In her own words: honouring Hanna Neumann

Image: Wikimedia Commons

Hanna Neumann (1914-1971, born Johanna von Caemmerer) was a German-born UK and Australian group theorist. She was the first woman Chair of Pure Mathematics in Australia. She had a fascinaging life story. With her husband Bernhard Neumann, they had five children, four of whom became mathematicians.

A new page on Facebook follows her story told in her own words, like a scrapbook of letters, documents and images – great use of facebook as a platform for telling oral history!

https://www.facebook.com/IHOWNeumann/posts/1103790999712245:0

if you are on Twitter, you can also follow this #NatSciWk, told in her own words (hashtags: #InHerOwnWords #AussieScientist).

The project is created by Women in Science Australia, Australian National Centre for the Public Awareness of Science (CPAS), the NFSA, and The National Museum of Australia.

Talking to crackpots, or how can we communicate science better?

It is widely acknowledged – by scientists at least – that today’s science has become so complex that it is no longer possible to be an encyclopaedic autodidact like it still was in the 17- 19 centuries. While there are still (very, very) few research scientists who have always worked outside academia, none of them are more active than scientists who are at least sometimes working within academia. Today almost all fields in 21st century physics and mathematics are very much community efforts. This does not only have to do with the need for laboratories, but with the sheer complexity of the knowledge accumulated to date even in the most theoretical fields. The stereotypical lone thinker is not only not the norm, but pretty much structurally impossible due to the complexity of what today counts as cutting-edge science.
Thanks to a friend, I came across a wonderful article about science communication written by Sabine Hossenfelder (Frankfurt Institute for Advanced Studies, Germany). She offers a sympathetic, sociological view on what many scientists tend to immediately dismiss as “big theory of everything science crackpots”, from the viewpoint of a professional physicist. 

“Sociologists have long tried and failed to draw a line between science and pseudoscience. In physics, though, that ‘demarcation problem’ is a non-problem, solved by the pragmatic observation that we can reliably tell an outsider when we see one. During a decade of education, we physicists learn more than the tools of the trade; we also learn the walk and talk of the community, shared through countless seminars and conferences, meetings, lectures and papers. After exchanging a few sentences, we can tell if you’re one of us. You can’t fake our community slang any more than you can fake a local accent in a foreign country.”

The problem is, she says, that science enthusiasts (both the “crazy” and the “non-crazy” varieties – though Foucault would tell you that the label “madness” reveals at least as much about the rules and structures of the society which surrounds a person, as about that person’s personality)

“know so little about current research in physics, they aren’t even aware they’re in a foreign country”.

So why do some [men] still persist in trying to offer their grand theories to society – from outside the “not-so-ivory towers” of contemporary universities?

 As for why they are (in Hossenfelder’s sample at least) all men: there is undoubtedly a link between what society thinks a scientist is, and does, a sort of warped folk-theoretical image of lone male geniuses in white lab coats. This is something that researchers of scientific masculity would be better able to analyse.

But I’d turn the question on its head and instead ask: why are we surprised that anybody else is interested in science? As scientists [I always use the word scientist to denote all fields of knowlege in English, like I would in Bulgarian or German, including the humanities] we know only too well that science is one of the most interesting things. So then the difference between “us” and then becomes one of access to the “right” kind of knowledge, which sociologically means access to the “right” kind of knowledge spaces and knowledge institutions. It is important to realise that not all crackpots are crackpots. Some, perhaps many, are curious minds who might have become scientists, had they taken another career track.

This has to do with the different possible purposes of the university: is it a Humboldtian institution aimed at creating public good and educating critical thinkers, or a factory producing skilled workers and commodified knowledge for the market? Of course, neither of these ideological forms exists in a pure way, but German universities are still closer to the form, and American ones to the latter. 

And indeed, as my autodidact friend commented, in Germany they don’t have such “crackpots” and his hypothesis as to why, is that Germany has widely available science libraries and a culture of using them. This should be changing with the advent of online science spaces, but hasn’t. Clearly, cultural change is lagging behind technological change, and there are still people interested in (and obsessed by) science who do not use the multiple and very useful online science forums.

