What’s the goal of mathematics?

Are we just trying to prove every theorem or find theories which lead to a lot of creativity or what?

I’ve already read G. H. Hardy Apology but I didn’t get an answer from it.

Answer

There was a book I read at one point, can’t remember which, that had the following parable in the introduction (paraphrasing from memory):

“There was once a group of people who wanted to get to a mountain far in the distance and climb it. Between them and the mountain, was a great desert they would have to cross. It was clear that the people had neither the knowledge to cross the desert nor to climb the mountain once they got there. So they began to study and work. At first, everyone worked on a bit of everything: how to carry water; how to avoid sand traps; how to climb safely; etc. Slowly, some people began devoting more of their time to studying the desert, and some to studying mountain climbing. And so the people studying the desert began to develop theories of sand dunes, wind, erosion, and so on; these theories were not really necessary in order to cross the desert, but the people studying the desert found them interesting nonetheless. Those studying mountain climbing were only interested in the desert-studies in so far as it allowed them to get closer to the mountain, and often complained that the desert-study people were wasting time considering theoretical questions that were unnecessary for the purposes of crossing the desert. The desert study people didn’t care: they had fallen in love with the desert and were intent on studying it, regardless of whether it helped them all get to the mountain or not.”

In the analogy, the mountain was the Theory of Everything from Physics; the Desert was mathematics. There was a time when mathematics’ main concern was really to help study the world (help us cross the desert), but it has moved on from that.

This doesn’t really answer your question. Perhaps the following won’t either: when I was in my early second year in grad school, and looking for an advisor, Hendrik Lenstra told me: “Ask yourself why you do mathematics. If the answer is not ‘Because I have to’ then quit grad school now.” Meaning: unless you would be doing mathematics in your free time, then don’t try it as your profession.

Attribution
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Arturo Magidin

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