Hacker News

1970-01-01
Solving Fermat: Andrew Wiles pbs.org

albert_e4 hours ago

This was an excellent introduction to this topic:

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).

WD-424 hours ago

It does. That’s all part of the drama.

One of the best books I’ve ever read.

placebo4 hours ago

Agreed. 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.

stogot4 hours ago

Would it be good on audio?

WD-424 hours ago

Maybe. Most of it is just good storytelling. There are some light equations and graphs occasionally.

chris_st4 hours ago

I'll check that out - I loved his "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography". Excellent introduction to cryptography.

tonyedgecombe4 hours ago

The BBC did an episode of Horizon on it.

https://www.bbc.co.uk/iplayer/episode/b0074rxx

clarkeni4 hours ago

It does! Very dramatic part of the book.

bambaxan hour 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?

wiz21can hour ago

I'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 ?

(the site is : "An ongoing multi-author open source project to formalise a proof of Fermat's Last Theorem in the Lean theorem prover.")

FeepingCreature4 hours ago

This is the most offensively-themed serious site I have ever seen.

energy1232 hours ago

It's fast, legible, dense and ad-free. Can't get any better than this.

libria41 minutes ago

The 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.

drivers992 hours ago

In 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.

fnands4 hours ago

In 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.

jebarker4 hours ago

On purely aesthetic grounds I'll take this over another substack-like site any day of the week.

NiloCK4 hours ago

Recent 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!

danbruc2 hours ago

There are 120 monomials of degree at most 7 in three variables. If we restrict the coefficients to the integers from -10 to +10, that makes 21^120 possible polynomials. And we need three of them, that makes 10^476. And we would still miss the specific counterexample because it includes a coefficient of 12 outside of our range. So I would say that you will never find this specific counterexample by chance and whether you could accidentally trip over any counterexample really depends on their density. And we have of course not addressed the question why you would search this specific region of the parameter space, why dimension 3, degree 7 and small integer coefficients? There might be good mathematical reason to look at this region, but it is probably non-trivial to even figure out where to look.

clircle2 hours ago

efficient mathematics hypothesis? What's that?

fancyfredbot2 hours ago

It'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.

mathisfun1232 hours ago

They're the same thing; knowledge markets are markets.

gosub10017 minutes ago

Not 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.

fnands4 hours ago

From 2000.

Posting because he's retiring this year?

matthewfelgate4 hours ago

I have a truly marvellous comment on this, which this comment box is too small to contain.

HarHarVeryFunny3 hours ago

FWIW, 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.

hn-front (c) 2024 voximity
source