Ask Lemmy

It's imaginary numbers. Full stop. No debate about it. The idea of them is so wild that they were literally named imaginary numbers to demonstrate how silly they were, and yet they can be used to describe real things in nature.

As far as I know, matrices were a "pure math" thing when they were first discovered and seemed pretty useless. Then physicists discovered them and used them for all sorts of shit and now they're one of the most important tools in in science, engineering and programming.

The invention of the number 0, the discovery of irrational numbers, or l the realization that base 60 math makes sense for anything round, including timekeeping.

Having watched all the veritasium math videos I feel like all the major breakthroughs in math were due to mathemicians playing around with numbers or brain teasers out of curiosity without a concrete use case in mind.

Riemann went nuts working on higher dimensional mathematics and linear algebra. At the time there was not a clear use case for math higher than like 3 or 4 dimensions, but he drove himself crazy discovering it anyways. Today, this kind of math underlies all of artificial intelligence

Imaginary numbers probably, they're useful for a lot of stuff in math and even physics (I've heard turbulent flow calculations can use them?) but they seem useless at first

Strangest? Functional analysis, maybe. I understand it's used pretty extensively in quantum field theory, although I don't actually know firsthand.

That's a body of mathematics about infinite-dimensional spaces and the operations on them. Even more abstract ways of defining those operations exist and have come up as well, like in Tseirlson's problem, which recently-ish had a shock negative resolution stemming from quantum information theory.

There's constructions I find weirder yet, but I don't think p-adic numbers, for example, have any direct application at this point.

Integration.