3 ms·
Solving Fermat: Andrew Wiles
- albert_e 3mo agoThis was an excellent introduction to this topic: https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem_(book) https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem_(book) by Simon Singh But I am not sure if the book covers the mistake and later correction. It has been more than a decade since I read the book (and became a fan of the author).
- chris_st 3mo agoI'll check that out - I loved his "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography". Excellent introduction to cryptography.
- clarkeni 3mo agoIt does! Very dramatic part of the book.
- WD-42 3mo agoIt does. That’s all part of the drama. One of the best books I’ve ever read.
- stogot 3mo agoWould it be good on audio?
- WD-42 3mo agoMaybe. Most of it is just good storytelling. There are some light equations and graphs occasionally.
- placebo 3mo agoAgreed. I bought it at the airport for a transatlantic flight the year it came out and started reading before lift off. Completed it before landing. Best flight ever.
- tonyedgecombe 3mo agoThe BBC did an episode of Horizon on it. https://www.bbc.co.uk/iplayer/episode/b0074rxx https://www.bbc.co.uk/iplayer/episode/b0074rxx
- cguess 3mo agoIt's the same show, Nova just rebranded it in the US. BTW, here's a full video of the BBC version but available everywhere. https://www.dailymotion.com/video/x223gx8 https://www.dailymotion.com/video/x223gx8
- matthewfelgate 3mo agoI have a truly marvellous comment on this, which this comment box is too small to contain.
- HarHarVeryFunny 3mo agoFWIW, it seems pretty clear that while Fermat briefly thought he had a proof, he fairly quickly realized it was flawed since he never mentioned this publicly and later went on to develop a proof just for the simple n=4 case. In 1847 Gabriel Lami presented a claimed (simple) general proof to the French Academy of Sciences, only for the flawed assumption in it to be pointed out immediately at the end of his presentation! This may have been the same proof that Fermat had in mind.
- alok-g 3mo agoOh, so if he later published a proof for a special case (and presumably had more paper available than the book's margin :-) ), that's convinces me that he never had a correct proof. Also that he was smart enough to realize that but perhaps just forgot to or didn't erase his original margin note. :-)
- NetMageSCW 3mo agoI assume you meant Gabriel Lamé
- fnands 3mo agoFrom 2000. Posting because he's retiring this year?
- FeepingCreature 3mo agoThis is the most offensively-themed serious site I have ever seen.
- fnands 3mo agoIn their defense, this probably looked really cool in 2000, when this was published (or at least, last updated). But agreed, that lime green is horrendous.
- jebarker 3mo agoOn purely aesthetic grounds I'll take this over another substack-like site any day of the week.
- energy123 3mo agoIt's fast, legible, dense and ad-free. Can't get any better than this.
- drivers99 3mo agoIn Firefox, I didn't see a reader view available (I wonder what determines that), but I was able to right click, Inspect, change the <body bgcolor="#CCFF33" ...> background to #ffffff Personally, I liked the design when zoomed in when combined with the rest of the page design. It reminds me of the 90s (Wired magazine, etc.). "Updated November 2000". That explains it.
- libria 3mo agoThe view-source is like a portal to Year 2000. Table-based layout, font tags, map/area tags. Only thing missing is an unnecessarily imported jQuery.
- smrq 3mo agoThat would be pretty anachronistic; jQuery didn't come around until six years later.
- NetMageSCW 3mo agoWell since jQuery was 6 years in the future, it is understandable they didn’t use it.
- NiloCK 3mo agoRecent LLM dingers like the Jacobian Conjecture counterexample have challenged the efficient mathematics hypothesis. The JC counterexample was so small in degree and coefficient. It should have been a "low fruit" in the scheme of things, but alas, unpicked for 50+ years with considerable attention from good mathematicians. With respect to FLT, my hopes have modestly increased that a truly marvelous demonstration of this proposition does in fact exist, that Fermat actually had it, and that it may someday be recovered! edit: some emphasis on modest. But let me be romantic here!
- clircle 3mo agoefficient mathematics hypothesis? What's that?
- fancyfredbot 3mo agoIt's a pun on "efficient markets hypothesis". The efficient markets hypothesis says the market prices incorporate all available information and there's no such thing as a cheap stock, so there's no easy money to be made by trading. The math equivalent is presumably that all easy problems have been solved and all open problems should be very very hard. This has turned out not to be the case as LLMs have found simple counterexamples to long held conjectures.
- mathisfun123 3mo agoThey're the same thing; knowledge markets are markets.
- gosub100 3mo agoNot really, the incentives for each are not binary values. There are bounties on the 10 millennium problems (that haven't been increased in 25 years), but there isn't much motivation beyond that. You get some street cred and your name in a prestigious journal. That's not-nothing but can't hold a candle to the potential fortunes of the market.
- wiz21c 3mo agoI'm not a mathematician and AI doesn't answer very well. Could someone tell us how big an endeavour this is: https://github.com/ImperialCollegeLondon/FLT https://github.com/ImperialCollegeLondon/FLT ? (the site is : "An ongoing multi-author open source project to formalise a proof of Fermat's Last Theorem in the Lean theorem prover.")
- jfengel 3mo agoEnormous. Wiles' proof is 129 pages long, and builds on results that require a vast amount of infrastructure to define. It's going to take dozens of person-years.
- bambax 3mo ago> NOVA: So Fermat's original proof is still out there somewhere. > AW: I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof. But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof. Yes, it's generally accepted that Fermat didn't in fact have a proof, with the tools available to him at the time. But wouldn't it be cool to send some AI on this chase and see what comes back? Is anyone attempting this?
- WheelsAtLarge 3mo agoWhat I find interesting in this show is that he took a hiatus from his profesorship to spend the time to find the proof. I think it was years. Also, he found the proof by providing a different conjecture(is that right) to solve Fermat. Higher mathematics is just a different world to those of us who haven't even a clue how that world functions.