 (Just to make it clear: I’m not at all claiming that German universities are intrinsically better, only that they are more public than market-oriented: they have a whole zoo of other interesting and frustrating problems, such as chronic underfunding, badly functioning internal stratification, inefficient bureaucracy, rigid professorial apparatus, no jobs between postdoc and professor, etc.)

Hossenfelder makes a pertinent observation about ways in which science communication can go wrong: 

“… in the absence of equations, they project literal meanings onto words such as ‘grains’ of space-time or particles ‘popping’ in and out of existence. Science writers should be more careful to point out when we are using metaphors. My clients read way too much into pictures, measuring every angle, scrutinising every colour, counting every dash. Illustrators should be more careful to point out what is relevant information and what is artistic freedom.

Her next point is a much less popular one but possible even more important. In my conversations with mathematicians, I’ve heard many frustrated mathematicians say similar things:

“…journalists are so successful at making physics seem not so complicated that many readers come away with the impression that they can easily do it themselves. How can we blame them for not knowing what it takes if we never tell them?”

So how should we communicate science better? 

First of all, we should communicate science much more. The public deserves to know if not the ins and outs of cutting-edge science, then at least be aware about its existence, and its significance. We must know where to get a map for the “countries” which we may one day (or never) want to visit in person.

Second, the public deserves to know that there are many different valuable types of knowledge, including very abstract or inapplicable fields. This cannot happen while even scientists on the same campus don’t know anything (or don’t even respect) the work done in other university departments.

Third, science must appear real, done by real humans of different genders, colours, classes, ages, voices, faces, talents, interests, family situations, bodily capacities, demeanours, etc. – as it really is, and not as it used to be in some imagined 18th century.

Fourth, science must be presented not simply as a ready product, but as the process and a journey that it is. If the public knew more about the blind alleys, difficulties and disputes along the way, people would not only see science as more real, but also would perhaps appreciate its value more. (Thanks to Marion for adding this point in the comments!) 

Fifth, science must appear fascinating,yet not easy: because it isn’t. It is damn difficult. And you need a group to do it with.

Sixth, and this will counterbalance some of the negative effects of number 4 above: we must get away with the pernicious ideas that difficult = undoable, or that failure = stupidity. In school, kids must learn to learn and to fall many times but never to give up; but also to be smart about finding the right sources to learn from. 

Then there will be more appreciation of science – and perhaps fewer “crackpots” who are curious but lost in the wilderness of unattained knowledge and seeking it in all the wrong places.

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)

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

Girls, math, and bullshit

After 9 years in the UK, I’ve reconciled myself to the realisation that I will always remain a foreigner. When I’m stressed, like when speaking to my bank on the phone today, my spoken expression and listening comprehension skills in English go out of the window. If someone woke me up at night, I’d speak to them in Bulgarian (my native language), but if I were really fast asleep, it would be Russian (my mother’s tongue which I learnt first).  But what is especially hard for a social scientist is that I am unable to overcome some taken-for-granted ideas that I had before coming here, and get used to their opposites which should be obvious to me. This evening I’m reminded of one: women and maths. This stuff is doing my head in. Each time I read about it, I get a headache. You know that peculiar blackout feeling when you hear something that is either blatantly, in-your-face, unjust or untrue, or something whose premises are so flawed that it’s not even wrong. I get that each time I encounter the obvious, common knowledge that women and math don’t mix. I just found an article about Shirley Conran’s new project aiming to make maths attractive to girls by convincing them that it will help them manage their personal finances. The article had the awesome title “Math is a feminist issue”, and it linked to what must be a very interesting and useful new report on women and the fear of mathematics. I’m sure it’s a very useful report. I must read it for my research. But I am stuck with the pdf like a horse in front of a river. I can’t read it because just reading the chapter titles makes me wince:

“1 Why maths and maths ability for women matter 13

2 Why confidence about maths ability matters 19

3 How do we know that women fear maths? 25

4 Why is maths perceived to be innately male? 29

5 Being female 37

6 Women’s education in history and the place of maths within it 47

7 Attacking the Maths Myth that drives the Fear Factor”

Clearly, I must have grown up with a different Myth. I grew up with the conviction, supported by empirical observations, that girls are better at all subjects. I don’t know why. And because I never had a reason to question this belief at the time I was at school or university, now I’m finding it really hard to accept that things are so obviously not the case. I don’t even know if my belief was justified about Bulgaria in general, or about Bulgarian “elite” primary and secondary schools. I may not be. Maybe I grew up in a bubble (a bubble in which all but one of my maths teachers were women, like almost all my other teachers; and in which schoolkids who were good at maths were equally likely to be girls or boys, and those who weren’t were more likely to be boys).

