Fermat’s Last Theorem is one of the long outstanding maths problems that remained unresolved in the maths community for over 350 years.
This was so, until Andrew Wiles solved it on 23 June 1993.
So what is Fermat’s Last Theorem and how did he solve it?
Well I’m not going to discuss how he solved it, I tried to follow his lecture on how he solved it and I got stuck 10 minutes into his 53 minutes lecture and it’s been downhill ever since.
In number theory, Fermat’s Last Theorem [sometimes called Fermat’s conjecture, especially in older texts] states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2.
Pierre de Fermat came up with this proposition [ an + bn = cn ] in 1637.
Although he claimed to have a general proof of his conjecture, Fermat left no details of his proof, because he say he ran out of space on his papers. No proof by him has ever been found.
So he ran out of space on his papers, resulting in no proof being written. He died without any proof of his theorem ever being found, hence Fermat’s Last Theorem.
This claim [theorem] became one of the most notable unsolved problems in mathematics.
So Fermat’s Last Theorem stayed for over 350 years without anyone solving or proving it.
After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, it was described as a “stunning advance” in the citation for Wiles’s Abel Prize award in 2016.
Sir Andrew Wiles first knew about Fermat’s Last Theorem in his teens when one day coming from school he decided to go to the library and in there he came across a book on Mathematics’s long unresolved equations.
It was during his adulthood as a mathematics lecturer, he decided to dedicate his time to solving Fermat’s Last Theorem. He spent about 7 years totally committed to solving this equation.
Spending 7 years being stuck to solve one problem is something that few people do. Spending 7 years trying to solve one equation is a mark of total commitment.
In an interview, Andrew Wiles was asked how do mathematicians do it, he had a number of interesting responses and I think that his responses are not only good mathematics tips but good life lessons as well.
He says that what you have to handle when you are doing maths equations is accepting that at some point you are going to be stuck.
It is important to accept the state of being stuck.
Some people find being stuck very stressful, even people who are good at mathematics get stressed when they get stuck on maths problems. However, being stuck is part of the process of solving math problems.
You have to accept that “being hard” is part of the process, you have to learn to enjoy the hard parts of solving maths problems.
Yes you don’t understand why this part is hard to solve, but you will have to have faith that you will understand later once you found the solution.
Anything in life [sport, entrepreneurship, relationships] where you have to do something new, you will go through a difficult period.
I think accepting that at some point you will hit potholes along the way, prepares you mentally to be resilient.
This process of being stuck is not something to be scared of, everyone goes through it.
Mathematics is difficult even for mathematicians, they also struggle with maths problems.
The difference is that good mathematicians are prepared to handle that struggle at a much larger scale than others who give up soon.
Those who succeed in mathematics and in life have built up resistance to setbacks. They are what Nassim Nicolas Taleb calls the antifragile.
Off-course some people are smarter than others but most people can be good at mathematics if they are prepared to handle the stress that comes with it.
Success is not simply a function of being smart, it is to a large extend a function of sticking with the problem much longer, trying different ways to solve it, instead of giving up at the first hurdle you encounter.
As Albert Einstein has said before:
“It’s not that I’m so smart, it’s just that I stay with problems longer.”
Genius is about stubbornness, refusing to let go of problems.
It took the mathematics community 358 years to prove Fermat’s Last Theorem, talk about staying with a problem for long.
PS: Next time can someone please give mathematicians enough paper to write their theorems and proofs 🙂