5 Greatest Discoveries in Mathematics #4
Fermat’s Last Theorem
An amateur mathematician, a scribble in a margin, and a 350 year old mystery. What could be a movie script for an exciting mathematical thriller is actually the real life story behind Fermat’s Last Theorem.
Pierre de Fermat was a French amateur mathematician who made numerous contributions to analysis and number theory in the early 17th century; however, his most enduring legacy involves a small note that he transcribed on the inside of Diophantus’ Arithmetica. Fermat was examining Diophantine equations of the form for integers.
When the solutions to the equation simplify into the Pythagorean triples that most of us learned in School, but Fermat had the insight to conjecture that for there are no integer solutions for, and that satisfy the equation.
In fact, in the margin he actually transcribed “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” It was this proposition of a marvelous proof that cemented Fermat’s legacy, as despite the wide publicity of the problem and efforts of thousands of mathematicians, the proof of his conjecture went unsolved for over 350 years.
It wasn’t until 1996 and using techniques entirely unavailable to Fermat that Sir Andrew Wiles at last proved Fermat’s conjecture in the affirmative, submitting a proof that surpassed 100 pages.
Did Fermat truly discover a simple elegant proof as he had claimed? It appears unlikely, but regardless, it’s clear that his work helped inspire push the boundaries of mathematical insight for hundreds of years after his death.