But I like having grown up in a bubble. I like the fact that the obviousness of “girls don’t like math, girls are no good at math” pisses me off. The really painful thing is that with each new item of information on the “women and maths” subject, doubt and desperation trickle in. I fear the thought that, if I had heard of this at a younger age, this belief might have turned into a self-fulfilling prophecy, and would have made me worse at maths – and worse at believing in my own capabilities, talents and worth. I hate the thought that there are young people out there growing up right now who entertain the freaking insane belief that interest and talent in various parts of human culture may have anything to do with their genitals.

Even less rationally, reading stuff which generalises a whole gender into one box according to a negative criterion, such as lack of ability or fear, makes me uncontrollably angry. When you, as a woman, read something like this, you just can’t win. If you happen to be bad at maths or hate it, well, there, there, little darling, we said it first, women suck at math. If you happen to be good at maths or like it, then you are not a woman, you’re an honorary man. &%£$@£$&?{}$£% Rage is not a good companion to research. Imagine, my research isn’t even about gender, actually, it’s about all mathematicians regardless of their gender. Imagine how angry I’d be if I were actually studying gender.

Incidentally, most of the female professional mathematicians I have talked to say that they were never aware of a negative gender stereotype in relation to maths when they were little. When they did realise it (often upon arriving to university), it was not a pleasant realisation.Some say that they were aware, but consciously rebelled or ignored it.

Perhaps we ought to not just combat the stereotype, but also shield from it those young kids who are lucky to don’t know about it yet…at least until they are old enough to be brave and rebellious rather than conformist?

P.S. Upon rereading, this sounds like an unusually personal and non-rational research-related blogpost. Unprofessional pubic expressions of unpolished thoughts, tut-tut. But it will have not been in vain, if it helps me at least read that report which, I’m sure, has lots of interesting and depressing data…

My pet hate: I wish people stopped opposing “math” to “creativity”!

What a bad article to read before going to bed at 1am. Now I won’t sleep, grr. No, the article itself isn’t bad, it is even making a valid point: “Creativity just as important as math and science”. What made me angry, you ask? 

The argument is always “science and math are essential, especially in today’s job market”. I agree, they are essential on the job market. Just as literacy, the ability to retell, interpret, improvise, communicate, the knowledge of history, cultures and languages. Many things are important “on today’s job market”. But I do wish people asked themselves more often what is essential for the development of a person, for the wellbeing of society, and for the enjoyment of life. Perhaps then – to come back to our “not enough people do math” problem which is only a symptom of  a bigger problem in the way we treat learning – more people would enjoy playing with maths. But Peter Lockhart said it better. I am going to shamelessly quote the first 1.5 pages from his amazing essay just to make sure that more people read it. Please, read it, whether you have always liked, hated, or been undecided about mathematics. I will check in my stats how many people click on the link.

Amusician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where wetake out our staff paper, our teacher puts some notes on the board, and we copy them ortranspose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. “I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.”

In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one. “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.” 

Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream. “Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”

Meanwhile, on the other side of town, a painter has just awakened from a similar nightmare…

I was surprised to find myself in a regular school classroom— no easels, no tubes of paint.”Oh we don’t actually apply paint until high school,” I was told by the students. “In seventh grade we mostly study colors and applicators.” They showed me a worksheet. On one side were swatches of color with blank spaces next to them. They were told to write in the names. “I like painting,” one of them remarked, “they tell me what to do and I do it. It’s easy!”

