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Category: rants

Je (ne) suis (pas) Mochizuki

Published January 12, 2015 by lievenlb

Apologies to Joachim Roncin, the guy who invented the slogan “Je suis Charlie”, for this silly abuse of his logo:

I had hoped the G+ post below of end december would have been the last I had to say on this (non)issue: (btw. embedded G+-post below, not visible in feeds)



A quick recap :

– in august 2012, Shinichi Mochizuki finishes the fourth of his papers on ‘inter-universal Teichmuller theory’ (IUTeich for the aficianados), claiming to contain a proof of the ABC-conjecture.

– in may 2013, Caroline Chen publishes The Paradox of the Proof, summing up the initial reactions of the mathematical world:

“The problem, as many mathematicians were discovering when they flocked to Mochizuki’s website, was that the proof was impossible to read. The first paper, entitled “Inter-universal Teichmuller Theory I: Construction of Hodge Theaters,” starts out by stating that the goal is “to establish an arithmetic version of Teichmuller theory for number fields equipped with an elliptic curve…by applying the theory of semi-graphs of anabelioids, Frobenioids, the etale theta function, and log-shells.”

[quote name=”Caroline Chen”]
This is not just gibberish to the average layman. It was gibberish to the math community as well.
[/quote]

“Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” wrote Ellenberg on his blog.
“It’s very, very weird,” says Columbia University professor Johan de Jong, who works in a related field of mathematics.”

– at the time i found these reactions premature. It often happens that the first version of a proof is not the most elegant or shortest, and i was hoping that Mochizuki would soon come up with a streamlined version, more accessible to people working in arithmetic geometry. I spend a couple of weeks going through “The geometry of Frobenioids 1” and recorded my stumbling progress (being a non-expert) on Google+.

– i was even silly enough to feed almost each and every one of Mochizuki papers to Wordle and paste the resulting Word-clouds into a “Je suis Mochizuki”-support clip. However, in the process I noticed a subtle shift from word-clouds containing established mathematical terms to clouds containing mostly self-defined terms:

.

the situation, early 2015

In recent (comments to) Google+ posts, there seems to be a growing polarisation between believers and non-believers.

If you are a professional mathematician, you know all too well that the verification of a proof is a shared responsability of the author and the mathematical community. We all received a referee report once complaining that a certain proof was ‘unclear’ or even ‘opaque’?

The usual response to this is to rewrite the proof, make it crystal-clear, and resubmit it.

Few people would suggest the referee to spend a couple of years reading up on all their previous papers, and at the same time, complain to the editor that the referee is unqualified to deliver a verdict before (s)he has done so.

Mochizuki is one of these people.

His latest Progress Report reads more like a sectarian newsletter.

There’s no shortage of extremely clever people working in arithmetic geometry. Mochizuki should reach out to them and provide explanations in a language they are used to.

Let me give an example.

As far as i understand it, ‘Frobenioids 1’ is all about a categorification of Arakelov line bundles, not just over one particular number ring, but also over all its extensions, and the corresponding reconstruction result recovering the number ring from this category.

Such a one-line synopsis may help experts to either believe the result on the spot or to construct a counter-example. They do not have to wade through all of the 178 new definitions given in that paper.

Instead, all we are getting are these ‘one-line explanations’:

Is it just me, or is Mochizuki really sticking up his middle finger to the mathematical community.

RIMS is quickly becoming Mochizuki’s Lasserre.

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what have quivers done to students?

Published May 14, 2011 by lievenlb

A few years ago a student entered my office asking suggestions for his master thesis.

“I’m open to any topic as long as it has nothing to do with those silly quivers!”

At that time not the best of opening-lines to address me and, inevitably, the most disastrous teacher-student-conversation-ever followed (also on my part, i’m sorry to say).

This week, Markus Reineke had a similar, though less confrontational, experience. Markus gave a mini-course on ‘moduli spaces of representations’ in our advanced master class. Students loved the way he introduced representation varieties and constructed the space of irreducible representations as a GIT-quotient. In fact, his course was probably the first in that program having an increasing (rather than decreasing) number of students attending throughout the week…

In his third lecture he wanted to illustrate these general constructions and what better concrete example to take than representations of quivers? Result : students’ eyes staring blankly at infinity…

What is it that quivers do to have this effect on students?

Perhaps quiver-representations cause them an information-overload.

Perhaps we should take plenty of time to explain that in going from the quiver (the directed graph) to the path algebra, vertices become idempotents and arrows the remaining generators. These idempotents split a representation space into smaller vertex-spaces, the dimensions of which we collect in a dimension-vector, the big basechange group splits therefore into a product of small vertex-basechanges and the action of this product on an matrix corresponding to an arrow is merely usual conjugation by the big basechange-group, etc. etc. Blatant trivialities to someone breathing quivers, but probably we too had to take plenty of time once to disentangle this information-package…

But then, perhaps they consider quivers and their representations as too-concrete-old-math-stuff, when there’s so much high-profile-fancy-math still left to taste.

