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Mathematical motivation and meagre contributions

14th August, 2019

I find myself in a mathematical rut more often than I would like. It is very easy, especially as a PhD student, I think, to become disillusioned with maths, the work that one can do, and academia as a whole. I realised only the other day, after talking to my family, some of the things that can contribute towards this. Hopefully this post can serve as a reminder to myself that I am human being who is trying to be a mathematician, and not the other way around.

These days, living abroad (away from friends and family), most of my social interactions take place with other mathematicians. This is great, because I do love talking about maths, but also has a rather negative effect. Namely, every single person in my office already has a PhD. Because of this, it’s very easy to feel like I know absolutely nothing about maths. Combine this with the typical thésard problem of “my thesis just has trivial results but even so my proofs are incomplete and bad”, reading things written by the geniuses of your field, and throw in a dash of “so much of academia is about trying to sell your maths as having either profitable (for the few) or military applications”, and it can be hard to enjoy maths at times.

By no means am I claiming to have a solution to this problem, but I have found a few things that help (some very obvious), so I thought I’d share them here for whatever small help they might be to anybody reading.

  1. Talk to people outside of maths as much as you possibly can, especially about things that aren’t maths. Family and friends are just so important.

  2. Don’t give up talking to mathematicians. One thing that prompted me to put down these thoughts on this blog was a Twitter thread this morning by John Baez that just got me so excited about maths again. Read things outside of your current work, and try to make time for learning maths that you find irresistibly intriguing, even if it’s completely unrelated to the work you have to do.

  3. Get involved in some community projects. I’ve been contributing to a translation project for Grothendieck’s EGA recently, and it’s been great for me personally: I can use the fact that I speak French and know enough about algebraic geometry to help make something that could hopefully help other people. I’ve also been working on LaTex support in riot.im, so that mathematicians can have an instant-messaging service, like Discord or Slack, where they can actually type how they would write: with nice maths symbols. In general, open-source projects are a great thing to get involved in.

  4. Take up bird watching. I know that not everybody might love these feathered friends as much as I do, but I’m far from the first to have written about what a great thing it can be. It’s not like you have to do it “seriously” either: I spend a lot of time just giving names to the pigeons I see every day, and watching how they interact with each other. As one of my favourite poets, Wendy Cope, so beautifully writes:

    ‘A great deal of anecdotal evidence suggests that we respond positively to birdsong.’
    — Scientific researcher quoted in The Daily Telegraph 8.2.2012.

    Centuries of English verse
    Suggest the selfsame thing:
    A negative response is rare
    When birds are heard to sing.

    What’s the use of poetry?
    You ask. Well, here’s a start:
    It’s anecdotal evidence
    About the human heart.

  5. As the above poem also suggests, spend time growing and learning as a human being. It’s said so often that it’s become cliché, but being a human being can be very hard. Poetry, music, books, and so on, are all ways that other human beings have tried to convey what they have themselves wanted to hear at one point or another, so listen to what they have to say. But don’t get so tied up in listening to artists that you forget to listen to everybody else.