“What’s the big deal about Fermat’s last theorem?” Yuri asked.“It’s famous,” I said. “So simple anyone can understand it, but it took centuries for mathematicians to prove it’s true.”With a note scribbled in the margin of a book in the 1600s, Fermat set in motion centuries of effort spent unraveling this enigma. It would require 358 years and the development of entirely new fields of mathematics to provide a definitive solution to what is now recognized as one of the greatest mathematical problems of all time.

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert’s program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Gödel stunned the world by proving that Hilbert’s goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system.Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Gödel’s incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before.