A View from Lockdown: Mathematics Discovered, Invented, and Inherited
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question:
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The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: Is new mathematics discovered or invented?
Using an example from my own mathematical work during the Coronavirus lockdown, I argue that there is also a third way: new mathematics can also be inherited. And entering into possession, making it your own, could be great fun.
1 Your Best Friend, the Subconscious I confess, with some embarrassment, that my life in lockdown is comfortable and happy. I wake up at sunrise and take an hour long walk in the local park (conveniently, a wilderisation project), meeting on my way only foxes and birds – among them the resident grey heron, Ardea cinerea, an elegant and dignified bird.1 After a light breakfast and coffee, I start doing mathematics, that is, I sit at my desk and look out of the window. Thinking is a hard job, and I soon become tired, move to a sofa and take a nap. On waking up, I am refreshed, and return to mathematics – and more 1
Today I have seen a relatively rare atmospheric phenomenon: a full arch double rainbow, of very intense colour, at the very moment when the rising sun was crossing the horizon. Some would perhaps see that as a good omen and symbol of hope, or a tribute to the National Health Service (badly painted rainbows are everywhere all over the country), but I instead started to recover, in my head, a geometric explanation of the old conundrum: why, in the two arches of a double rainbow, colours change in opposite orders: from blue to red in the inner, and from red to blue in the outer arch? I leave this problem to the readers as an exercise.
A. Borovik (*) Department of Mathematics, University of Manchester, Manchester, UK © The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 A. Wonders (ed.) Math in the Time of Corona, Mathematics Online First Collections, https://doi.org/10.1007/16618_2020_6
A. Borovik
often than not I have some new ideas for my work; they came to me during my sleep. This cycle is repeated, with breaks for meals and tea. My wife uses meals for briefing me about COVID and other news, I myself do not follow current affairs. Perhaps at this point I have to touch on one of the best kept secrets of mathematics: mathematics is done in the subconscious.
A mathematician has to maintain good relations with his or her subconscious. The subconscious is not a properly domesticated beast, but it responds well to attention and kindness. It is like our rabbit, Cadbury the Netherland Dwarf (one of the wilder breeds of pet rabbits). When he is in good spirits, Cadbury grooms me, combing with his incisors the skin on my arm, apparently trying to relieve me of my (non-existent, I hope) fleas – this is a natural social behaviour of rabbits. While I doze, my subconscious combs the deepest recesses of my memory for morsels of mathematics which could be relevant to, or just somehow associated with the mathematics that I am trying to do in my conscious state. The subconscious is a wordless cr
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