In 1637 the great king of amateur mathematicians — Pierre de Fermat — wrote his most famous theorem in the margin of his copy of Arithmetica, which stated that that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. But an even more interesting was his little note in the margin, which read that the proof was too big to fit into it. What happened later is that this apparently simple problem became known as the most difficult problem of mathematics. Greatest mathematicians tried to solve Fermat’s last theorem for 358 years, including Euler, Hilbert, Kronecker and others. But it was finally solved in 1995 by the great Andrew Wiles.
This remarkable story ended more than 350 years of reign of Fermat’s last theorem as the king of the most difficult math problems. But don’t worry, as long as there are mathematicians there will be unsolved problems, and, actually, there is a number of important problems, which belong to the list of the so called Millennium Prize Problems. The list holds 7 problems (1 of which is already solved), the award for which is 1 million dollars. Riemann hypothesis is arguably the most important one, or at least the most famous one. And it is a problem proposed by Bernhard Riemann (1859) about the location of the nontrivial zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2.
So let’s take a closer look at what the Riemann hypothesis is all about. Here are two videos, the first one is a nice presentation of the history behind it, whereas the second one is a great lecture by Dan Rockmore.