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Mathematician's anger over his unread 500-page proof

126 points| ca98am79 | 11 years ago |newscientist.com | reply

114 comments

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[+] DMac87|11 years ago|reply
This and many comments seem to miss the facts, at least as presented on the ABC conjecture's wikipedia page http://en.wikipedia.org/wiki/Abc_conjecture:

- An error was found in 2012 and was just recently (Nov 2014) corrected - He's re-released his notes & lectures on the subject - A workshop will be held on the topic in March

That doesn't seem to be unusual / isolationist behavior, though it's obviously a complicated topic and since Fermat's Last Theorem has been deemed 'solved' already, the fact that it makes a FLT proof easier isn't much appreciated by the press / community.

[+] placebo|11 years ago|reply
No doubt the guy's exceptionally brilliant, and perhaps one day a mathematician with enough motivation to do it will spend a very long time trying to understand and decipher what he constructed, but my take on it is that anyone that wants to communicate a message, no matter how brilliant, should also go to the trouble of making it as legible as possible to others.
[+] therobot24|11 years ago|reply
This is actually a major gripe of mine when reading papers - not enough effort to communicate the math so it's readable. It's really frustrating to decipher a paper when there's a lot of hand waving. It's 10x worse when buzzwords or unimportant relationships are also included.
[+] zokier|11 years ago|reply
I read the report linked in the article and Mochizuki et al do not seem to think that studying this would take prohibitively long time. Some select quotes:

> During these lectures, Yamashita warned that if you attempt to study IUTeich by skimming corners and “occasionally nibbling” on various portions of the theory, then you will not be able to understand the theory even in 10 years; on the other hand, if you study the theory systematically from the beginning, then you should be able to understand it in roughly half a year.

> Unfortunately, however, there appear to exist, especially among researchers outside Japan, quite strongly negative opinions and antagonistic reactions to the idea of “studying the theory carefully and systematically from the beginning”.

>From the point of view of achieving an effective solution to this sort of problem [=education], the most essential stumbling block lies not so much in the need for the acquisition of new knowledge, but rather in the need for researchers (i.e., who encounter substantial difficulties in their study of IUTeich and related topics) to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.

[+] Florin_Andrei|11 years ago|reply
If it's in your interest that I understand what you're saying, and you make it too hard for me to parse your stuff down to a comprehensible level - then it's your fault, not mine.
[+] serf|11 years ago|reply
maybe he'll pull a Galois and submit a suitable paper shortly before a pistol duel.
[+] gecko|11 years ago|reply
He did the entire 500-page paper in isolation and refuses to lecture on it in any capacity anywhere other than his own university. He may be right, and he may not be, but his failure to get an answer from the community is his fault, not theirs.
[+] roberthahn|11 years ago|reply
Minhyong Kim (cited from the article) makes a good point: that "any journal would probably require independent reviewers who have not studied under Mochizuki to verify the proof."

Given that, Mochizuki is stuck between a rock and a hard place - anyone he brings up to speed automatically becomes disqualified to independently review his work.

I'm not so sure this is entirely his fault.

EDIT: tpyo

[+] jblow|11 years ago|reply
Math is supposed to be about pursuit of truth, not how congenial you are.
[+] hoopism|11 years ago|reply
Don't feel bad. I can't get coworkers to read 2 page approach docs.
[+] ableal|11 years ago|reply
I not too sure about emails with ten lines.
[+] jackmaney|11 years ago|reply
> If nobody understands a mathematical proof, does it count?

Nope. That's the social aspect of mathematics: your proofs have to be comprehensible and considered to be correct by those in the mathematical community that read them (at least peer review) before they're accepted.

[+] mathattack|11 years ago|reply
A professor once defined a proof as "That which is convincing", and we were free to say, "I am not convinced"

While the topic being proven may be technically correct, the act of proving is a social act. The formal notation just makes this more precise than human language.

[+] fargolime|11 years ago|reply
There's also a luck aspect. Perhaps Mochizuki's proof is comprehensible but no one has the desire to read it. A mathematician or scientist should be prepared to be a lone wolf, never receiving recognition and their groundbreaking ideas never known to another.
[+] cLeEOGPw|11 years ago|reply
A proof, even if true, is worthless if it is unusable by others to build proofs on top of it.
[+] nabla9|11 years ago|reply
Hopefully someday, model checkers and proof assistants can help mathematicians to put these monster proofs into format that can be verified with computer.
[+] deepsun|11 years ago|reply
When I was a student, I started making such a system. It would also be very beneficial for students for explaining complex proofs.

