Math. The dreaded word.
Everyone seems to hate math. For its unintuitive! It’s like, math doesn’t give a damn what we think is possible, or what we think is absurd. Math does exactly what it wants to do, because that’s all it can do. We may not always understand it, but sometimes, once in a blue moon, we get a peek behind the curtain. Once every few hundred years, we can prove that cicada mating rituals are related to weather on Mars, and briefly glimpse the universe in its true glory.
But what if math is not math, but really everything? What if physics is math? Like just maths?
Consider Monstrous Moonshine.
Pretty, Isn’t it?
Monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. (*Wiki)
Professor Richard Borcherds of Cambridge University was awarded [August 1998] the Fields Medal, the mathematicians’ equivalent of a Nobel Prize, for proving a highly abstruse result in number theory called the moonshine conjecture.
It seems it was given this name because it was based on a coincidence between a result in number theory and the number of symmetries in an exotic concept called the Monster object. It was thought so unlikely that two such distinct areas of mathematics should have anything in common that the conjecture was described as moonshine, and the name has stuck.
Professor Borcherds was quoted as saying, “I was over the moon when I proved the moonshine conjecture”, a nice conflation of two of the common evocations of the Moon in the language.
Moonshine originally meant the same as moonlight. In A Midsummer Night’s Dream, Snug asks whether the moon will shine the night they perform their play, and Bottom replies in a brief panic: “A calendar, a calendar! Look in the almanack; find out moonshine, find out moonshine!” It still has this literal meaning in poetical or elevated contexts but we no longer use it in that way in daily life, unlike the matching sunshine. Instead, it commonly means something insubstantial or unreal, and so foolish or visionary.
It is now known that lying behind monstrous moonshine is a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, having the monster group as symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas.
This makes me wonder, what if physics is also a part of mathematics?
Read this paper on On a Final Theory of Mathematics and Physics. Maybe it’s true! Worth a read.