After class I spoke with the teacher. “So your students don’t actually do any painting?” I asked. “Well, next year they take Pre-Paint-by-Numbers. That prepares them for the main Paint-by-Numbers sequence in high school. So they’ll get to use what they’ve learned here and apply it to real-life painting situations— dipping the brush into paint, wiping it off, stuff like that.
Of course we track our students by ability. The really excellent painters— the ones who know their colors and brushes backwards and forwards— they get to the actual painting a little sooner; and some of them even take the Advanced Placement classes for college credit. But mostly we’re just trying to give these kids a good foundation in what painting is all about, so when they get out there in the real world and paint their kitchen they don’t make a total mess of it.”

“Um, these high school classes you mentioned…”

“You mean Paint-by-Numbers? We’re seeing much higher enrollments lately. I think it’s mostly coming from parents wanting to make sure their kid gets into a good college. Nothing looks better than Advanced Paint-by-Numbers on a high school transcript.”

“Why do colleges care if you can fill in numbered regions with the corresponding color?”

“Oh, well, you know, it shows clear-headed logical thinking. And of course if a student is planning to major in one of the visual sciences, like fashion or interior decorating, then it’s really a good idea to get your painting requirements out of the way in high school.”

“I see. And when do students get to paint freely, on a blank canvas?”

“You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I’ve got a degree in Painting myself, but I’ve never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board.”

***

Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

…

An important article by Paul Mason at The Guardian today:

Private schools know how to game elite universities – state-educated kids don’t have this privilege

The argument Mason makes is that school graduates in the UK make uninformed choices about university courses. The problem isn’t necessarily scarce information, quite the contrary:

“Other opinions are available of course – and that’s the problem. This year, a quarter of a million 16-year-olds will make their A-level choices relying on hearsay, myth and information that is outdated or uncheckable. Those choices will shape their options when it comes to university – and the courses they apply for will then shape their chances of getting in.”<\blockquote>
…

“Why should this matter to the majority of young people, who do not aspire to go to an elite university? And to the rest of society? First, because it is creating needless inequality of opportunity and is just the most obvious example of how poor access to informal knowledge penalises state school kids. Second, because in an economy set to be dominated by information and technology, those 15,000 people who can attempt further maths each year are the equivalent of Aztec gold for the conquistadores. Their intelligence will be the raw material of the third industrial revolution.

There is no reason – other than maintaining privilege – to avoid presenting subject and course choices clearly, logically and transparently. When the system fails bright kids from non-privileged backgrounds, we all lose.”<\blockquote>

Some possible solutions perhaps:

– Better (not necessarily more) online information accessible to all students; a publicly available depository of previous student experiences and statistics on post-A-level trajectories;

– The communication between universities and schools needs to be improved: on the one hand, both universities and schools complain that the other side does not understand their difficulties and poses unreasonable demands; yet on the other hand, both sides complain that the other side is not willing to engage more fully in communication. Where is the truth? Universities have outreach programmes, plenty of information on their websites – but perhaps not the right kind?
The STEM ambassadors initiative is great, but (a) there is a need for ambassadors not only from “STEM” jobs, and also, howeevr successful they are, it’s a charity and they aren’t reaching all the schoolchildren.

– Why is it that universities aren’t more involved in designing, redesigning, updating, A-level syllabuses and monitoring their teaching at 6th form? Is it because university staff are too busy, don’t care, because they have no clue about earlier pedagogy? Or because schools don’t want universities messing into school territory and for example shifting curricula too much towards high-achievers? All viable concerns, but surely a better balance can be found, with more productive involvement and less disruptive meddling of universities into schools! I have heard colleagues involved in admissions sigh that schools just don’t always teach the kids what they really need to know – not just for the entrance exam, but more importantly, for being able to thrive in university. Thinking skills, thinking outside the box, creative and disciplined and active learning… if this really is true, then it’s horrible for both schools and universities in the UK and something has to be done.

