Samiul Bashar Samin
In one sense, there’s less mystery in mathematics than there is in any other human endeavour. In math, we can really understand things, in a deeper way than we ever understand anything else. (When I was younger, I used to reassure myself during suspense movies by silently reciting the proof of some theorem: here, at least, was a certainty that the movie couldn’t touch.) So how is it that many people, notably including mathematicians, feel that there’s something ‘mysterious’ about this least mysterious of subjects? What do they mean?
Granted, not all mathematical mysteries have the character of rigorously proving what common sense would predict. Math, you might say, is a conspiracy theorist’s dream: it’s the one part of life where, when you see things match up, the odds are excellent that it’s not just a coincidence, that there is a deep explanation waiting to be unearthed. On the other hand, precisely because the entire subject is shot through with non-coincidental patterns, once you’ve spent enough time doing math, you might stop being so surprised by them. You might come to see them as just part of the terrain.
To put it mildly, this hasn’t been my experience, or the experience of anyone else I know who works in any part of math. Yes, sometimes people are surprised; surprises are part of the thrill of what we do. But the surprises are surprises only because of their rarity, because of all the other times when things worked out pretty much the way the experts expected them to.
So maybe the right question is: after a mathematical pattern has been explained – not only proved but, let’s say, proved in 20 different ways, really exhaustively understood, like the Pythagorean Theorem – is there still a residual mystery about it? I would say that there is, but it takes some effort to put our finger on it.I feel confident in saying that, yes, there is something mysterious about math – but the main thing that’s mysterious is why there isn’t even more mystery than there is.