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#proof#fermat#book#available#didn#counterexample#https#later#years#efficient

Discussion (35 Comments)Read Original on HackerNews

albert_e•about 21 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).

tonyedgecombe•about 21 hours ago
The BBC did an episode of Horizon on it.

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

cguess•about 10 hours ago
It'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
chris_st•about 21 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.
WD-42•about 21 hours ago
It does. That’s all part of the drama.

One of the best books I’ve ever read.

placebo•about 21 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.
stogot•about 21 hours ago
Would it be good on audio?
WD-42•about 21 hours ago
Maybe. Most of it is just good storytelling. There are some light equations and graphs occasionally.
clarkeni•about 21 hours ago
It does! Very dramatic part of the book.
FeepingCreature•about 21 hours ago
This is the most offensively-themed serious site I have ever seen.
energy123•about 19 hours ago
It's fast, legible, dense and ad-free. Can't get any better than this.
fnands•about 21 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.

drivers99•about 19 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.

libria•about 18 hours 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.

smrq•about 16 hours ago
That would be pretty anachronistic; jQuery didn't come around until six years later.
NetMageSCW•about 15 hours ago
Well since jQuery was 6 years in the future, it is understandable they didn’t use it.
DStiego•about 12 hours ago
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.
jebarker•about 21 hours ago
On purely aesthetic grounds I'll take this over another substack-like site any day of the week.
bambax•about 18 hours 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?

NiloCK•about 21 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!

danbruc•about 19 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.
clircle•about 19 hours ago
efficient mathematics hypothesis? What's that?
fancyfredbot•about 19 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.

mathisfun123•about 19 hours ago
They're the same thing; knowledge markets are markets.
wiz21c•about 18 hours 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.")

jfengel•about 16 hours ago
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.

fnands•about 21 hours ago
From 2000.

Posting because he's retiring this year?

matthewfelgate•about 21 hours ago
I have a truly marvellous comment on this, which this comment box is too small to contain.
HarHarVeryFunny•about 20 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.

alok-g•about 17 hours ago
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. :-)
NetMageSCW•about 15 hours ago
I assume you meant Gabriel Lamé