– It seems to me that University outreach initiatives such as “Widening Participation” need to be far better developed and embedded into university work. At present, university staff mostly don’t participate – and understandably so, since it is an additional task on top of their already high workloads, and there are already penalties for spending too much time on supervising students and preparing lecture materials if you neglect research and especially publishing. At the same time, there are increasing amounts of administration to be done (as all long-serving academics will confirm, the advent of computers has NOT decreased the amount of paperwork). There is a fundamental imbalance in the way staff are assessed and appraised for job purposes. For example teaching and other “good academic citizenship” behaviour such as administrative work or pastoral care are insufficiently rewarded, whilst research is rewarded – but only through publications in “4 or 5-star journals” (yes, that’s the actual term, I’m not making it up). In this context, when academics are already stretched to do more research, and cope with teaching and admin as much as they can, and most of them routinely work overtime to accomplish their research projects and/or plan lecturers, and/or finish marking – how can we even expect anyone but the young and idealistic academics (the ones most in need of a career boost) to even consider being involved in communication with schools?

– Would it make sense to bring back grammar schools? From the few grammar schools that still exist, it seems that it is a good model… here I must let experts talk, because I know precious little about the UK secondary education system and my impression is largely anecdotal.

Why there are so few women in tech…

Why are there so few women in technical professions? Are women bad at programming? Do they keep rejecting programming jobs? Do they fail to fit into the culture of tech companies? Actually, all of these reasons aren’t true.

Here’s a nice long (and depressing) article (don’t forget to read the comments, as well as this discussion thread)…

http://valleywag.gawker.com/this-is-why-there-arent-enough-women-in-tech-1221929631

 

What do women think? (some quotes from the article on valeeywag)

“They didn’t want us. Too many still don’t. –spence900“

And…

“I no longer touch code because I couldn’t deal with the constant dismissing and undermining of even my most basic work by the “brogramming” gulag I worked for. And that started even when I was in school. I was the ONLY female in my university’s mid-level programming courses and even though I worked to hard to always be in the top 95% of the curve, if a pasty white guy with thin-rimmed glasses and a tee-shirt with an “ironic” phrase doubted me, I was wrong.

I spent my life around midWestern dudes and high school jocks, but there is no misogyny like silicon valley nerd misogyny –whoa-disillusionment“

And more…

“Dude, I have a Masters in CS, programming certifications, experience in mobile dev, and years of experience. I am also a woman, laid off in January. I have yet to find a job. I’m either too “senior” or “not senior enough.” Sight unseen I’m rejected many times.

I am not entry level so I can’t be one of the token hires to show that a company supports women in tech […]

Somehow women in tech may get the mascot entry level coding jobs, maybe, but there ARE some of us with experience that hit a block as soon as we are out of entry level and remain in tech, not switching to project management or marketing.

I’m quite often the finalist in interviews, never being hired. And their teams remain all dudes. I’m told I’m too senior when I apply down the experience chain. I still do it, because I need the regular gig. The truth is, most places where I live won’t hire women beyond entry level in development groups and if you are beyond that with experience managing dev groups even, with a Master’s degree even, forget it. Perhaps someone who does some html work or marketing, but not in the tech group. I’ll hit the nail on the head perhaps sooner or later, but it’s very ironic they like to say they are begging for talent. But they have to have a certain look. And not be over 35.

I was told to get more education, experience, etc, got it and even then, my progress up the chain had at least a 5-7 year lag to any dude with less education and experience. Why did I get a Master’s in CS, because I had to to prove things. Why did I get certifications? Why do I go the extra mile outside of work? Because on the face of it, a dude is given credit for just looking like a dude in tech. Even with these things, I just may be considered on par with a dude without them most of the time.

Not all places are sexist, not all upper leadership is sexist, but the places that aren’t are so few. […]

Fuck the whole tech business for telling Congress they cannot find talent so give them more H1-Bs. There are people like me out there and most of us are just not the ingenue anymore. I have to say, dudes are always surprised when, after forties, mid-forties, unless they are directors or VPs, they are not hot on the market anymore. It happens to dudes too, and often the most Libertarians of them are shocked when at fifty, they are laid off for just being old. It happened to a dude I know recently. That kind of thing they thought only happened to the unqualified or maybe whiny women or something […]

