Greatest problem in mathematics

What do you think is the greatest mathematics problem of all time. In my opinion Fermat's last theorem is a very attractive problem - you can explain it to almost anyone and they will get the jist of it. I just think it's an extremely beautiful problem and one that you would have absolutely no idea of how to solve it (I know the outline of how the proof works).
The most attractive unsolved problem currently is probably the Reimann hypothesis, that has a substantial amount of evidence for it, but in maths, evidence doesn't mean much (as shown several times in the past) until you can provide a rigorous proof that gives an answer beyond all doubt. I hope to see it solved in my lifetime, but who knows.

So the question is, what is your favourite problem in mathematics, solved or unsolved?

Reply 1

Zacken

The irrationality of

\zeta(5)

Is there a positive non-integer

x

such both

2^x

and

3^x

are integers?

The Collatz conjecture

Reply 2

16Characters....

Not mentioning mathematics when on a date

Reply 3

Zacken

Original post by 16Characters....

Not mentioning mathematics when on a date

Getting a date in the first place

Reply 4

Gregorius

Original post by Ano123

What do you think is the greatest mathematics problem of all time.

Of all time? The fundamental theorem of arithmetic. Extraordinarily mysterious and, to paraphrase Whitehead on Plato, much of the history of mathematics has been a series of footnotes to it.

Reply 5

Steve Tomlinson

I tried to put the solving to Collatz up, but it didn't have columns so if you go to Facebook PRIME/TWIN PRIME/GOLDBACH NUMBER COUNTING/THEREFORE REIMANN! you will see a sound solving of Collatz' Conjecture. And how to count primes. S'cool!