contradictory.”

On this basis, Hubble proceeded to estimate the distance of galaxies beyond the “local group” in which Cepheids could be detected with the 100-inch telescope. He argued that with increasing distance one could expect the Cepheids to fade out first, then the irregular variables, then the blue giants, until only the very brightest of stars would be seen. He found that the data, although somewhat meager, indicated that the very brightest stars in late-type spirls are of about the same absolute luminosity. This upper limit of stellar luminosity appeared to be about 50,000 times that of the sun. The “brightest star” criterion of distance enabled Hubble to extend the extragalactic distance scale to about 6,000,000 lightyears. In view of the criticism to which this criterion has been subjected since Hubble’s day, it should be noted that he was fully aware that a risk was involved in regarding the images in question as individual stars; but he pointed out that, regardless of their real nature, the objects selected a brightest stars appeared to represent strictly comparable bodies. (In 1958 Allan Sandage showed that they are bright couds of ionized hydrogen.)

To extend the distance scale farther, Hubble used information gained from the fact stars could be detected in some of the spirals in the great Virgo cluster. Analysis of this large sample collection provided average characteristics of galaxies which could be used as statistical criteria of distance for more remote galaxies. For measurements of the depths of space, Hubble concentrated on the brightest members of clusters of galaxies. He regarded the clusters as so similar that the mean luminosity of the ten brightest members or even the individual luminosity of, say the fifth-brightest member formed a convenient measure of distance. In this way he build up his distance scale to 250 million light-years.

By 1929 Hubble had obtained distances for eighteen isolated galaxies and for four members of the Virgo cluster. In that year he used this somewhat restricted body of data to make the most remarkable of all his discoveries and the one that made his name famous far beyond the ranks of professional astronomers. This was what is now known as Hubble’s law of proportionality of distance and radial velocity of galaxies. Since 1912, when V. M. Slipher at the Lowell Observatory had measured the radial velocity of a galaxy (M 31) for the time by observing the Doppler displacement of its spectral lines, velocities had been obtained of some forty-six galaxies, forty-one by Slipher himself. Attempts to correlate these velocities with other properties of the galaxies concerned, in particular their apparent diameters, had been made by Carl Wirtz, Lundmark, and others; but no definite, generally acceptable result had been obtained. In 1917 W. de Sitter had constructed, on the basis of Einstein’s cosmological equations, an ideal world-model (of vanishingly small average density) which predicted red shifts, indicative of recessional motion, in distant light sources; but no such systematic effect seemed to emerge from the empirical data. Hubble’s new approach to the problem, based on his determinations of distance, clarified an obscure situation. For distances out to about 6,000,000 light-years he obtained a good approximation to a straight line in the graphical plot of velocity against distance. Owing to the tendency of individual proper motions to mask the systematic effect in the case of the nearer galaxies, Hubble’s straight-line graph depended essentially on the data obtained from galaxies in the Virgo cluster. These indicated that over the observed range of distance, velocities increased at the rate of roughly 100 miles a second for every million light-years of distance (500 kilometers a second for every million parsecs).

Further progress depended on the extension of the observations to greater distances and fainter galaxies. The spectroscopic part of the work was undertaken by Milton L. Humason, Hubble’s colleague at Mount Wilson. Within two years, with the aid of a new type of fast lens suitable for the difficult task of photographing the exceedingly faint spectra of remote galaxies, Hubble’s law was extended to a distance of over 100 million light-years, the straight-line relationship between velocity and distance being maintained. This result has come to be generally regarded as the outstanding discovery in twentieth-century astronomy. It made as great a change in man’s conception of the universe as the Copernican revolution 400 years before. For, instead of an overall static picture of the cosmos, it seemed that the universe must be regarded as expanding, the rate of the mutual recession of its parts increasing with their relative distance.

Hubble’s discovery stimulated much theoretical work in relativistic cosmology and aroused great interest in fundamental papers on expanding world models by A. Friedmann and G. Lemaître that had been written several years before but had attracted little attention. The interpretation of the straight line in Hubble’s graph of velocity against distance and of its slope were eagerly discussed. The constant ratio of velocity to distance is now usually denoted by the letter H and is called Hubble’s constant. It has the dimensions of an inverse time—its reciprocal, according to Hubble’s original determination, being approximately two (since revised to about ten) billion years. If the galaxies recede uniformly from each other, as was suggested by E. A. Milne in 1932, this could be interpreted as the age of the universe; but, whatever the true law of recessional motion may be, Hubble’s constant is generally regarded as a fundamental parameter in theoretical cosmology.

