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As a mathematician, what does mathematics mean to you, and why do you believe it to be important?

It’s the best model mankind currently has to explain our observations of the world/universe around us. Stephen Wolfram has some intriguing thoughts on this, it’s worth checking his writing.

I’ve always struggled with applied mathematics — everyone asks, without an application, what’s the point? And much of the great works in mathematics were discovered, or created, depending on your point of view, as solutions to observation. This is how the calculus was defined, by both Leibniz and Newton. Mathematics allowed Einstein to define the theories of Relativity, based on observations. But what’s really exciting to me about mathematics is work in “pure” mathematics, and theoretical physics which is just all maths.

In theoretical physics, mathematics itself describes physical phenomena which must exist in order for the broader theories to exist. Working through insanely-complicated equations, something is found to be missing. And that must exist for everything else to exist. And so the sequence is taken in reverse — for the maths to work out, for all the surrounding maths to work out, there must be this something we can only define mathematically but must be able to observe. This was how black holes were discovered. This is how the Higgs boson was discovered. These were objects only defined through mathematics, that were then, later, found in nature.

I find this absolutely…amazing, incredible, spellbinding, I can’t find the right word.

But, Wolfram has ideas about this — as in, we’ve only been able to find such observations, and were destined to find such observations, because we’re theorizing and looking at everything through one language of mathematics.

But “pure” mathematics is…pure beauty, I’d say. It’s one giant, endless puzzle. Andrew Wiles used the metaphor of a great mansion, in total darkness. Every time you find a solution, a small light turns on and you can begin to understand other problems, and find their solutions, and more light turns on. There’s no known application to much of pure mathematics, but wandering through it and understanding problems, finding solutions, “discovering” (I prefer to say) proofs — even if they’ve already been solved or discovered — is an entire universe to play in. For me, it’s boundless confusion and joy combined. I’ll never publish a proof, but maths is one of the greatest pleasures I’ve ever been part of.

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