
Mathematician's anger over his unread 500-page proof - ca98am79
https://newscientist.com/article/dn26753?cmpid=NLC%7CNSNS%7C2015-0108-GLOBAL
======
DMac87
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](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.

~~~
lotsofmangos
Hey, it's New Scientist -
[http://www.wired.com/images_blogs/beyond_the_beyond/2009/07/...](http://www.wired.com/images_blogs/beyond_the_beyond/2009/07/020709.jpg)

The angry isolated maths geek sells better.

This happened to Scientific American though and I stopped buying it.

On a long enough timeline, it seems all popular science magazines may turn
into Focus.

------
placebo
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
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.

~~~
RBerenguel
If you've gone through paper-publishing, editors ask for pretty large
reductions. A 29 page paper can easily be a 50-60 pages paper with "decent
details" or a 150 pages paper with clear explanations of all details.

~~~
raverbashing
Sure, publish the reduced paper in the journal, then have the "Scenic Guide"
in your webpage or ArXiv, or wherever

Or, I dunno, just create a subreddit or a StackOverflow page for it

~~~
RBerenguel
This assumes infinite time to add all minutiae to LaTeX. Not everyone works
directly on that, almost everyone thinks on paper, develops ideas on paper and
then TeXifies it. In my case, most of the "it is clear that" never made it
into any version of the final file.

~~~
raverbashing
Well, you certainly don't need all the minutiae, but some hand holding,
especially on specific papers that deal with some theorems that might not be
so well know would be helpful.

------
gecko
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.

~~~
jblow
Math is supposed to be about pursuit of truth, not how congenial you are.

~~~
lomnakkus
Like it or not, but math these days is a kind of social activity.

------
hoopism
Don't feel bad. I can't get coworkers to read 2 page approach docs.

~~~
ableal
I not too sure about emails with ten lines.

------
jackmaney
> 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
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.

~~~
Retra
Proof is "that which is convincing to a fair and rational mind." It should
compel a rational actor into the verifiable mitigation of some risk.

This particular fuss is one of the side effects of mathematicians' failing to
properly adopt computers into their process. One of these days we will not
accept a proof unless it is computer verified, and there will be no social
aspect to it.

It should not matter if your proof is 10,000 pages if a computer can follow
it.

~~~
lacker
It is still better to have a clean 1-page proof. There is no direct value for
proving a theorem. Mathematics is nice because it's useful for further
mathematics, useful for real-world applications, and beautiful. A 10,000 page
proof that only a computer can follow is none of these things.

~~~
Retra
It is the second thing. Anyway, the number of pages is arbitrary -- it is a
function of your language and terminology. Not every proof can be simplified,
so surely there exist useful proofs that require 10,000 pages minimum for a
given finite set of terms.

So you are very wrong. You are essentially asserting that the only mathematics
worth doing is easy or already known in some compact form.

~~~
jackmaney
> surely there exist useful proofs that require 10,000 pages minimum

The classification of finite simple groups "consists of tens of thousands of
pages in several hundred journal articles written by about 100 authors,
published mostly between 1955 and 2004."[1]

[1]:
[http://en.wikipedia.org/wiki/Classification_of_finite_simple...](http://en.wikipedia.org/wiki/Classification_of_finite_simple_groups)

~~~
Retra
That is a long proof, yes, but it doesn't support my point. One could easily
imagine a formalization that could compress all that work into a single
sentence. What you can't do is compress _all_ proofs to single-sentence proofs
using a finite number of unique symbols.

------
mietek
_> Grigori Perelman, another mathematician who refused to engage with the
mathematical community_

That’s not quite it.

[http://www.newyorker.com/magazine/2006/08/28/manifold-
destin...](http://www.newyorker.com/magazine/2006/08/28/manifold-destiny)

~~~
wetmore
That article isn't quite it either:
[http://en.wikipedia.org/wiki/Manifold_Destiny#Controversy](http://en.wikipedia.org/wiki/Manifold_Destiny#Controversy)

------
nabla9
Hopefully someday, model checkers and proof assistants can help mathematicians
to put these monster proofs into format that can be verified with computer.

~~~
kodis
Yes, assuming that there remain any proofs which the model checkers and proof
assistants haven't already discovered!

