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.

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.

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.

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

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.

The math fun fact I remember best from college is that Charles Boole invented Boolean algebra for his doctoral thesis and his goal was to create a branch of mathematics that was useless. For those not familiar with boolean algebra it works by using logic gates with 1s and 0s to determine a final 1 or 0 state and is subsequently the basis for all modern digital computing

Integration.

Non-Euclidean geometry was developed by pure mathematicians who were trying to prove the parallel line postulate as a theorem. They realized that all of the classic geometry theorems are all different if you start changing that postulate.

This led to Riemannian geometry in 1854, which back then was a pure math exercise.

Some 60 years later, in 1915, Albert Einstein published the theory of general relativity, of which the core mathematics is all Riemannian geometry.

A brain teaser about visiting all islands connected by bridges without crossing the same bridge twice is now the basis of all internet routing. (Graph theory)

I work with a guy who is a math whiz and loves to talk. Yesterday while I was invoicing clients, he was telling me how origami is much more effective for solving geometry than a compass and a straight edge.

I'll ask him this question.

Does this count? Because it really is wtf.

https://en.m.wikipedia.org/wiki/Fast_inverse_square_root

If I recall correctly, one mathematician in the 1800s solved a very difficult line integral, and the first application of it was in early computer speech synthesis.