The main problem is not in model checker (there are plenty of them already), but to automatically convert between a model checker syntax (that looks rather like a programming language), and regular math paper syntax (which is free-form English, so you need general AI for reading that).

I was already quite experienced programmer at that time, but realized the UI/UX problem is too big for me alone, even if I'm going to parse some simplified English.

But with simplified English, the problem is definitely solvable, someone just needs to put their time/money in that. Once UX is good enough for mathematicians, professors or students, it will lift off and be the Wikipedia for Mathematics.

[+] kodis|11 years ago|reply
Yes, assuming that there remain any proofs which the model checkers and proof assistants haven't already discovered!
[+] fibo|11 years ago|reply
Often happens that after an hard proof there are less t'han 10 People that can understand it. Also happened for Fermat Conjecture proved in 1997, after 5k years! Also with shorter proofs can be tricky. I studied at University a proof of Stoker Theorem by Poincaré that fits in one page, but, trust me that it is really diabolic.
[+] pfortuny|11 years ago|reply
You probably mean 5C=D years but the logic is the same... :-)
[+] mathattack|11 years ago|reply
He has also criticised the rest of the community for not studying his work in detail, and says most other mathematicians are "simply not qualified" to issue a definitive statement on the proof unless they start from the very basics of his theory.

Math this advanced can be very hard to follow. There are more incentives to do original work than check someone else's, especially when they have drifted far off the mainstream. It takes a special arrogance to say, "You have to come to me" and then be angry when nobody follows.

[+] ObviousScience|11 years ago|reply
> "simply not qualified" to issue a definitive statement on the proof unless they start from the very basics of his theory

How is it arrogant to say people need to study the whole branch, from the beginning, rather than just try to cherry pick a few advanced parts of it, if he really did come up with a substantially new branch?

That sounds more like practicality than arrogance to me.

[+] cromwellian|11 years ago|reply
In other news, engineers refuse to do a code review of a pull request with 1 million lines of code changed.

As has been mentioned elsewhere, the issue may be the "code bomb" nature of the way the paper was published, and if it was released in even smaller chunks, it may have garnered more analysis.

[+] hiou|11 years ago|reply
> This sense of stubbornness, dignity and pride is a part of what gives him the personality necessary to embark on a project like this

It is always interesting to me, as I see it often in the software world, that people expect extraordinary people to behave like ordinary people.

[+] udev|11 years ago|reply
I feel for the guy.

At the same time one can argue that if len ( Proof1 ) < len ( Proof2 ), where Proof1 and Proof2 are of the same theorem, then Proof1 imposes less cost, and hence is more valuable, since it will be easier to teach, use. etc.

[+] trhway|11 years ago|reply
a frequent situation is that the first proof is really long and convoluted. Later, after building up of much of a theory construction blocks around, the proof becomes "simpler" (i.e. simpler combination of well established in that area "blocks") and that is what frequently taught later to students and to "outsiders".

For such first long proofs among the best approaches is to throw it to the pack of hungry wolves ... err ... students and first years PhD-s and let them gnaw on it (with presenting their progress on weekly department seminars - thus saving time to more valuable members of the department and providing the students with real-life experience of a mathematician) Well, at least this is how it was done back then at our University (in Russia :).

[+] wetmore|11 years ago|reply
This would be relevant if there was another proof of the ABC conjecture available.
[+] lambdasgr|11 years ago|reply
He probably should try to use Coq proof assistant. If Coq proves his proof, then mostly like it's correct. Of course, it's easier to say than to do, not a trivial work, and he's the only one who can do it, since he's the only one who can understand the proof.

But if he indeed able to write the entire proof in Coq, then I'm sure at that point, his proof will be much cleaner as well.

Then again, this will never happen.

[+] wetmore|11 years ago|reply
That is like a complete no-go. It took something like 6 years[0] to formalize the proof of Feit-Thomson, one of the first "long" proofs in group theory, and that was done by experts who understood both Coq and the proof. In the time it would take him to write the proof in Coq, dozens of mathematicians could learn the theory and independently verify it.

[0] http://www.msr-inria.fr/news/feit-thomson-proved-in-coq/

[+] tottenhm|11 years ago|reply
> If nobody understands a mathematical proof, does it count?

That depends. If it deals with integers, yes. If it deals with real numbers, no.

[+] whitten|11 years ago|reply
boo. hiss. (and actually a clever reply tottenhm)