In the early 1930’s Humason obtained red shifts indicating velocities of recession up to about one-seventh the velocity of light. This was remarkably high for astronomical objects; and Hubble tended to prefer the neutral term “red shift” to “velocity of recession,” since he believed that, although no other explanation could compete with the Doppler interpretation of the spectra, it was possible that some hitherto unrecognized principle of physics may be responsible for the effects observed. This became a central problem for him in the course of the 1930’s and was one of the objectives of his detailed investigations of the distribution of galaxies. These investigations were of two kinds: surveys of large areas of the sky penetrating to moderate depths, and surveys of selected small areas to the limits of observability.

Hubble’s study of the large-scale distribution of galaxies over the sky produced two important results. At first sight, this distribution appeared to be far from isotropic. No galaxies were found along the central region of the Milky Way, and outside the zone of avoidance the number of galaxies observed appeared to increase with galactic latitude. Hubble showed that these observations could be explained as the effect of an absorbing layer of diffuse matter surrounding the main plane of the Milky Way, and that when this effect was taken into account there were no significant major departures from isotropy in the distribution of galaxies. These conclusions were of great significance for the structure of our own galaxy and also for cosmology because they strengthened the case for regarding the system of galaxies as constituting the general framework of the universe.

In regard to the distribution of galaxies in depth, a preliminary reconnaissance by Hubble indicated that this was uniform. Guided by this information, surveys were made by him and by N. U. Mayall to determine the total number of galaxies in a square degree of the sky brighter than certain limiting magnitudes—for instance, nineteenth or twentieth magnitude. The analysis of these surveys presented Hubble with a difficult theoretical problem, and he enlisted the support of R. C. Tolman, a distinguished theoretical physicist and relativity expert at the California Institute of Technology, Pasadena. The crux of the problem concerned the statistical relationship between apparent brightness and distance; but the apparent brightness of a remote galaxy, corrected for all “local” effects such as the dimming due to interstellar absorption of light in our own system, depends not only on the intrinsic brightness of the galaxy but also on its red shift; and the effect of this is greater for the more remote, and therefore fainter, galaxies. (Moreover, the intrinsic brightness of a remote galaxy when the light left it may not be the same statistically as at later epochs.) The red shift, whatever its cause, diminishes the energy of the light from a galaxy and makes it appear fainter than would be the case otherwise. Moreover, the true absolute magnitude (the bolometric magnitude) depends on the total radiation of all wavelengths, whereas the magnitude registered on the photographic plate is confined to certain parts of the spectrum; and the red shift complicates the problem of converting from photographically determined apparent magnitudes to bolometric magnitudes.

As a result of his investigations with Tolman, Hubble was inclined, from about 1936, to reject the Doppler-effect interpretation of the red shifts and to regard the galaxies as stationary. He claimed that uniformity of distribution in depth was compatible with this assumption. On the other hand, if the galaxies are receding, uniformity in depth can be reconciled with the observations only if there is also a positive curvature of space, the required radius being about 500 million light-years, which was actually less than the range of the 100-inch reflector for normal galaxies. Theoretical cosmologists, notably G. C. McVittie in the late 1930’s and Otto Heckmann in the early 1940’s, criticized Hubble’s analysis and rejected his conclusions but respected his observational achievements.

One of the curiously baffling problems concerning galaxies that engaged Hubble’s attention related to the sense of rotation of spiral arms. According to some theoretical astronomers, notably Bertil Lindblad, these arms opened up in the same sense as they rotated about the nucleus, whereas other astronomers believed that they trailed. The question was difficult to resolve, because if a galaxy is seen at the right orientation to observe the arms clearly, it is not easy to tell which is the near and which the far side. With his intimate knowledge of galaxies, Hubble selected as a favorable test object NGC 3190 and in 1941 obtained the necessary spectroscopic and photographic material with the 100-inch reflector. He concluded that there was no reason to doubt that this spiral trails its arms. In the last year of his life, radio and optical evidence was forth-coming that the same situation prevails in our own galaxy.

In 1942 war again caused Hubble to divert his energies from astronomy. He had long been aware of the dangers that threatened the free world and was chairman of the Southern California Joint Fight for Freedom Committee. After the United States entered the war, he sought active service in the army but was asked instead by the U.S. War Department to become chief of ballistics and director of the Supersonic Wind Tunnel Laboratory at the Aberdeen Proving Ground, Maryland. He remained there until 1946 and was awarded the Medal of Merit for his services.

After the war Hubble devoted much time to plans relating to the Hale 200-inch telescope. He became chairman of the Research Committee for the Mount Wilson and Palomar Observatories and was largely responsible for planning the details of the Palomar Observatory Sky Survey that was made with the forty-eight-inch Schmidt telescope. Toward the end of 1949 the 200-inch was at last available for full-time observation, and Hubble was the first to use it. The first major advance after its introduction was Baade’s discovery that all extragalactic distances had been underdetermined by a factor of about two. One of the reasons for this conclusion went back to Hubble’s discovery in 1932 that the globular clusters in M 31 appeared to be, on the average, four times fainter than those in our own galaxy.