~~~
marcosdumay
The space of proofs is enormous. Model checkers and proof assistants will
probably become user friendly much sooner than they'll get good enough
heuristics to navigate such spaces.

------
dzdt
There is a really good article here :[http://projectwordsworth.com/the-
paradox-of-the-proof/](http://projectwordsworth.com/the-paradox-of-the-
proof/). That is from May 2013; the situation is basically unchanged since.

~~~
dang
[https://news.ycombinator.com/item?id=5685166](https://news.ycombinator.com/item?id=5685166)

------
fibo
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
You probably mean 5C=D years but the logic is the same... :-)

~~~
rando3826
What are C=D years?

~~~
noblethrasher
C and D are the Roman numerals corresponding to 100 and 500 respectively.
Hence, 5C = D.

But, the larger point was that took 500 (5C) rather than 5000 (5K) years to
prove Fermat's Last Theorem.

------
mathattack
_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
> "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.

~~~
mathattack
This requires years of in-depth study without guideposts.

If it's a brand new field, help people along the way. (Write books, explain
the concepts globally, create projects for Phds, etc.)

~~~
ObviousScience
As I recall, he's personally tutoring at least one other mathematician, doing
lectures, etc -- that is, I'm pretty sure he's doing the last two of your
suggestions. Writing books, of course, is a multi-year process in addition to
his other work.

The problem is that they're disqualifying people who study under him in this
manner from verifying his work, which seems like something of a catch-22.

~~~
mathattack
It's tough, but that standard exists for a reason. They want it to be somewhat
arms length. But this means that if you go too far off the beaten path, it's
hard to follow.

~~~
ObviousScience
I agree that the standard exists for a reason; my point was that it's unfair
to characterize him as not trying.

The standard doesn't just make it hard to follow someone who sets out a new
branch in depth - it makes it virtually impossible for an extended period of
time, because it disqualifies anyone he guides. Such a standard requires that
we essentially wait 5+ years (at best) until either high quality maps or
guides trained by the initial guided group exist. (And even then, we'll
probably wait longer.)

It's not exactly fair to paint that fact as a failing on his part to educate
others -- it's a nasty corner case in a generally good academic standard.

------
cromwellian
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
_> 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.

~~~
rando3826
Fuck you (I'm extraordinary)

------
udev
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.

~~~
wetmore
This would be relevant if there was another proof of the ABC conjecture
available.

~~~
udev
just take len ( Proof2 ) = infinity

------
lambdasgr
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
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/](http://www.msr-
inria.fr/news/feit-thomson-proved-in-coq/)

~~~
lambdasgr
"Oh my god, it's such a big project, nobody should do it alone". It's very
obvious, isn't it? 500+ pages of abstract proofs need to be expressed into
some kind of programming language. Not to mention, the worst case is that he
doesn't even know what coq is, or have never used a programming language
(probably just TeX, since he's mathematician) and will take him sometime to
pick it up, and then learn how to express his idea using it, etc ...

Look at the linux kernel we have right now, let's go back to early 90s, and
should we tell Linus not to do it because it's so big? And did it end up Linus
doing it all alone himself?

Coq is certainly not a short term solution, but definitely a valid one if no
one else wants to read his proof, and it's very important for him validate it.

The reason I bring Coq up is that in general, I do feel proving things in
maths is very much like writing a program in a programming language. Maybe the
500+ pages of proof is like a spaghetti code, refactoring might make it more
readable, or more clear, so people are more likely to study it. Or the 500+
pages of proof is very elegantly constructed, just need someone to appreciate
it. Coq can certain help in both cases.

But then is it worth it for him to do it? That's really he's judgement call
based on how important the proof is, what he see he can get out of this, etc.

Remember that line from the article you quoted: "Fun ~enormous!"

