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Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

nature.com

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Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#11

Post by aidos »

sk2code wrote: post #5

If interested there is a very good book about this subject: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-P...

Ha. I've read it as "Fermat's Last Theorem" - guess that's the UK name.

For anyone who hasn't read them Simon Singh's books are great introductions to subjects by tracking their history. In this case mathematics, but he also has one about cryptography [1] and another on the space and the universe [2].

[1] http://www.amazon.co.uk/Code-Book-Science-Secrecy-Cryptograp...

[2] http://www.amazon.co.uk/Big-Bang-Important-Scientific-Discov...

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#12

Post by Kenji »

I have a question about these hundreds-of-pages long proofs. Who can check such long proofs and be confident about it? To study a document of this size and advanced content rigorously, you would need years - and even then, it is not certain that you didn't overlook something. How can I ever be confident in such proofs until they are checked in, say, Coq or something?

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#13

Post by frutiger »

indifferentalex wrote: post #4

I know he has other sources of income but the fact that this extremely smart and dedicated person, in an age of professional lifestyle bloggers, "travellers" and other celebrities, is rewarded for his efforts and can just go out and buy himself a brand new Ferrari with the prize money makes me smile.

> "travellers"

I sincerely do not understand what was meant by this.

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#14

Post by kirrent »

Kenji wrote: post #12

I have a question about these hundreds-of-pages long proofs. Who can check such long proofs and be confident about it? To study a document of this size and advanced content rigorously, you would need years - and even then, it is not certain that you didn't overlook something. How can I ever be confident in such proofs until they are checked in, say, Coq or something?

In this case, each chapter of the proof was sent off to different people so they could spend time studying a smaller section of the proof. Famously a significant mistake was discovered during this review that took Wiles a year to fix.

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#15

Post by 7373737373 »

Kenji wrote: post #12

I have a question about these hundreds-of-pages long proofs. Who can check such long proofs and be confident about it? To study a document of this size and advanced content rigorously, you would need years - and even then, it is not certain that you didn't overlook something. How can I ever be confident in such proofs until they are checked in, say, Coq or something?

I have the same questions when reading something like this. Expert verification seems more like an appeal to authority and intuition instead of a definite proof with formal rigorosity. Locally, there is always structure, but in pure mathematics even these steps require such an in depth understanding that trusting experts as an outsider seems to be impossible, it could as well be magic. As a programmer, I have a quite mechanistic understanding of the world, projects like http://us.metamath.org/index.html seem to make it much more understandable.

I'm wondering, if the longest path to the theorem "2 + 2 = 4" is 150 layers deep in this system, how deep would this proof be?

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#16

Post by noir_lord »

delightless wrote: post #10
6502nerdface wrote: post #8

Earlier quoted context omitted.

> the fact that this extremely smart and dedicated person [...] is rewarded for his efforts Yeah, all he had to do was prove Fermat's Last Theorem.

And then wait 22 years.

The note to pay him should have been in the margins but there wasn't enough room.

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#18

Post by kyzyl »

adenadel wrote: post #2

There's a really nice documentary on Andrew Wiles and Fermat's Last Theorem https://vimeo.com/18216532 It even gives a high level description of the methods used for those who are interested.

"It was so simple! Just add 3-gamma to the M-structure!" slaps forehead

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#19

Post by kyzyl »

indifferentalex wrote: post #4

I know he has other sources of income but the fact that this extremely smart and dedicated person, in an age of professional lifestyle bloggers, "travellers" and other celebrities, is rewarded for his efforts and can just go out and buy himself a brand new Ferrari with the prize money makes me smile.

I dunno, the prize might be a little overblown. All-in it seems like a pretty marginal improvement if you ask me.

Re: Fermat's Last Theorem Earns Andrew Wiles the Abel Prize

#20

Post by jdietrich »

adenadel wrote: post #2

There's a really nice documentary on Andrew Wiles and Fermat's Last Theorem https://vimeo.com/18216532 It even gives a high level description of the methods used for those who are interested.

There's a striking moment at about 41:00 where Wiles tearfully describes his ultimate breakthrough. Mathematicians and others in the hard sciences are often perceived as cold and joyless, but this is a remarkable counterexample.
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