During the last years of his life Hubble suffered from a heart ailment. He died suddenly in 1953 from a cerebral thrombosis while preparing to go to Mount Palomar for four nights of observing.

A man of wide interests, Hubble was elected a trustee of the Huntington Library and Art Gallery in 1938. He bequeathed his valuable collection of early books in the history of science to Mount Wilson Observatory. He was a skilled dry-fly fisherman and fished in the Rocky Mountains and also on the banks of the Test, near Stockbridge, Hampshire, where he and his wife (the former Grace Burke, whom he married in 1924) used to stay with English friends.

Hubble’s great achievements in astronomy were widely recognized during his lifetime by the many honors conferred upon him. He gave the Halley lecture at Oxford in 1934, the Silliman lectures at Yale in 1935, and the Rhodes lectures at Oxford in 1936. In 1948 he was elected an honorary fellow of Queen’s College, Oxford, in recognition of his notable contributions to astronomy.

Hubble’s work was characterized not only by his acuity as an observer but also by boldness of imagination and the ability to select the essential elements in an investigation. In his careful assessment of evidence he was no doubt influenced by his early legal training. He was universally respected by astromers, and on his death N. U. Mayall expressed their feelings when he wrote: “It is tempting to think that Hubble may have been to the observable region of the universe what the Herschels were to the Milky Way and what Galileo was to the solar system.”

fff4978.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#73 2016-01-18 19:35:42

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

57. Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.

During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason. Kepler described his new astronomy as "celestial physics", as "an excursion into Aristotle's Metaphysics", and as "a supplement to Aristotle's On the Heavens", transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.

ea436109.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#74 2016-01-29 02:24:45

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

58. Captain James Cook (7 November 1728 – 14 February 1779) was a British explorer, navigator, cartographer, and captain in the Royal Navy. Cook made detailed maps of Newfoundland prior to making three voyages to the Pacific Ocean, during which he achieved the first recorded European contact with the eastern coastline of Australia and the Hawaiian Islands, and the first recorded circumnavigation of New Zealand.

Cook joined the British merchant navy as a teenager and joined the Royal Navy in 1755. He saw action in the Seven Years' War, and subsequently surveyed and mapped much of the entrance to the Saint Lawrence River during the siege of Quebec. This helped bring Cook to the attention of the Admiralty and Royal Society. This notice came at a crucial moment in both Cook's career and the direction of British overseas exploration, and led to his commission in 1766 as commander of HM Bark Endeavour for the first of three Pacific voyages.

In three voyages Cook sailed thousands of miles across largely uncharted areas of the globe. He mapped lands from New Zealand to Hawaii in the Pacific Ocean in greater detail and on a scale not previously achieved. As he progressed on his voyages of discovery he surveyed and named features, and recorded islands and coastlines on European maps for the first time. He displayed a combination of seamanship, superior surveying and cartographic skills, physical courage and an ability to lead men in adverse conditions.

Cook was killed in Hawaii in a fight with Hawaiians during his third exploratory voyage in the Pacific in 1779. He left a legacy of scientific and geographical knowledge which was to influence his successors well into the 20th century and numerous memorials worldwide have been dedicated to him.

James-Cook.jpg-3653.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#75 2016-01-29 15:44:44

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 48,425

Re: crème de la crème

59. Aristotle (384-322 BC) was a Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, whereafter Proxenus of Atarneus became his guardian. At eighteen, he joined Plato's Academy in Athens and remained there until the age of thirty-seven (c. 347 BC). His writings cover many subjects – including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theater, music, rhetoric, linguistics, politics and government – and constitute the first comprehensive system of Western philosophy. Shortly after Plato died, Aristotle left Athens and, at the request of Philip of Macedon, tutored Alexander the Great starting from 343 BC. According to the Encyclopædia Britannica, "Aristotle was the first genuine scientist in history ... [and] every scientist is in his debt."

Teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books. The fact that Aristotle was a pupil of Plato contributed to his former views of Platonism, but, following Plato's death, Aristotle immersed himself in empirical studies and shifted from Platonism to empiricism. He believed all peoples' concepts and all of their knowledge was ultimately based on perception. Aristotle's views on natural sciences represent the groundwork underlying many of his works.

Aristotle's views on physical science profoundly shaped medieval scholarship. Their influence extended into the Renaissance and were not replaced systematically until the Enlightenment and theories such as classical mechanics. Some of Aristotle's zoological observations, such as on the hectocotyl (reproductive) arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic.

In metaphysics, Aristotelianism profoundly influenced Judeo-Islamic philosophical and theological thought during the Middle Ages and continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. Aristotle was well known among medieval Muslim intellectuals and revered as "The First Teacher".

His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his literary style as "a river of gold" – it is thought that only around a third of his original output has survived.

aristotle.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

Board footer

Powered by FluxBB