~~~
etc
Writing a program is exactly the same thing as proving a mathematical
statement. This is an extremely cool and deep result. Start with the Church-
Turing thesis and go from there.

~~~
sukilot
Except in Math we accept duck-typed functions to prove our results. Advanced
math is not fully rigorous and often has mistakes.

------
sosuke
He will be doing a workshop:

RIMS Joint Research Workshop: On the verification and further development of
inter-universal Teichmuller theory (in Japanese)
[http://www.kurims.kyoto-u.ac.jp/~motizuki/2015-03%20IUTeich%...](http://www.kurims.kyoto-u.ac.jp/~motizuki/2015-03%20IUTeich%20Program%20\(English\).pdf)

March 9-20 2015

------
sramsay
I understand the trouble, but in this case it seems like the trouble might
well be worth it. If the ABC conjecture is proven, the consequences are quite
substantial:

[http://en.wikipedia.org/wiki/Abc_conjecture#Some_consequence...](http://en.wikipedia.org/wiki/Abc_conjecture#Some_consequences)

------
fsakura
On a side note: What is the Latex font name used in this document (Published
by Shinichi Mochizuki)?

[http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verifica...](http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf)

Looks really nice to eye.

~~~
alex-g
Computer Modern
[http://en.wikipedia.org/wiki/Computer_Modern](http://en.wikipedia.org/wiki/Computer_Modern)

------
tottenhm
> 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
boo. hiss. (and actually a clever reply tottenhm)

------
chocolateboy
s/anger/frustration/

------
MrBra
"An overview of Inter-universal Teichmüller Theory and [...] how we can begin
to understand this theory":

[http://www.quora.com/Joseph-Heavner/Posts/An-overview-of-
Int...](http://www.quora.com/Joseph-Heavner/Posts/An-overview-of-Inter-
universal-Teichm%C3%BCller-Theory-and-Shinichi-Mochizukis-proof-of-the-ABC-
Conjecture-along-with-th)

Also, from an anonymous post on 4chan @
[http://boards.4chan.org/sci/thread/6931488/are-you-ready-
for...](http://boards.4chan.org/sci/thread/6931488/are-you-ready-for-
interuniversal-mellin-transform#p6956712) :

"How to understand IUTeich from the bottom up:

\- Algebra (Israel Gelfand)

\- The Method of Coordinates (Israel Gelfand)

\- How to Prove It: A Structured Approach (Daniel Velleman)

\- Kiselev's Geometry - Planimetry and Stereometry

\- Trigonometry (Israel Gelfand)

\- What Is Mathematics? An Elementary Approach to Ideas and Methods (Richard
Courant)

\- A Course of Pure Mathematics (G.H. Hardy)

\- Linear Algebra (Kenneth Hoffman and Ray Kunze)

\- Elementary Differential Equations (William Boyce and Richard DiPrima)

\- Topology (James Munkres)

\- Calculus On Manifolds (Michael Spivak)

\- Principles of Mathematical Analysis (Walter Rudin)

\- Real and Complex Analysis (Walter Rudin)

\- Functional Analysis (Walter Rudin)

\- Partial Differential Equations (Lawrence Evans)

\- Analysis On Manifolds (James Munkres)

\- Abstract Algebra (David Dummit and Richard Foote)

\- Algebraic Topology (Allen Hatcher)

\- Introduction to Smooth Manifolds (John Lee)

\- Foundations of Differentiable Manifolds and Lie Groups - (Frank Warner)

\- Galois Theory (Harold Edwards)

\- Linear Representations of Finite Groups (Jean-Pierre Serre and Leonhard
Scott)

\- A Classical Introduction to Modern Number Theory (Kenneth Ireland and
Michael Rosen)

