How is a theorem born?

A nice short review of Cédric Villani’s book, Birth of A Theorem (by Stephen Muirhead, PhD student at UCL)

http://chalkdustmagazine.com/blog/review-of-birth-of-a-theorem/

 

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Money for nothing, research grants for free

This really is not some value-neutral fascinating social phenomenon such as the currently  en vogue “academic acceleration“: it is a bad use of academic time! Sure, some of the literature discussing “acceleration” is good, but I have a feeling it dance s around the subject a bit too much. Thanks to Jan Blommaert for calling the spade a spade (and apologies for the distasteful crib of Dire Straits lyrics in the title):

After submitting, we heard that a total of 147 applications had been received by the EU. And that the EU will eventually grant 2 – two – projects. In a rough calculation, this means that the chance of success in this funding line is 1,3%; it also means that 98,7% of the applications – 145 of them, to be accurate – will be rejected. And here is the problem.

[M]any millions’ worth of (usually) taxpayers’ money will have been used – wasted – in this massive and mass grantwriting effort. Several hundreds of researchers will have been involved, each spending dozens if not hundreds of their salaried working hours on preparing the application, and hundreds of university administrators will have been involved as well, also spending salaried working hours on the applications. These millions of Euros have not been used in creative and innovative research – they weren’t spent on doing fieldwork, experiments or tests, nor on writing papers and holding presentations in workshops and symposiums. They were spent on – nothing.”

Jan Blommaert, “Rationalizing the unreasonable: there are no good academics in the EU”, 10 June 2015, https://alternative-democracy-research.org/2015/06/10/rationalizing-the-unreasonable-there-are-no-good-academics-in-the-eu/


(Image: Milena Kremakova ®2007)

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The Perils of Maths

This would be funny if it weren’t real. When I read this story I first thought it was a remake of the old joke about Al-Gebra (check out the link for a detailed history of this dangerous terrorist movement):

“At New York’s Kennedy airport today, a person later discovered to be a public school teacher, was arrested trying to board a flight while in possession of a ruler, a protractor, a drafting triangle, a compass, and a calculator.

During a press conference the Attorney General said he believed the man was a member of the notorious al-Gebra movement and the FBI intends to charge him with transporting weapons of math instruction. […]”

(from Weapons of Math Instruction, http://daryld.com/weapons-of-math-instruction/)

And there was another joke, about a postdoc from Iran flying to a conference and working last minute on his paper about “blowing up points on a plain”.

But alas. This week, a real mathematician, Guido Menzio of the University of Pennsylvania, recipient of the 2015 Carlo Alberto Medal for best Italian economist under 40, was questioned and removed from a flight because a fellow passenger thought that his differential equations were “in Arabic”, he was concentrating too hard, and suspiciously avoiding questions, and the flight attendants had to investigate the complaint.

Dr Menzio was brought back with an apology and the 40-minute flight did leave, with a 2 hour delay.

The whole story (written up with some good humour): https://www.washingtonpost.com/news/rampage/wp/2016/05/07/ivy-league-economist-interrogated-for-doing-math-on-american-airlines-flight/

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Serge Lang (1927–2005)

“Why did Bourbaki stop writing?” The answer is that they discovered that Serge Lang is one person.

The story about “this notation sucks” and other interesting stuff about his life and work… http://www.ams.org/notices/200605/fea-lang.pdf

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The disposable academic

An old article in the Economist about what happens after PhD (spoiler: not so good things)… still true.

http://www.economist.com/node/17723223

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Fields medalist Klaus Roth (1925-2015) has left a fortune to health charities

Klaus Roth, Britain’s first Fields Medalist, who died last year at the age of 90, has left over £1.3 mln to the charities Chest, Heart and Stroke Scotland and MacMillan Cancer Support in Inverness, Scotland. How wonderful to read not only about a life full of mathematics, but also that is has been rewarded financially. It is not so often that I read of a successful professional mathematician who has passed away in their old age, and with a substantial fortune.

Roth’s life story is fascinating. One of the many British scientists of German origin, Klaus Friedrich Roth was born in Breslau (today Poland) in 1925 and came to Britain as a 8-year old child in 1933 with his Jewish-German parents. He went to St.Paul’s school in London and then studied mathematics in Cambridge. He was good at maths, but his anxiety during exams was so bad that he graduated with a 3rd class degree and his tutor advised him to “some commercial job with a statistical bias”. So Roth taught maths at school (Gordonstoun, in Scotland) for a year and then was accepted onto a Masters course at UCL. He went on to become a lecturer at UCL after completing his Masters. Times were different. Today he might not have made it to a MMath course so easily, let alone receive a lectureship so soon after. He would have had to move countries many times before having a shot at getting a permanent job somewhere.