I do think it’s a load of crap when you see support for getting girls in tech, when there are women in tech. It’s the same crap – as long as you are entry level and no competition for jobs, then it’s okay. That is the case everywhere from Google to Etsy to most hip companies. Seriously, Etsy brags on bringing in da womenz to code. At entry level. Where older dudes can schoolz the womenz on being developers, women far away from threatening the dudes who have real power in their tech. Meanwhile, they had and have higher level jobs in tech that they claim they cannot get women to take – they interview and no woman they like will work for Etsy, so they HAVE to fill all with men. At some point, they just gave up (they wrote this to the public) and put effort into only entry level bringing the women in. I guess bringing them in at a higher level would be quite upsetting. Or just one into tech management. MMMM, how’s about hiring just ONE woman as a tech director from the outside or something, Etsy? Meanwhile they get pats on the back for having a caste system, essentially, institutionally put in place.

Ironically, it can be the older “conservative” businesses where it is less sexist and ageist. Ironically I tell you it’s many times the men older than 45 that have given me my best jobs – those chubby old graying dudes, not the biker, 10% body fat dudes. The hipsters, they are actually more sexist as a group. So you can take that as you will. –ReadyReady“

Maths at your fingertips (rambly post, spuriously connected to its title)

This will be a short rambly post because I have low-grade fever and am working from home. First, here is some awesome mathematical eye candy on John Baez’s website.

http://www.math.ucr.edu/home/baez/

Baez is a mathematical physicist who works on an astounding array of topics within  information geometry, network theory, and the Azimuth Project (which is one of my favourite links on the Links page) and is interested in global ecology.

The beauty of research is that you can do it anywhere. Even from home when you’re ill. Unless you are too ill to think, of course.  When I’m too ill to think, I sleep, drink tea or play silly games like 2048 for hours on end. Warning: if you tend to get addicted to simple computer games, don’t click on that link. It could ruin your week and awaken your nintendo thumb (a type of repetitive strain injury with which you will be intimately familiar, if you are a simple-games addict, unlike my doctors back in 1998). But aside from the perils of 2048,  for the stage that I’m at in this project, it really helps to have an internet connection – because I’m looking up various mathematical websites at the moment. But even if I didn’t have a laptop or the internet, I could do mathematics (with the caveat explained in the next paragraph). In fact, I would probably learn more if I didn’t have Internet – because I’d spend no time on blogging and 2048 – and so would you, because you would read a proper book instead of the rough prose of blog posts. The same applies to sociological research – later once I have more “data” to analyse I won’t need the Internet at all, just a laptop and a quiet place (or even just a notebook and a pen). So yeah, research is awesome, provided the topic fascinates you. Otherwise it’s a drag to be on your own and have to do it..and this is where 2048 begins to look more and more appealing.

You may have noticed that I’m having trouble categorising my posts – most are categorised within several categories which kind of defies the purpose. Perhaps I need to learn more about category theory. Perhaps I need to learn more anyway because it sounds fascinating and also like something very linked to philosophy (which is one of my main points of interest in mathematics).  By the way, identifying my own mathematical interests feels embarrassing since I don’t know much mathematics YET, but I have decided not to be put off by my temporary stupidity and instead see things like Kenyan runners who “think you are as good as your greatest day, even if you have not had it yet.“. 

I hope to return to more sensible blog posts soon – I have one in mind about the Q-step initiative and about a fascinating thing that happened in my local Maths department last week (it was visited by artists and I had the most fun days of my fieldwork so far!). Three… two… one… 2048.

Work and careers in mathematics: What exactly do I want to know?

In this post I try to summarise the main questions of my study.

This is a three-year study (official summary here) about the working lives and career trajectories of scientists in the mathematical and computer sciences in the UK and Germany.  My main focus is on the early stages of career  – whether in academia, industry, or elsewhere – and how career and life intersect in the “working life” of a mathematician. Think of it as an extended CV focusing not only on key events in the working biography but also including key life events (such as moving countries, leaning a language, having children) and all the decision making and chance involved in the actual unfolding of your life which remains hidden between the lines of the official CV.

