by Jonathan Kujawa
On March 15th it was announced that Andrew Wiles won the 2016 Abel Prize. Established in 2002, the Abel Prize has become arguably the most prestigious prize in mathematics. In contrast to the Fields medal, which is awarded to those under 40, the Abel prize set itself as the prize which recognizes long term contributions to mathematics.
In keeping with tradition (see here: 2015, 2014) we're taking the opportunity to check out the math of behind the Abel Prize. This is the rare instance when the prizewinner's work appeared in the New York Times and may well need no introduction. Wiles won for
…for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.
— from the Abel Prize Announcement
Fermat's Last Theorem (FLT) is the claim that, for any n greater than or equal to three, there are no integer solutions to the equation
That is, you can't find numbers a, b, and c from among 0, 1, -1, 2, -2,… which can be plugged into
and have the same number on both sides of the equal sign. The same goes if the six is replaced with a 3, or 2016, or 187,201, or any other number greater than or equal to three.
If you haven't heard of FLT before, it's hard to see why anyone should give a rat's rear end about whether nor not there are integer solutions to this equation. On the other hand, Fermat conjectured FLT in 1637 and here we are in 2016 giving Wiles the Abel Prize for proving that yes, indeed, there are no such solutions. Something interesting must be going on.
