While mathematicians differ, one of the hardest math problems of all time is the proof of Fermat's last theorem. This venerable mathematician wrote a note in the margin of his copy of the ancient Greek tome "Arithmetica" indicating that he had arrived at a proof that the equation x^n + y^n = z^n had no solutions in integer form where n > 2 and x, y and z were not zero.
Fermat's theorem was found shortly after his death in 1665 but was not successfully proven until 1995. Because of all of the mathematical tools that were put to work in finding the proof, many mathematicians wonder whether Fermat had actually developed a proof on his own, without all of the other forms of assistance. This is a mystery that remains beyond solving.
In terms of importance it has to be Riemann Hypothesis. One consequence that is close to what i do would be that the Miller Primality Test would become the fastest deterministic primality
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There is probably no such thing as "The World's Hardest Math Problem" however there are very hard math problems that can be found online. The hardest interesting math problems
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A line splits a triangle into two new figures with equal perimeters and areas. Prove that the
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The Riemann Hypothesis. It has encouraged a lot of math, but nobody has any idea how to solve it. 24/7
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