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
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.
Yes, with million-to-one odds. Though I'd say "error or equivalent shortcoming, for the general case".
> that perhaps is more straightforward than Wiles's?
I don't recall a mathematical definition of "straightforward", but yes. Ignoring minor improvements, I'd guess there's a much better proof...though that might require a century of new developments in related parts of mathematics, before we'll have the necessary tools to write it down.
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.
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 out I wasn't a mathematician or very well connected, he said "doesn't matter: Get to your national broadcaster and ask them to verify the story"
So I rang the ABC and asked to speak to the Science Desk. This was at around 7am by this time. I was connected immediately to Robyn Williams, the premier science communicator at the ABC, despite having no name, no evident back story or trust. He was absolutely delightful to talk to, agreed with a laugh that he often got excited calls about people squaring the circle or finding repeat patterns in PI digits and was used to crank callers, listened to me, probably did some checks and then said he'd contact somebody at Cambridge and see what the gen was. My memory is he called me back a little while later saying they'd confirmed a room was booked for a significant public announcement seminar, and thanked me for the tip. This was a long time ago, it's equally likely I misremembered and he gave me a name to check with in the UK and I did the leg work. The point is, I wasn't just told to bugger off.
Nowadays it would be all over twitter. John was a bit old school and liked phone calls. They had internet emails in 92 of course I think he just liked the physicality of a call.
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[ 2.8 ms ] story [ 34.5 ms ] threadOne 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
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.
Yes, with million-to-one odds. Though I'd say "error or equivalent shortcoming, for the general case".
> that perhaps is more straightforward than Wiles's?
I don't recall a mathematical definition of "straightforward", but yes. Ignoring minor improvements, I'd guess there's a much better proof...though that might require a century of new developments in related parts of mathematics, before we'll have the necessary tools to write it down.
"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! Found it. This is a better clip. https://www.youtube.com/watch?v=BaKyvr4ar1Q
Bob Dylan reflecting on his early work https://www.youtube.com/shorts/Fh3pAJf-vdU
I wish to live my life so I can say one day 'Nothing I ever do again will.."
So I rang the ABC and asked to speak to the Science Desk. This was at around 7am by this time. I was connected immediately to Robyn Williams, the premier science communicator at the ABC, despite having no name, no evident back story or trust. He was absolutely delightful to talk to, agreed with a laugh that he often got excited calls about people squaring the circle or finding repeat patterns in PI digits and was used to crank callers, listened to me, probably did some checks and then said he'd contact somebody at Cambridge and see what the gen was. My memory is he called me back a little while later saying they'd confirmed a room was booked for a significant public announcement seminar, and thanked me for the tip. This was a long time ago, it's equally likely I misremembered and he gave me a name to check with in the UK and I did the leg work. The point is, I wasn't just told to bugger off.
Nowadays it would be all over twitter. John was a bit old school and liked phone calls. They had internet emails in 92 of course I think he just liked the physicality of a call.
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