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How Math’s Most Famous Proof Nearly Broke (2015)
- oxymoron 8y agoIs it really fair to say that Wiles proof is the most famous in mathematics? Seems to me like something like the Euclid’s proof of the infinitude of the primes might be more well known? Or the standard geometrical proof of Pythagoras theorem?
- skh 8y agoIt’s certainly true that far more people understand and know how to prove the infinitude of the primes than understand/know how to prove Wiles’ proof. Wiles’ result has received far more press coverage in the last 30 yeas though. In this sense it is more famous.
- deleted 8y ago[deleted]
- drej 8y agoI can recommend Simon Singh's book on this topic, his writing is rather captivating (The Big Bang is one of the best books I've read, so is the Code Book). He also made a BBC documentary on the topic. https://simonsingh.net/books/fermats-last-theorem/ https://simonsingh.net/books/fermats-last-theorem/
- ElCapitanMarkla 8y agoI'd also recommend his The Code Book - https://simonsingh.net/books/the-code-book/ https://simonsingh.net/books/the-code-book/ Nice easy reading on the history of codes.
- misil 8y agoI also want to urge anyone with even just a fleeting interest in mathematical topics like this to go out looking for said BBC documentary. It's a marvelous portrait of the characters and backstories behind this proof.
- ngcc_hk 8y agoIt is a good book but the last chapter is a rush.
- ddoran 8y ago+1 for the movie. It used to be on youtube but I can't find it right now. Perhaps the BBC had it removed. This is the finest moment in the movie, for me, when Wiles describes the moment when everything clicked. The whole movie is well worth watching. https://www.youtube.com/watch?v=SccDUpIPXM0 https://www.youtube.com/watch?v=SccDUpIPXM0
- soegaard 8y agoLook at Vimeo instead.
- xiaoxiae 8y agoThat was quite an enjoyable read. It's so interesting that a problem so simple to explain would require hundreds of pages of proof. I'm really interested in whether the Collatz conjecture will be proven too.
- kzrdude 8y agoMaybe you'll like this FLT related story too, it's the most worthwhile numberphile video: https://m.youtube.com/watch?v=nUN4NDVIfVI https://m.youtube.com/watch?v=nUN4NDVIfVI
- jeff76 8y agoThis brings up a question I have. Is there a way we can code up proofs in a computer language and have it checked for correctness? If so, how? What resources can I follow up on? Can current technologies check really complicated proofs like this one?
- mehrdadn 8y agoI know Coq exists but that's about it https://coq.inria.fr/ https://coq.inria.fr/
- gabrielmoshe 8y agoYes! There are several different languages and systems used for coding proofs. Coq [1] is probably the most well known. But, as you alluded to, it is not convenient (or easy) to code all proofs in such a style. 1. https://coq.inria.fr/ https://coq.inria.fr/
- davidgrenier 8y agoAt OPLSS 14, Andrew Appel characterized programming in Coq as the world's best video game, I would have to say it's a close second. I recall it was accessible if you had programmed in an ML, start here: https://softwarefoundations.cis.upenn.edu/ https://softwarefoundations.cis.upenn.edu/
- kurlberg 8y agoVoevodsky developed Univalent Foundations in order to catch subtle mistakes in his (and others) result: "Only then did I discover that the proof of a key lemma in my paper contained a mistake and that the lemma, as stated, could not be salvaged. Fortunately, I was able to prove a weaker and more complicated lemma, which turned out to be sufficient for all applications. A corrected sequence of arguments was published in 2006. This story got me scared. Starting from 1993, multiple groups of mathematicians studied my paper at seminars and used it in their work and none of them noticed the mistake. And it clearly was not an accident." More details on page 8 in the IAS newsletter article https://www.ias.edu/sites/default/files/pdfs/publications/letter-2014-summer.pdf https://www.ias.edu/sites/default/files/pdfs/publications/le... There is also a Quanta article: https://www.quantamagazine.org/univalent-foundations-redefines-mathematics-20150519/ https://www.quantamagazine.org/univalent-foundations-redefin...
- heinrichf 8y agoAn amazing (word of a number theorist) documentary from the BBC's Horizon program: https://www.dailymotion.com/video/x223gx8 https://www.dailymotion.com/video/x223gx8 You can see Wiles crying when he talks about his work.
- MaxBarraclough 8y agoInteresting read. Wikipedia recounts the tale as well - https://en.wikipedia.org/w/index.php?title=Fermat%27s_Last_Theorem&oldid=871657366#Wiles's_general_proof https://en.wikipedia.org/w/index.php?title=Fermat%27s_Last_T...
- waynecochran 8y agoWhat are the practical ramifications of FLT? It sounds like there may be crypto implications w elliptical curves.
- claudiawerner 8y agoWhat's interesting about FLT is that in the sense of proving a hypothesis, although the attempts themselves have lead to failures in their objective, they often illuminated whole new areas of mathematics, but this realization only comes somewhat later than when the proof is realized. It was obvious that a particular attempt had failed relatively quickly, but the lessons learned and their applications required a keen (creative mathematical) eye to spot. Badiou (a continental political philosopher interested in the philosophy of mathematics) uses FLT as an example in political contexts, to what extent we can say that a utopian vision has failed even if it results in disaster, we should be (and some have been) looking out for the lessons which are learned after failure.
- ngcc_hk 8y agoHuman as an individual is not a number. Yes may be for the philosopher king for an ideal which not everyone agree or vote for may or may not come or forever waiting, we just kill millions and millions. Maos has it and starve 30 millions. Soviet Union. USA has its Vietnam and 2nd Iraq war. I am not saying we should not try but Great Saint begot Great Thief. Be afraid of people who sit in their arm chair and talk about scarifie for the ideal.
- waynecochran 8y agoThat last sentence about Badiou, whoever that is, was a sharp turn to the left.
- SolarNet 8y agoAs the article said, none really. It's more the tools that were created to solve it that are useful. FLT is like the Apollo mission of Mathematics and has been for hundreds of years. A crazy dream of no direct immediate practical value, but the pursuit of which sparks innovation and dreams.
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- nyc111 8y agoA 200 page proof even if it is correct may not be the most elegant proof for this problem since Fermat noted that his proof was too long to fit on the margin. This suggests at most a one page proof. Also I'm curious if it can be proved that only one proof is possible. There are several independent proofs of the Pythagoras theorem.
- coraltime 8y agoFermat could have been mistaken about his proof, however.
- nyc111 8y agoThat's a possibility. But I still think there must be a more direct proof. A shorter proof that can be understood by anyone who is familiar with Euclid. I believe a proof by using only mathematical methods known to Fermat must be possible.
- Retra 8y agoYou can make any proof as short as you want. Length of proof means almost nothing; it is a function of the language you choose to use.
- nyc111 8y ago> You can make any proof as short as you want. If so why did Wiley choose to write a 200 page proof while he could have stated it in one sentence?
- Retra 8y agoBecause he was writing for a specific class of predetermined parsers, rather than an arbitrary one which was optimized for his proof.
- deleted 8y ago[deleted]