[nimonian]

It's a delightful counterintuition that your gut feeling is mostly wrong: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

Far from being motivated by some applications, the most useful discoveries in mathematics are usually discovered "for their own sake" and their application is only discovered later. Sometimes centuries later!

[skybrian]

If so that seems like an opportunity for people who want to work on applied math? There’s a big backlog of techniques that so far have not been useful.

[mswphd]

I've seen this floated as a response to the current anxieties over LLMs in math. Namely in applied math, LLMs being good at pure math may actually allow the import of pure math techniques. Unclear if that will pan out, but it's interesting to consider.

[kcexn]

Absolutely! The backlog is enormous though, and much of mathematics requires a great deal of work to understand it to the depth required before a novel application becomes apparent.

[transitorykris]

Parents reads as a comment on the usefulness of applying mathematics to problems in the world (applied mathematics) and discovering mathematical problems that push mathematics forward (pure mathematics) in the process. Pure mathematics is incredibly important, but I’d hardly count it as useful if we need to wait centuries.

[aleph_minus_one]

> but I’d hardly count it as useful if we need to wait centuries.

This is not the fault of the mathematicians.

[dennis_jeeves2]

>are usually discovered "for their own sake"

Like prime numbers? (used in cryptography)