alt.hn

7/27/2026 at 8:42:46 PM

Solving Fermat: Andrew Wiles

 https://www.pbs.org/wgbh/nova/proof/wiles.html

by 1970-01-01

7/28/2026 at 2:40:09 PM

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).

by albert_e

7/28/2026 at 2:44:57 PM

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.

by chris_st

7/28/2026 at 3:03:21 PM

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

One of the best books I’ve ever read.

by WD-42

7/28/2026 at 3:15:10 PM

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.

by placebo

7/28/2026 at 3:13:52 PM

Would it be good on audio?

by stogot

7/28/2026 at 3:20:14 PM

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

by WD-42

7/28/2026 at 2:45:21 PM

It does! Very dramatic part of the book.

by clarkeni

7/28/2026 at 3:09:43 PM

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

by FeepingCreature

7/28/2026 at 4:45:47 PM

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

by energy123

7/28/2026 at 5:09:10 PM

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.

by drivers99

7/28/2026 at 3:11:54 PM

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.

by fnands

7/28/2026 at 6:19:17 PM

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.

by libria

7/28/2026 at 7:58:10 PM

That would be pretty anachronistic; jQuery didn't come around until six years later.

by smrq

7/28/2026 at 8:36:43 PM

Well since jQuery was 6 years in the future, it is understandable they didn’t use it.

by NetMageSCW

7/29/2026 at 12:15:19 AM

The background is so green that when I go look at a website with white background afterwards, the white will appear like red because the cells for green in my retina have been depleted.

by DStiego

7/28/2026 at 3:19:13 PM

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

by jebarker

7/28/2026 at 6:15:38 PM

> 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?

by bambax

7/28/2026 at 3:21:58 PM

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!

by NiloCK

7/28/2026 at 5:14:59 PM

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.

by danbruc

7/28/2026 at 4:36:30 PM

efficient mathematics hypothesis? What's that?

by clircle

7/28/2026 at 4:48:58 PM

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.

by fancyfredbot

7/28/2026 at 4:53:26 PM

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

by mathisfun123

7/28/2026 at 6:43:23 PM

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.

by gosub100

7/28/2026 at 7:11:18 PM

> There are bounties on the 10 millennium problems (that haven't been increased in 25 years) ...

Strictly speaking, if you constructively prove P=NP and the solver has reasonable time complexity, e.g. quadratic, it could make you incredibly rich. If you don't attract the wrong kind of attention from the world's intelligence agencies first...

by rheniumclass

7/28/2026 at 7:15:55 PM

i think you have no idea what you're saying...

> That's not-nothing but can't hold a candle to the potential fortunes of the market.

a market is where things are sold and bought. there are lots of markets which aren't as well capitalized as financial markets - your local farmer's market doesn't "hold a candle to the potential fortunes of the market" but it's still a market (and presumably the efficient market hypothesis still applies).

by mathisfun123

7/29/2026 at 11:32:34 AM

The markets arent efficient without enough participants. This is why the price of gasoline only fluctuates cents between competitors, but vehicle prices fluctuate thousands. It's a very simple concept that you aren't seeing.

The market for solving math problems is tiny compared to selling/ running algos for trading. You solve a pure math problem you might get accolades from some professors.

by gosub100

7/28/2026 at 3:03:14 PM

From 2000.

Posting because he's retiring this year?

by fnands

7/28/2026 at 6:10:06 PM

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.")

by wiz21c

7/28/2026 at 8:21:25 PM

Enormous.

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.

by jfengel

7/28/2026 at 2:57:21 PM

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

by matthewfelgate

7/28/2026 at 3:48:38 PM

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.

by HarHarVeryFunny

7/28/2026 at 7:06:49 PM

Oh, 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. :-)

by alok-g

7/28/2026 at 8:40:05 PM

I assume you meant Gabriel Lamé

by NetMageSCW