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

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

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

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

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

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

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

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

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

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

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

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

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