I’m looking to interview mathematicians/computer scientists with a range of experiences – postdocs, before and soon after Habilitation, PhD students or people who started a PhD and dropped out, established mathematicians with longer careers (research and/or teaching, academia or industry…), researchers who are unemployed, on career break or new career direction, on parental leave, international and native students etc. I’m also interested in international trajectories, gender-related issues, family, health, “life outside mathematics”, and any other important aspects of a biography.

In order to see the bigger picture and get a better sense of historical change in how careers unfold, the study also looks at the biographies of more established or retired scientists, as well as younger university students in maths and related subjects and their career plans (whether they consider a future career in research or not). A comprehensive study comparing generations of mathematicians would be great…maybe that will be my next project!

Here are the initial research questions – which become more detailed as the research progresses. (I say “mathematician” for short, but I mean “researcher in mathematics or computer science”):

The life and “career trajectory” of a mathematician: What careers and livelihoods do people have in mathematics? How are actual lives different from common stereotypes? How is one’s working life shaped by working as a mathematician? What would have been different, if he or she weren’t a mathematician? What does the lifecourse of a mathematician look like – what key stages, events, breaks, dis/continuities does it have?

The work of a mathematician: What is it that mathematicians do? How do they work with research objects which are immaterial, yet real at the same time? What is the social, political and material “scaffolding” that makes their work possible: institutions, social relations, epistemic communities and cultures, daily routines, employment arrangements, etc.? Where do proofs come from? What is the role of different technologies, such as computers, blackboards or coffee machines? What technologies, tricks, tacit rules, institutional arrangements are needed for the creation, maintenance and transmission of mathematical knowledge?

Who is a mathematician: What does it mean to be a mathematician? Why do mathematicians do maths, and what else do they (have to, enjoy to) do? How do others decide that you are ‘fit’ to be a mathematician? How, in practice, does one get to become a mathematician? How does one choose in what bit of mathematics to specialise? How does one learn to speak like a mathematician? I want to know in what terms mathematicians talk about their own lives, how they make sense of their profession

Mathematical institutions and social environment: But I’m not only concerned with individuals. A sociologist cannot understand mathematical lives separated from the institutions that mathematicians ‘inhabit’ (in sociology slang, “institutions” here refers to the network of visible and invisible rules, spaces and traditions which enable humans to practice mathematics: such as universities, funding bodies, journals, conferences, invisible “institutions” such as mathematical notation, fields of mathematics and so on…)  How do these institutions function, according to what rules, and who makes up those rules? It is all very good to say that mathematics is the ideal objective science, or at least as close to objective as any field of inquiry can be. But even so, the living, breathing and thinking mathematicians that create and use and explain this beautiful and objective science also inhabit the same real imperfect world as everyone else.  Mathematicians also negotiate ‘mundane’ things such as finding jobs, writing down the stuff they have thought about, going to work, arranging childcare and so on. How do they square these two worlds, of ‘mathematics’ and of ‘everyday life’, and how do they translate between them? More importantly, how do they themselves see these two (or maybe just one?) world?

Related to the last question, in what direction is the mathematical world changing and how have political and economic realities in the UK and Germany (and Europe and the world) affected it? In particular, I want to know to what extent the overall trend for insecure academic jobs and complex career paths spanning multiple countries is affecting the men and women who do research in the mathematical or computing sciences.

Germany and the UK
The fieldwork will be conducted in the UK and in Germany and will also look at the different pathways in which marketisation and internationalisation of science (pure and applied mathematics in particular) is happening in both countries. Germany and the UK are the two largest mathematics research communities within the EU, and leading partners – and competitors – for each other. Within UK’s collaborative mathematics research portfolio, collaborations with Germany are the second most significant ones after those with the US (followed by China, France and India); for Germany, the situation is the same. The relative average impact of papers co-authored by UK and German researchers is higher than that of UK-authored papers, or of UK collaborative papers with researchers from other countries; the same holds true from a German standpoint. The two countries are part of a global mathematics community and participate in a lively exchange of mathematical ideas and of mathematicians, but their different education and science policy trajectories mean that German and British mathematicians get exposed to very different institutional environments. There are complex interactions and permeable boundaries between the German and UK ‘mathematical worlds’ in terms of job opportunities, research funding, conferences, collaboration structures (interestingly, especially at early-career level, these are mostly one-directional: German graduates into UK jobs). From both a German and a British perspective, comparisons between Europe’s two largest and most prolific national mathematical communities are useful. In Germany, the neoliberal narrative has only more recently coexisted with that of university as a public good. In fact, marketisation is sometimes seen as a superior alternative and as a panacea to the problems created by the hierarchical rigidity, administrative complexity, and inefficiency of traditional German universities. From a German perspective in particular, it is interesting to study the bad as well as the good effects of marketisation on academic work, labour and careers in Britain.

