Greatest Mathematical Puzzle of the modern age?

[Einstein]

What is the greatest Mathematical puzzle that is unsolved? and why?

[HallsofIvy]

Why some people still think they have a "simple" proof of Fermat's last theorem!

[Tyger]

the question of the non-trivial zeros of the Rieman Zeta Function.

[Greg Bernhardt]

goldbach's conjecture?

[KLscilevothma]

4 color theorem.

Though it was proven by powerful computers by considering thousands of cases, mathematicians still want to find out a mathematical proof.

[STAii]

Can you please (all) explain (a little bit) about each of these theories ?
Thanks ! [:D]

[KLscilevothma]

http://www.math.gatech.edu/~thomas/FC/fourcolor.html

[Turtle]

Riemann conjecture. But I think it has a proof? Or is it the poincare conjecture?

[FZ+]

It most definitely doen't have a proof yet. We don't even know if it's true.

To summarise, the Reimann conjecture is the idea that there is "some" function which can be used to calculate the sequence of prime numbers. The best lead is the zeta function, which has a number of similarities with what we know of the prime number sequence.

[Brad_Ad23]

These are pretty much the hardest problems:

http://www.claymath.org/Millennium_Prize_Problems/

[plus]

Originally posted by STAii
Can you please (all) explain (a little bit) about each of these theories ?
Thanks ! [:D]

You could just search on Google.

To be fair there are lots and lots of very difficult problems, but many are more famous than others. Solving many of the problems around today is impossible considering the mathematics available. e.g. Fermats last theorem was famous because it was first posed 100s of years ago, and because so many people wanted to solve it, and were putting effort in, then as soon as it was solvable, it was.

Many other problems are equally as hard, but it is not worth a top notch mathematician putting in 10 years constantly not to be guaranteed a result.

[LakeMountD]

Originally posted by Brad_Ad23
These are pretty much the hardest problems:

http://www.claymath.org/Millennium_Prize_Problems/

yeah i was reading about that.. very very cool.. haha well i would get my pencil and paper out and start crunching those primes but it looks like the at&t computers already took out the first billion [8)]

[Guybrush Threepwood]

Originally posted by plus

e.g. Fermats last theorem was famous because it was first posed 100s of years ago,

a bit off the topic but that must be 300+ years ago
about Fermat (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fermat.html)
and I like Goldbach's conjecture better. it has a simple statement....

[quartodeciman]

'greatest' can mean different things. But for something with real consequences to other math research, it has to be the riemann hypotheses.

[LakeMountD]

http://www.sciencenews.org/20030614/bob10.asp
possible solution to the poincare conjecture by a russian mathematician