Hi, in 1637, Pierre de Fermat, and I just love
that name, wrote one of the most famous claims
in mathematical history. He said that he had
discovered a proof, but get this, the margin
of the book was too small to contain it. Yeah,
he really did. The claim became known as Fermat's
Last Theorem. The problem itself was easy to
state, but proving it, well, that was pretty
difficult. For more than, get this, 350 years,
some of the world's greatest mathematicians,
start with Euler, tried and failed to find a
proof. And then, years later, 1993. a new story
emerged. Andrew Wiles announced he had solved
it. Now, Wiles had worked largely in secret for
seven years on the problem. He had devoted much
of his life to this problem that had fascinated
him since he was a child. Then, when he presented
his work, It was an extraordinary moment in mathematics.
One of mathematics' oldest unsolved problems
was solved. But then an error was discovered.
There was a gap in the proof. Imagine what that
must have felt like after seven years. Years
of work. After publicly announcing the results.
After the mathematical world celebrated. The
proof did not work. So, Wiles returned to the
problem. And for months, he tried to repair the
gap. Again and again, his ideas failed. He later
described reaching a point where he felt he had
exhausted every possibility. The proof that had
seemed complete might not ever work. And then,
more than a year after the original announcement,
Wiles returned to an earlier approach that he
had set aside. And suddenly, He saw how two ideas
that each had failed on their own could work
together. And then he got some help from a mathematician,
Richard Taylor, and between them, they repaired
the gap. The proof was complete. We remember
this story as one of mathematics' greatest triumphs.
But the triumph includes the error. It includes
the failed repairs, the discouragement, and the
long period when Wiles did not know whether the
problem could be solved. The mistake did not
erase the seven years of work that came before
it, and it did not make Andrew Wiles a failure.
Instead, the mistake became part of the discovery.
And I find something deeply human about this
story. See, we often imagine accomplishment as
a smooth path from determination to success.
And once the finished work is presented, the
wrong turns disappear from view. But the finished
proof does not tell the entire story. The complete
story includes the moment when the proof was
incomplete. Wouldn't you agree, perseverance
is not the ability to avoid failure. And if you're
like me, perseverance is the courage to face
what does not work, to learn from it, and then
return to the problem once more. So in whatever
problem you are stuck in, maybe this story gives
you hope to persevere to the end.