“Definition”

For now, I define “mathematician or computer scientist” narrowly: as a scientist working professionally in the mathematical and computing sciences (regardless of whether it is pure, applied, both, or somewhere in between, or whether the mathematician rejects the pure/applied divide). S/he is usually attached to a university or research institute. S/he may be, or have been until recently, involved in teaching and/or writing and/or research. At the moment I focus mainly on mathematicians who do research, although it is interesting to see alternative pathways, e.g. mathematicians who have wanted to do research, and have ended up branching out in other activities, e.g. specialising in school teaching.

 

Basic premises

I’m starting this project with two very simple conjectures.

First, working in mathematics is just like any other job. It can be described in terms such as work, employment, career, labour, profession, livelihood, labour market, or vocation. It involves things that one does every day, and things one must (or must not) do, in order to qualify as a mathematician. It combines aspects of intellectual, physical, and emotional labour. It can involve mundane tasks, creativity, management, reading, writing, public speaking, publishing, editing, advising younger people or one’s peers, thinking, discussing, presenting ideas, experiments (physical or imagined), the need to organise people, things and ideas, travel, job-hunting, and much more. Mathematical research and teaching is organised into a sectoral ‘labour market’ with its own sub-labour markets – or at least can be analysed in labour market terms or as a “subsector” of science, as is common nowadays. The mathematical community has its internal formal and informal networks. It has rules and freedoms, and usually-taken-for-granted truths (or conventions, as the French sociologists Boltanski and Thevenot would put it). A sociologist can discover trends and compare mathematical (working) lives to ones in other careers and jobs.

Second, however, working in mathematics is different from all other jobs, in and out of science. It has specifics which make it special and distinct. Working as a mathematician affects your career, your life course, your options and choices, your difficulties, your social and spatial mobility, potential circles of friends or partners, the meaning you attach to work, the reasons and motivations that urge you to work, and the variety of typical and unique life-paths that you are likely to experience throughout the span of your working life. In other words, being a mathematician shapes your identity and your biography in a unique way, as well as just providing you with something to do and putting bread on the table (how easy it is to earn one’s livelihood as a mathematician, man or woman, is a related question).

Nonmathematician studying mathematicians: an “outsider” researcher

I am not a mathematician which makes me an outsider to the world of mathematics.

I studied mathematics until the end of high school and very much enjoyed it – but the only career option I could think of using a mathematics entrance exam was economics, which I didn’t like at the time. The thought of becoming a mathematician just hadn’t crossed my mind. Perhaps this was because I come from a relatively small, industrial Bulgarian city, and I didn’t know any scientists or researcher in real life  Or perhaps I just wasn’t that good at mathematics. Anyway, now I am convinced it is very important for school students to be exposed to as many career ideas as possible, because who knows how many better choices could be made by young people after school.

I went to university to study European Studies and later Sociology which had no mathematics courses (apart from very little applied statistics in 2001-2). But I find mathematics fascinating and have often wondered what it would have been like to study mathematics in university and this project gave me an opportunity to find out more. This past academic year I attended lectures and seminars with the first year cohort of mathematics students in a British university, in order to understand a little better what it is that mathematicians do. I also read anything I can understand, and talk to many professional mathematicians as often as I can.

And, as the long-term partner of a former PhD student and current academic mathematician, and a postdoctoral researcher myself, I guess I am also a “participant observer” or “insider” in a certain limited sense.

Long story short, although I’m very much a non-mathematician, I can hopefully understand something of what makes mathematicians love their job.