Category Archives: Coffee + chalk

Conference: Association for the Philosophy of Mathematical Practice

There’s a very interesting conference in Paris right now. Such a pity I’m not there. In fact, this post only appears now, because I only just found out about it. Looking forward to reading the papers.

3rd Congress of the Association for the Philosophy of Mathematical Practice (APMP) Paris, Institut Henri Poincaré, 2-4 November 2015


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The height of civilisation: mathematics, comfy chairs and afternoon tea. #Reasons_why_I_like_my_fieldwork


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A mathematician’s nightmare: Lockhart’s lament

I might have posted this already, but here it is again for George! One of my favourite texts written by a mathematician about mathematics and the way in which it is (but ought not be) taught.

Click to access LockhartsLament.pdf

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Group theory in simple English

Are you sick of academese? Or maybe your field really is so hard that the thought of explaining your research to your grandma has never even crossed your mind? Now you have a chance to explain a hard idea (e.g., your research topic) in simple words – in fact, with only the 1,000 most used words! A friend who is a group theorist has just made group theory sound awesomely simple: 

A group is a set of things with a way of putting two things together to get another thing. One type of group is all the ways of moving three things in space to a different place, and in fact if space was “bigger” we could get a bigger group by having more things to move. If we only do some but not all of these moves we can get a smaller group, but sometimes this will only be a little bit smaller than the group that we started with. I am interested in trying to find all of these slightly smaller groups in the situation where we are trying to move ten add six or ten add seven things.

And here is a longer explanation of Hilbert’s Hotel:

The House of Mr Hilbert:
Suppose that you are a person who has a big house where other people can give you money in order to come and live in a room for a short time. (click here to read the rest) …

Try it out here and post the results in the comments!

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Journal: science in culture

Turns out, I’ve missed three interesting conferences on mathematics in culture

Must keep an eye on this in the future!
More events at
AHRC Science in culture theme

Simplistic, but quite to the point…

“I’ve never been female, but I’ve been black all my life and so let me perhaps offer some insight from that perspective. I got to see how the world around me reacted to my expressions of these ambitions. All I can say that is the fact that I wanted to be a scientist, an astrophysicist was, hands-down, the path of most resistance through the forces of society. … Now here I am, I think, one of the most visible scientists in the land. And I look behind me and I say, ‘Where are the others who might have been this?’ And they’re not there. And I wonder: Where is the blood on the tracks that I happened to survive that others did not simply because of the forces of society that prevent it at every turn?”
Those questions are proving to be as difficult to resolve as any in physics.” Astrophysicist Neil deGrasse Tyson

What’s it about women and science?

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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.

Baez is a mathematical physicist who works on an astounding array of topics within  information geometrynetwork 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.


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.

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