31–40 of 46 posts
(disclaimer: I haven't watched this yet) Mathematicians / folks knowledgeable on the subject - do you think Fermat had an error in his (lost) proof? Or that there exists a solution that perhaps is more straightforward than Wiles's? My understanding is that Wiles had to use a ton of math (and invent some new math?) that had not yet been invented in Fermat's time.
Q.E.D. we agree and we all shout hurra
as he confirms what Fermat
jotted down on that margin
which could have used some enlarging
I've only skimmed it but Simon Singh's book on it seems reasonably accessible to non-experts One interesting thing of FLT is Wiles is on record as saying it opened the door (I think. This is from memory) to Langlands Program, a series of mathematical connections Harder problems of course exist, Riemann Hypothesis et al but FLT still took hundreds of years to solve
Unfortunately this clip cuts just before the most emotional part. At 01:29 as he's about to break down, he says – this is my memory, sorry, paraphrasing: "Nothing I ever do again…" – and then, having barely held it together for the last 30 seconds, he has to stop. It brings me to tears every time I watch it. A man realising the sheer magnitude of the thing he did. It's the most relevant part for humanity today. Ah! F…
Andrew Wiley gently smiles, does his thing an voila! Q.E.D. we agree and we all shout hurra as he confirms what Fermat jotted down on that margin which could have used some enlarging
Feeling the finality
Of his greatest achievement
He couldn't believe it
But it's true, now he's feelin' blue
So between me and you:
Think twice before you do
I live in Australia. One day I received a very excited phonecall at a ludicrously early time from a Canadian Mathematician I knew (John McKay, Concordia. He's dead now but had been a figure in my childhood from his time in Edinburgh in the 60s. he had worked with John Conway early in both their careers) telling me this was rumoured to be coming, and asking me to get the word out and find out what I could. I pointed o…
I've only skimmed it but Simon Singh's book on it seems reasonably accessible to non-experts One interesting thing of FLT is Wiles is on record as saying it opened the door (I think. This is from memory) to Langlands Program, a series of mathematical connections Harder problems of course exist, Riemann Hypothesis et al but FLT still took hundreds of years to solve
In fact the Langlands programme began with Langlands writing his ideas in a letter which he wrote to Andre Weil because of his association with the TSW conjecture.
I enjoyed this explanation https://youtu.be/4dyytPboqvE?is=VFFjLHSk7vgosN54 by Ed Frenkel.
(disclaimer: I haven't watched this yet) Mathematicians / folks knowledgeable on the subject - do you think Fermat had an error in his (lost) proof? Or that there exists a solution that perhaps is more straightforward than Wiles's? My understanding is that Wiles had to use a ton of math (and invent some new math?) that had not yet been invented in Fermat's time.
For one thing, Fermat wasn’t actually a “professional” mathematician. He was a lawyer and judge and was known for having remarkable intuition but not really troubling himself too much with details of proofs etc. For example Descartes famously called him a “deficient mathematician”[1] in an angry exchange of letters over a technique that Fermat had discovered to geometrically construct a tangent to a particularly problematic curve called Descartes’ Folia using a technique we would now recognise as being the definition of the derivative as the limit of the difference quotient.
[1] Explained entertainingly here https://youtu.be/xKfEmbWBgvM?is=qLnPvPXGDqgJCDC3
Earlier quoted context omitted.
It's not just that he formulated the problem, though. It was specifically the fact that he claimed he had a proof which led to the proof, and it was only because people credibly believed he had one that they spent so much effort trying to (supposedly, re-)discover it.
> and it was only because people credibly believed he had one that they spent so much effort trying to (supposedly, re-)discover it. That's not true. Even early on, most mathematicians doubted he had a proof. But I'd check out the history of the problem as described on Wikipedia. There was considerable research into the problem before Fermat, and general research into Diophantine equations had gone on for over a thou…
(disclaimer: I haven't watched this yet) Mathematicians / folks knowledgeable on the subject - do you think Fermat had an error in his (lost) proof? Or that there exists a solution that perhaps is more straightforward than Wiles's? My understanding is that Wiles had to use a ton of math (and invent some new math?) that had not yet been invented in Fermat's time.
Pretty sure Fermat didn’t have a proof. For one thing, Fermat wasn’t actually a “professional” mathematician. He was a lawyer and judge and was known for having remarkable intuition but not really troubling himself too much with details of proofs etc. For example Descartes famously called him a “deficient mathematician”[1] in an angry exchange of letters over a technique that Fermat had discovered to geometrically co…
Descartes was himself a lawyer (by training) then there were Leibnitz, Cayley, Viete. If you include Physics you will get a bigger list.
Descartes and Fermat ran a mutual admiration society, don't read to much into it.
Both had independently come up with coordinate geometry, linking algebra and geometry
I agree Fermat probably had a wrong proof but curb your condescension towards lawyers making contributions in mathematics.