Mathematics has been a big part of my life since middle school, when, out of curiosity and with encouragement of my teacher, I became interested in solving mathematical puzzles and participating in inter-school competitions. Subsequently, it led me to studying applied math in the university and later doing research and teaching fluid mechanics as an engineering professor. Ironically, ever since research became my career, I somehow stopped being particularly curious about the mathematics itself, and started treating it as tool for doing my work.
About a year ago, I read book called “Is God a mathematician?“ by Mario Livio. It prompted me to think about math from less utilitarian and more philosophical perspective. A curious feature of math is that it can be considered both as a human creation (e.g., a language that is useful for performing calculations and expressing laws of physics) and as something existing on it’s own and what humans only discover (e.g., like the natural laws themselves). It seems that the latter aspect is definitely present, despite Albert Einstein’s belief that math is, essentially, a set of human-made tools. In 1960, Eugene Wigner, a Nobel laureate physicist, even wrote a paper in Communications in Pure and Applied Mathematics entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” which discussed precisely that – how it is possible that exercises in “pure” mathematics prompt post-factum discoveries of natural phenomena.
As a personal takeaway from reading Livio’s book, I feel a bit better about spending time thinking about mathematics per se without worrying whether it is particularly relevant for my field of research or whether a particular research question has already been answered. It is also kind of amusing to learn that even intellectual giants like Richard Feinmann went through a variation of this thinking process with surprising results, e.g. when he consciously decided to apply himself to re-tracing the steps of a well-known solution describing spinning plates that eventually lead to a Nobel-prize-level breakthrough.