When given the option, students prefer you to tell them monstrous-moonshine stories even though they can barely prove simplicity of $A_5$, they want you to give them a short-cut to the Langlands programme but have never had the patience nor the interest to investigate the splitting of primes in quadratic number fields, they want to be taught schemes and their structure sheaves when they still struggle with the notion of a dominant map between varieties…

In short, students often like to run before they can crawl.

Working through the classification of some simple quiver-settings would force their agile feet firmly on the ground. They probably experience this as a waste of time.

Perhaps, it is time to promote slow math…

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wankers

Published April 10, 2008 by lievenlb

You may not have noticed, but I’m in a foul mood for weeks now because of comments and reactions to the last line of the post on Finding Moonshine. I wrote

Du Sautoy is a softy! I’d throw such students out of the window…

and got everyone against me for this (first floor) defenestration threat…

That’s OK! I sometimes post what’s on my mind and if you don’t like it you are free to leave a comment, and, usually I won’t even bother to reply to it. But occasionally, stuff is bottling up un-healthily.

So, I thought it was a good idea to have a prolonged easter-vacation, somewhere in the south of France. The weather, food, rest, drinks, company and all that were just gorgeous

but …

A quick recap. Here’s the relevant section in duSautoy’s book again :

One of my graduate students has just left my office. He’s done some great work over the past three years and is starting to write up his doctorate, but he’s just confessed that he’s not sure that he wants to be a mathematician. I’m feeling quite sobered by this news. My graduate students are like my children. They are the future of the subject. Who’s going to read all the details of my papers if not my mathematical offspring? The subject feels so tribal that anyone who says they want out is almost a threat to everything the tribe stands for.
Anton has been working on a project very close to my current problem. There’s no denying that one can feel quite disillusioned by not finding a way into a problem. Last year one of my post-docs left for the City after attempting to scale this mountain with me. I’d already rescued him from being dragged off to the City once before. But after battling with our problem and seeing it become more and more complex, he felt that he wasn’t really cut out for it.
What is unsettling for me is that they both questioned the importance of what we are doing. They’ve asked that ‘What’s it all for?’ question, and think they’ve seen the Emperor without any clothes.
Anton has questioned whether the problems we are working on are really important. I’ve explained why I think these are fundamental questions about basic objects in nature, but I can see that he isn’t convinced. I feel I am having to defend my whole existence. I’ve arranged for him to join me at a conference in Israel later this month, and I hope that seeing the rest of the tribe enthused and excited about these problems will re-inspire him. It will also show him that people are interested in what he is dedicating his time to.

For starters, I’m getting old so I’m from those long-forgotten days when you had to do a Ph.D. to prove that you could conduct research independently.

A fortiori this meant that the topic of your thesis was your own choice and interest. The role of your Ph.D. advisor was to get you going and, occasionally, to warn you when you were straying too far afield but that was it.

You, and only you, were responsible to get the thesis finished and defended.

Today, the Ph.D. is just another item on the market to be consumed.

Graduate students shop around looking for the advisor having the best sales-pitch, offers the best deal and, if possibly, the best after-phd service aka the promise of an academic career.

Topic and main outline of the proofs are provided by the advisor and an exceptionally good student today means that (s)he proved a few results along the way on her/his own.

University policy and the promotion-rat-race appear to make the Ph.D. more important to the advisor than to the defendent.

Independence of research today means that after your PhD is obtained, you ditch your advisor and try to get into the slipstream of another more powerful guru, having better after-phd service prospects…

For those who stick with their old advisor, the moment of truth comes when they fail to get a renewal of their grant or a permanent position.

At that time one can hear complaints such as : “That persons’ student got ranked ahead of me and I always thought you were better than that person?” or “The better ranked people for the position are all doing that topic instead of ‘ours’, so I guess your topic isn’t so important after all!”. duSautoy’s captures it all in this one key sentence :

They’ve asked that ‘What’s it all for?’ question, and think they’ve seen the Emperor without any clothes.

As if, failing to get a permanent position is the advisors fault, more than yours…

Just for once, try to be honest to yourself : count the number of hours a day your brain-power gets you over 120 IQ. Substract from this the number of hours a day lost surfing the web idly, trying to read unreadable hep-th papers, socializing, kissing asses, socializing, doing fun things with you fellow graduate students, socializing, working on a relation, chatting, texing, emailing insults but softening it all with a closing smily 🙂 , socializing, etc… (you know the daily-drill of a 20-30-something phd-student a lot better than I do)

I’ll be damned if you get a positive outcome. But if you do, I’ll be happy to take you on as a PhD student…

Well, it’s no threat, it’s a promise : the first ex-student who gets me into a ‘why was it all good for?’ discussion will experience first floor defenestration! (provided I’ll get my window open in time)

And, to soften it all, I’ll add the obligatory 🙂

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