Math Is Fun Forum

Kurre

Member

Registered: 2006-07-18

Posts: 280

Unproved theorems

I have heard there are some very old theorems that have not been proven and that there is a prize if you prove one. Im just curoius on what kind of problems they are. Can anyone give me a link to them with a good description??

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Unproved theorems

Off the top of my head, Goldbach’s conjecture:

http://en.wikipedia.org/wiki/Goldbach's_conjecture

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Unproved theorems

I don't know how old this is.  Define f:

f(1) = 0
f(n) = f(3n+1) if n is odd
f(n) = f(n/2) if n is even

Try out a few:

f(5) = f(15 + 1) = f(16) = f(8) = f(4) = f(2) = f(1) = 0
f(20) = f(10) = f(5) = 0 (as above)

It is unknown whether all values of n will go down to 0.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: Unproved theorems

The Millennium Prize Problems are the most popular unsolved problems in mathematics which have a prize:

http://en.wikipedia.org/wiki/Millenium_problems

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Unproved theorems

The Millennium Prize Problems are the most popular unsolved problems in mathematics which have a prize:

http://en.wikipedia.org/wiki/Millenium_problems

And the most advanced

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Unproved theorems

In Wikipedia, there's a page about unsolved problems:
http://en.wikipedia.org/wiki/Unsolved_p … athematics

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IPBLE:  Increasing Performance By Lowering Expectations.