Klaus Roth went on to make important contributions to number theory (analytic theory of numbers and more precisely Diophantine approximation) and to live happily with his wife, Dr Melek Khairy, until her death in 2002.  Pity the article in the Scotsman mentions only the lovely story of how they met (classroom romance! she attended his lectures at UCL), and that they did not have children, but omits the fact Dr Khairy was a medical and experimental psychologist at Imperial College London. Plenty of happy marriages in their generation were composed of an academic husband and a homemaker wife, with or without offspring. But when someone, especially a woman, of that generation isn’t a homemaker, this is worth mentioning. In fact I assumed that until I googled her name for no particular reason, only to come across a bunch of paper she had published in the 1950s and 60s.

Another relevant biographical detail is that she died of cancer in 2002. After her death Roth moved to live in a nursing home in Inverness. This may be why he felt so committed to the cause of health and cancer support in particular.

In the book Art in the Life of Mathematicians (edited by Anna Kepes Szemerédi and viewable on google books) there is a chapter written by the editor which is entitled “Conversations with Klaus Roth” (pp. 249-253). Klaus and Melek were avid dancers and loved Latin music and Mahler.

Klaus Roth got the Fields Medal in 1958 for his contribution to the Thue-Siegel theorem. Roth’s theorem proves that any irrational algebraic number has an approximation exponent equal to two (https://en.wikipedia.org/wiki/Thue%E2%80%93Siegel%E2%80%93Roth_theorem).

More about the story: http://www.scotsman.com/news/mathematician-leaves-1m-to-help-sick-patients-in-inverness-1-4111648

 

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Happy Pi day!

Freie Universität Berlin  

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Foggy thoughts

Warning for sociologists: This text is an intuition piece. It is replete with imperfect metaphors. It is the backstage of my thinking about my research. Please don’t cite.]

I have had this intuition for years now, but have not been able to put it in words.

The intuition is based on different “data”. The first layer of data is my subjective experience and affective responses when thinking about or doing mathematics, vs when thinking about or doing sociology*. I know that “own affective experience” is a very, very flawed source of data from a sociological perspective. Yet from a psychology or psychoanalysis perspective it does give some information. Perhaps it gives more information about the individual’s neuroses than about the subject; then, so be it: I’m sure that’s useful as well since I’m a researcher and it is helpful to know more about your own biases. Plus it has been nagging me for several years so I’d better write it down than continue ignoring it. The second layer of data is communications with sociologists vs communication with mathematicians. And the third layer is observations of other sociologists communicating to eath other and doing sociology vs mathematicians communicating to each other or doing mathematics.

So here it goes. I believe there’s something symptomatic about the shift that happens in my head when I think about mathematics. Thinking about maths brings a small surge of pure joy and curiosity. Math questions are like new games. They sound, for lack of a better word, “fun”. There is no anxiety about them, no need to prove myself. There is a curiosity about this “thing” that is entirely separate from me. In comparison, sociology makes me anxious, doubt my abilities, lost. Picture being in a fog. Like that old soviet “hedgehog in the mist” cartoon https://en.m.wikipedia.org/wiki/Hedgehog_in_the_Fog. That’s what it’s like. When a sociology paper has one point to make and  is simple to understand, I find it boring. When it’s complex, I often don’t know where I am and is it bullshit, or am I stupid for not understanding it. With maths, there are terms I don’t understand, but in general maths is a clearer, less scary place.

It may be that I should do maths and not sociology, maybe that’s how my brain works. But I have no proof for such a simplistic view of human intelligence – I simply don’t believe that brains are so easily categorised, and even if they were, how am I to tell that I’m “good at math” more than I am “good at sociology”. Or it may be that the reason for my personal lack of anxiety is thatmaths maths is not my profession but my hobby. Given that I am a person who tends to get anxious about stuff, perhaps maths would cause me anxiety, if I were actually a mathematician? This may be so. But even if it is, I suspect that’s not the only reason. 

I think the crux of the reason is that social science comes with less intrinsic, existential security than maths. I am a human, and I realise that understanding how the complex entity made up by us humans involves constant feedback loops. I can pretend to be objective for a limited time or a particular question, but at the bottom of my pretense I know that it’s false. In contrast, maths is something that can be played with. It’s a dangerous animal with big teeth, but it is honest. Social science is a fluffy cuddlly animal which is however stealthy and able to manipulate your mental state. Playing with social science makes me anxious because there are not only areas that I don’t “yet” know. There are areas that are, by definition, unknowable. This freaks the hell out of me. I can imagine playing at maths with abandon if I had the skills. In fact, with my existing skills, at my level of knowledge, I have played with abandon [for example when struggling with the homeworks when I was following the undergraduate maths course in 2013, even when I could not do them, I still found them fun].

