A View from Lockdown: Mathematics Discovered, Invented, and Inherited

Abstract

ALEXANDRE BOROVIK A. 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 examples 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. ES . This paper is written in lockdown and can serve as a testimony in support of the apparently self-evident, but largely ignored principle:The most important resource for a (pure) mathematician's research is uninterrupted time for thinking. University administrators and research funding bodies systematically ignore it, and the bureaucratic burden imposed by them strangulates mathematics research. A short breathing space provided by lockdown could make miracles. J 2020. Y ,The soul is silent. If it speaks at all it speaks in dreams.Louise Glück 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. After a light breakfast and coffee, I start doing mathematics, that is, I sit at my desk and look out of the window. This 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 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

Finite group actions on abelian groups of finite Morley rank

“…My paper [4] is a chapter in the book Math in the Time of Corona, to be published by Springer. It contains a lighthearted story of working on Theorem 1 under the constraints of lockdown.…”

“…It contains a lighthearted story of working on Theorem 1 under the constraints of lockdown. The text here is a formal write-up of my original sketch referred to in [4] and shared with the circle of my close mathematical collaborators. The sketch was written as a stream of consciousness and recorded my experiment which would be bizarre outside of lockdown: I decided to try to develop a piece of mathematics without any use of external sources of information, as if this was done in a prison.…”

“…I am grateful to Elizabeth Loew and Alice Wonder who kindly invited me to contribute to the book Math in the Time of Corona. I was writing my chapter [4] in parallel with working on this paper, and their support was most encouraging.…”