Banach spaces (and other limericks)

If M’s a complete metric space,
And non-empty, it’s always the case,
If f’s a contraction,
Then under its action,
Exactly one point stays in place!

A mathematician confided
That a Moebius* strip is one sided
And you get quite a laugh
When you cut it in half:
In stays in one piece when divided.

The topologist’s child was quite hyper
Till she wore a Moebius diaper.
The mess on the inside
Was thus on the outside:
It was easy for someone to wipe her.

(From: Wikipedia – mathematical joke)

Hitler learns topology

I felt like this learning first year Analysis…

Why are mathematical research jobs stressful?

Here is an article in the Guardian about the stresses of academic research, written by a postdoc in pure mathematics. Having spoken to quite a few early career mathematicians, I think it’s pretty spot on… Has that been your experience?

I am a postdoc pure mathematician. I’m paid to do something I love. I don’t have to be in at nine, and I don’t have to wear a tie. Often I don’t have to be in at all, and on these occasions I don’t have to wear anything. No pushy managers above me, no responsibility for juniors below me. But I drink too much, haven’t had a good night’s sleep since last year and my diaries refer regularly to depression since I began myPhD. Why?

You and your research

One of the best things I have ever read about research. An honest, straight-forward, down-to-earth and inspiring text.

Richard Hamming

“You and Your Research”

Transcription of the
Bell Communications Research Colloquium Seminar
7 March 1986

It’s a pleasure to be here. I doubt if I can live up to the Introduction. The title of my talk is, “You and Your Research.” It is not about managing research, it is about how you individually do your research. I could give a talk on the other subject – but it’s not, it’s about you. I’m not talking about ordinary run-of-the-mill research; I’m talking about great research. And for the sake of describing great research I’ll occasionally say Nobel-Prize type of work. It doesn’t have to gain the Nobel Prize, but I mean those kinds of things which we perceive are significant things. Relativity, if you want, Shannon’s information theory, any number of outstanding theories – that’s the kind of thing I’m talking about.

Now, how did I come to do this study? …

Read the rest here  (courtesy Gabriel Robins, professor of computer science at Virginia University)


2048 algorithm

Lo and behold, someone has actually written an algorithm for winning 2048. Where did I find it? Well, of course, on stackoverflow.

If you’re sick of 2048, try this spoof by Jenny Peng:

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.

Links to maths

I’ve updated the Links page - check it out, it’s getting huge! My head is spinning from so many maths initiatives. Give me suggestions for more links, please!

Why do we (still) need to know more about female scientists?

Seemingly progressive posts such as “Eight women scientists that you need to know about” make my blood boil with anger. True, I had only heard about four of these eight scientists. You should read the article, it’s short, informative, and thought-provoking, and has inspiring historic portraits of the scientists at work – pictures which would have made at least one male relative of theirs mutter “she should be in the kitchen, not in the lab”. Their life histories made for an enjoyable and useful read on a Monday morning (and yes, that counted as research reading, aren’t I lucky). But this article was also a grim reminder of the fact that feminism has frozen in the first mile of a double marathon towards gender equality.

Why do we need to know more about female scientists?

Because of articles like this – how about some more female scientists? Are there really only eight?! And how about trying to read an article about the 800 or more male scientists who have made awesome discoveries that we also need to know about – I’m sure there’s lots that we don’t know about them? But no, that would not make for a nice news item or facebook trending post take because it would take longer than a Monday morning coffee break to read.

Because women who succeed in doing what they like and are good at (scientists or others) are still newsworthy. WTF?! Surely, not the ones who excel in anything related to the home, food or childrearing, that’s not news – women are just naturally good at it, haha.

Because becoming a scientist is a hard thing, and being a woman unfortunately continues to create more invisible barriers to a successful practicing of science than being a man does.

Because, if you take ten minutes to read their bios on Wikipedia, you will notice that most of them were at some point excluded, denied recognition, or discriminated against on the basis of being women. Nothing to do with their research, that was OK – in fact, it was good enough for others to gain credit for it sometimes. WTF?!

