Solving Fermat: Andrew Wiles

albert_e 3 hours ago | parent | next [-]

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).

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WD-42 3 hours ago | parent | next [-]

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

One of the best books I’ve ever read.

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placebo 3 hours ago | parent | next [-]

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.

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stogot 3 hours ago | parent | prev [-]

Would it be good on audio?

	▲	WD-42 3 hours ago \| parent [-]
		Maybe. Most of it is just good storytelling. There are some light equations and graphs occasionally.

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tonyedgecombe 3 hours ago | parent | prev | next [-]

The BBC did an episode of Horizon on it.

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

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chris_st 3 hours ago | parent | prev | next [-]

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.

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clarkeni 3 hours ago | parent | prev [-]

It does! Very dramatic part of the book.

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NiloCK 3 hours ago | parent | prev | next [-]

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!

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danbruc 42 minutes ago | parent | next [-]

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.

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clircle an hour ago | parent | prev [-]

efficient mathematics hypothesis? What's that?

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fancyfredbot an hour ago | parent [-]

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.

	▲	mathisfun123 an hour ago \| parent [-]
		They're the same thing; knowledge markets are markets.

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FeepingCreature 3 hours ago | parent | prev | next [-]

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

	▲	drivers99 an hour ago \| parent \| next [-]
		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.
	▲	energy123 an hour ago \| parent \| prev \| next [-]
		It's fast, legible, dense and ad-free. Can't get any better than this.
	▲	fnands 3 hours ago \| parent \| prev \| next [-]
		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.
	▲	jebarker 3 hours ago \| parent \| prev [-]
		On purely aesthetic grounds I'll take this over another substack-like site any day of the week.

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fnands 3 hours ago | parent | prev | next [-]

From 2000.

Posting because he's retiring this year?

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matthewfelgate 3 hours ago | parent | prev [-]

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

	▲	HarHarVeryFunny 2 hours ago \| parent [-]
		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.