\- Introduction to Analytic Number Theory (Tom Apostol)

\- Modular Functions and Dirichlet Series in Number Theory (Tom Apostol)

\- Riemannian geometry (Peter Petersen)

\- The Theory of the Riemann Zeta-Function (Edward Charles Titchmarsh)

\- An Introduction to Teichmüller Spaces (Yoichi Imayoshi and Masahiko
Taniguchi)

\- A Course in p-adic Analysis (Alain Robert)

\- Foundations of p-Adic Teichmuller Theory (Shinichi Mochizuki)

\- Mochizuki's papers at [http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-
english.htm...](http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html)
"

------
sshaginyan
Guys. This is my problem with reading white papers. People use notations and
assumptions which I am not familiar with. Hence, I have to go decipher what
people are trying to day. There needs to be a course for math notation. Is
there a book or a online course I can take to familiarize myself with math as
a language.

~~~
eru
They use (slighly) different notions in different parts of mathematics. And
usually, it's not just the notation that's difficult, but the concepts
themselves.

In general, you are best off studying introductory texts to the topics you are
interested. You will pick up the notation.

------
robbrulinski
This man invented bitcoin.

~~~
taternuts
I thought he looked familiar... I definitely remember his photo making the
rounds as "Potential Satoshi"'s when that was the media craze of the week

~~~
bengali3
yup, i recognized the photo as well [http://chartgirl.com/wordpress/wp-
content/uploads/2013/05/SA...](http://chartgirl.com/wordpress/wp-
content/uploads/2013/05/SATOSHI_large.jpg)

~~~
psychometry
Do you people not understand most of that infographic is a joke?

------
MicroBerto
What real-world purpose does this conjecture hold, and why is its proof of any
importance?

~~~
bengali3
see

[http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem](http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem)

[http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Monetar...](http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Monetary_prizes)

~~~
tedunangst
? The Fermat prize money has already been collected. If the real world purpose
of this conjecture is to collect prize money, it won't be that prize.

------
briantakita
I have a similar issue with a philosophy that I'm creating.

There are some barriers. Off the top of my head...

1\. The reader has to care enough to expend time & energy to understand the
concepts

2\. The reader comes in with an Existential Context that may have to be
suspended or expanded. This is tricky because Existence is a fractal of nuance
and it's difficult to know when there's a misunderstanding. Conversations &
isolating examples help.

3\. The reader has to be willing to adopt the new Existential Context while
reading the works.

4\. The more ridged & complex the context, the more the reader has to deny
self.

------
mhomde
I'm kinda amazed that no one has been able to write a proof solving AI yet.
While a human AI is a very daunting task in order to capture "humaness" and
large problem-set it would seem to me that an AI working solely as a domain
expert within maths should be much more feasible.

Shouldn't you be able to build a database of all current proofs and have a
computer be able to cross-reference and extrapolate from that? Sure it would
be far from trivial but it seems doable. Mathematica/Wolfram for instance
should be half way there.

Here's the golden chance for a programmer to win x amount of Nobel prizes! :)

~~~
tsomctl
There are computer generated proofs. They are also completely unreadable, much
less understandable, by humans. In reality, most of mathematics is based on
set theory, which makes it hard for computers to reason about proofs. There is
currently an effort to rebase mathematics on type theory, which would allow
computers to verify and create proofs much more easily. However, basically all
of mathematics has to be reproved using this new foundation. To give an
example, group theory as taught in undergraduate classes depends completely on
sets. A group itself is a set with additional properties. Subgroups are
defined in terms of set intersection and union. Type theory is still in its
infancy, and this stuff is still being figured out. In terms of Mathematica,
it doesn't know jack shit about complicated math theorems. Can it tell you if
a group is solvable?

~~~
mhomde
Yeah, classifying math aspects and creating relations between different proofs
is probably one of the thornier issues I'd guess. It does feel however that
mathematics is a domain where an AI should be able to train itself in some way