The second layer of data is talking to sociologists vs talking to mathematicians. Oversimplifying grossly, sociologists make me nervous, and mathematicians put me at ease. This is also a limited data source because, since I’m no mathematician, I’ve not had “real” math conversations at a professional level. The only conversations I’ve had have been me asking people to explain some late-school or beginner-undergraduate math to me; or non-professional conversations which are more like the stuff friendship is made of (even more curiously: friendly chats with mathematicians usually end up being about fascinating things, objects, facts or questions. Friendly conversations with sociologists – remember that I am a sociologist, so this complaint is as much about me, as about my other sociology friends, and perhaps it is fully my fault and not theirs! – are much more often conversations full of anxiety, worry, complaint, or gossip).

With this caveat (being a non mathematician, I can’t say what it is really like to be a mathematician talking to mathematicians) , I’ve found my own math conversations with mathematicians relaxing, while I find sociology conversations with sociologists make me nervous and I’m never sure whether and how much I understand (even when I’m the one explaining). And it’s not like math is binary: it is not true that you either understand or not. Quite the contrary, it’s full of intuitions, and for someone like me who knows very little, I often think I grasp the main gist, but can’t express it or remember it for very long. But when I understand, it feels satisfying, even if this understanding is fleeting and would require further work to solidify.  With sociological concepts, I never know really where I stand. To use some mathematical jargon: there is ALWAYS scope for a nasty counterexample; sociology problems are NEVER “well-posed problems”. 

Now that makes sense. What doesn’t really make sense is the following: why is it that mathematicians are so inventive and playful when they explain maths, and why are we sociologists, contrarily, so “up in arms” as if we are defending our baby and not just a piece of text? It’s like they don’t take math seriously. Sociologists talk like it’s super serious. This is my third layer of data, watching people talk shop among themselves. Mathematicians are almost always ready to crack a little joke. They are constantly on the hunt for the most colourful, excessive metaphor to verbalise their train of thought, even if it’s obviously an imperfect metaphor. And somehow, coupled with strict notation, these imperfect metaphors lead to more rigorous explanation than sociologists can achieve. Mathematicians simplify. They draw pictures on the blackboard and speak in simple words while being certain that they won’t be misunderstood by their audience. Sociologists (and here I lump together anthropologists, historians, philosophers, literature theorists) tend to choose the more complicated words. The more boring ones. The more clinical ones. Sociologists tend to talk in long convoluted sentences. We don’t like saying something that’s not true – but the result is that we end up entangling ourselves in our complicated strings of ambiguous thought. I’m being very uncharitable here. I’m speaking about sociologists like a mathematician would. Mathematicians think we should cut the bullshit and get to the point. That we overcomplicate simple things, and create a veil of magic about things that could be expressed simply – and that the fact that we overcomplicate for the very understandable reason that we are aware that we can never be perfectly clear about the social world, doesn’t make overcomplication right. I’ve been told by several mathematicians that they want to hear something that’s both surprising, and true, but often sociology is either boring, or untrue, or both [Granted, maybe mathematicians haven’t read/heard enough good social science , but I think we should take this accusation seriously just in case it’s true].

Part of this third layer of data is text (i.e. sociologists talking to each other in writing, and mathematicians talking to each other in writing, i.e. publications). In publications, this is even more clear. The amount of hilarious gems, jokes and informal expressions in math papers (amidst the hard stuff that I don’t understand because I don’t know the math) makes reading sociology papers, in comparison, like trying to chew dry bread. I say gems and dry bread…but perhaps a better [though of course still imperfect] metaphor is that math papers are unabashed and unadorned, while sociology papers tend to be self-conscious and uptight. Just as mathematicians are more like children and sociologists are more like self-conscious teenagers [metaphor warning!]. Importantly, this does not mean that math papers are imperfect and sociology papers aren’t. Quite the contrary. Math papers never reveal the actual train of thought. They show a cleaned up version of the proof, usually achieved through retracing the proof’s journey in reverse order. All the intuitions have been erased, all the blind alleys undone, all the errors swept under the carpet. A math paper is very much a cleaned up, polished performance. But somehow, despite this despotic form / format, well written math papers manage to sound genuine. To be fair, well written sociology papers are also crafted. But maybe because we sociologists are more verbose – and because we are judged by the quantity of papers by our institutions? – it is rare to find a sociology paper which is written tightly and does not go on about boring stuff in a stilted language for too long. I have read good sociology/anthropology texts, and my math friends tell me they have read plenty of atrociously written math papers. So maybe I’m wrong with this observation. But I’m yet to be convinced about being wrong!

I’m deliberately not going to polish and clean this up just yet. I want to sit and think about whether the main argument makes sense and then get down to expressing it better. And the main argument is that math’s intrinsic, existential security fosters certain behaviours which, compared to the behavious fostered by the social sciences, seem less neurotic and less self-referential. Ultimately, mathematicians play with objects; ultimately, we sociologists play with ourselves.

* I say “sociology” as a shortcut. I don’t mean all of sociology but only the type that I am doing in this project. What I mean is qualitative sociology, extensive case study method, reflexivity, ethnography, similar to what Burawoy does here http://burawoy.berkeley.edu/Methodology/ECM.ST.pdf

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