Because yesterday, when I heard that some friends have recently had a baby, I instinctively asked “girl or boy?” even though I can’t think of even one reason why the answer to that question should make a difference. But of course it will. (Un)helpful statistics, stereotypes, expectations, images and key words describing the likely life course, appearance, occupation, interests and possible futures open to persons of the male and female genders spring to mind immediately upon determining the sex of a newborn. Will people still care about that when that baby is an adult and wants, for example, to work as an astronomer? I hope not, but I’m afraid that they will.

Oh, just one thing <clambers onto soap box again>. Wikipedia has a special entry on “Female scientists before the 21st Century”. It seems to suggest that it has become easy enough – or at least relatively easier – for women to be scientists in the past couple of decades than it was previously. And it has. But it has not become equally easy to men, and it has not become sufficiently easy. 

And then, intersectionality. Combine class, race, wealth, disability, sexual orientation, and a bunch of other things that also mess up with our futures, making sure that the most talented, hard-working or brilliant people don’t  have a better chance.

We’re still far from a time when a person’s gender will not be the first thing we notice about them. Yes, there are numerous exceptions – but the point is, we have gone far in promoting exceptions, but we have not yet managed to create a world that supports a regularity, a world in which the particular set of sexual organs, secondary sexual characteristics and learned behaviours have no bearing to how well someone does their job.

Now, off that soapbox and back to my research desk before I evaporate in a puff of angry steam.


P.S. Maria Mitchell – first American professional astronomer who was female. And another reason why Quakers are cool.

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

What is this study trying to find out? Perhaps I should spell it out in a separate post. This post basically fits into almost all categories on this blog… but that’s ok, I suppose it is because it’s actually a summary of the blog rationale.

So. (said with a German accent).

What careers and livelihoods do people have in mathematics? How are working lives shaped by working as a mathematician? What would have been different, if they weren’t mathematicians? What does it mean to be a mathematician? What does the lifecourse of a mathematician look like? What key stages, events, breaks, dis/continuities does it have? 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. Who is a mathematician?

But I’m not only concerned with individuals. A sociologist cannot understand mathematical lives separated from the institutions that mathematicians ‘inhabit’. 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 and breathing and thinking mathematicians that create and use and explain mathematics also inhabit the same real imperfect world as everyone else; they also negotiate ‘mundane’ things such as finding jobs and writing down the stuff they have thought about; 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?

Outsider researcher

As someone who is not a mathematician, I am an outsider to the world of mathematics. A lot has been written about insider and outsider sociological research, so I won’t expand on this here just yet. I will, later. But I’ll also make sure I discuss this with others, some of whom will be sociologists, and some mathematicians (and maybe some will be neither!).


For now, I define “mathematician” narrowly: as a scientist working professionally in the field of mathematics (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 involved in teaching and/or writing and/or research. At the moment I focus only on mathematicians who do research, although it would be 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 Boltanski and Thevenot would put it). A sociologist can discover trends and compare mathematical (working) lives to ones in other careers and jobs.

Second, 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).

Is there a life after grad school? The story of a Computer Science PhD

Here’s an interesting interview with PhD student in Die Zeit (my translation)

CAROLA DOERR, 29, gained her PhD from Saarland University and the Max Planck Institute for Informatics. 

A wrong decision

Will I wake up some day and just know it for sure? Do I want to work in science or in industry? This decision gave me stomach ache for a long time while I was doing my PhD. I had previously spent two years working for McKinsey who then funded my PhD. My topic was random algorithms. In addition, I held a post at the Max Planck Institute for Informatics [Computer Science] in Saarbrücken and a grant from Google. I never had to worry about money. But I asked myself: Which lifestyle is right for me? Which goes better with family?

After submitting my PhD, I first worked part time at McKinsey and the Max Planck Institute, because I still couldn’t make a decision. At some point, however, I realised that it would be difficult to reconcile the lifestyle of a consultant with my desire to have children. At the Max Planck Institute, already two colleagues had children. I asked the director how he assessed my chances for a permanent position in science. He was quite confident . These were three signals for me. Now I live in Paris and work at the Pierre-and-Marie-Curie-University. I have a permanent research job and I can decide freely how much teaching I want to do. My husband is a professor at another university in Paris. Our daughter is seven months old.

If you read German, here is the full article with five more stories by PhD students in other subjects:




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