this post was submitted on 26 Jun 2025

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148

What is the strangest math that turned out to be useful? (lemmy.world)

submitted 1 day ago by gedaliyah@lemmy.world to c/asklemmy@lemmy.world

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There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”

Are there examples like this in math as well? What is the most interesting "pure math" discovery that proved to be useful in solving a real-world problem?

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[–] CanadaPlus@lemmy.sdf.org 2 points 13 minutes ago* (last edited 13 minutes ago)

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.

[–] JackbyDev@programming.dev 31 points 6 hours ago (3 children)

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.

[–] CanadaPlus@lemmy.sdf.org 2 points 48 minutes ago* (last edited 27 minutes ago) (1 children)

I mean, quaternions are the weirder version of complex numbers, and they're used for calculating 3D rotations in a lot of production code.

There's also the octonions and (much inferior) Clifford algebras beyond that, but I don't know about applications.

[–] silasmariner@programming.dev 1 points 14 minutes ago

Yeah but aren't quaternions basically just a weird subgroup of 2x2 complex matrices?

[–] chunes@lemmy.world 1 points 2 hours ago (3 children)

I don't really get 'em. It seems like people often use them as "a pair of numbers." So why not just use a pair of numbers then?

[–] CanadaPlus@lemmy.sdf.org 3 points 34 minutes ago* (last edited 27 minutes ago)

They also have a defined multiplication operation consistent with how it works on ordinary numbers. And it's not just multiplying each number separately.

A lot of math works better on them. For example, all n-degree polynomials have exactly n roots, and all smooth complex functions have a polynomial approximation at every point. Neither is true on the reals.

Quantum mechanics could possibly work with pairs of real numbers, but it would be unclear what each one means on their own. Treating a probability amplitude as a single number is more satisfying in a lot of ways.

They don't exist is still a position you could take, but so is the opposite.

[–] JackbyDev@programming.dev 2 points 1 hour ago* (last edited 1 hour ago)

I totally get your point, and sometimes it seems like that. Why not just use a coordinate system? Because innsome applications the complex roots of equations is relevant.

If you square an imaginary number, it's no longer an imaginary number. Now it's a real number! That's not something you can accomplish with something like a pair of numbers alone.

[–] justastranger@sh.itjust.works 2 points 1 hour ago

Because the second number has special rules and a unit. It's not just a pair of numbers, though it can be represented through a pair of numbers (really helpful for computing).

[–] alt_xa_23@lemmy.world 8 points 4 hours ago (3 children)

I'm studying EE in university, and have been surprised by just how much imaginary numbers are used

[–] CanadaPlus@lemmy.sdf.org 1 points 32 minutes ago (1 children)

From what I've seen that's one example where you could totally just use trig and pairs of numbers, though. I might be missing something, because I'm not an electrical engineer.

[–] silasmariner@programming.dev 1 points 11 minutes ago

You can, they map, but complex numbers are much much easier to deal with

[–] underscores@lemmy.zip 3 points 2 hours ago* (last edited 1 hour ago)

EE is absolutely fascinating for applications of calculus in general.

I didn't give a shit about calculus and then EE just kept blowing my mind.

[–] pineapplelover@lemm.ee 3 points 4 hours ago

I was gonna ask how imaginary numbers are often used but then you reminded me of EE applications and that's totally true.

[–] ikidd@lemmy.world 6 points 4 hours ago

Integration.

[–] amelia@feddit.org 18 points 6 hours ago (1 children)

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.

[–] Buddahriffic@lemmy.world 4 points 3 hours ago

Huge in 3d graphics and AI.

[–] Feathercrown@lemmy.world 6 points 5 hours ago

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

[–] Etterra@discuss.online 19 points 10 hours ago (1 children)

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.

[–] chonglibloodsport@lemmy.world 11 points 7 hours ago (1 children)

60 was chosen by the Ancient Sumerians specifically because of its divisibility by 2, 3, 4, and 5. Today, 60 is considered a superior highly composite number but that bit of theory wouldn’t have been as important to the Sumerians and Babylonians as the simple ability to divide 60 by many commonly used factors (2, 3, 4, 5, 6, 10, 12, 15) without any remainders or fractions to worry about.

[–] Allero@lemmy.today 1 points 3 hours ago (1 children)

12 is the most based number in that respect IMO.

But then...hey, we use that for hours!

[–] MeThisGuy 1 points 1 hour ago

and in parts of the world for inches to a foot. pretty useful for carpentry for example

[–] saimen@feddit.org 18 points 12 hours ago (1 children)

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.

[–] moseschrute@lemmy.ml 4 points 7 hours ago (1 children)

It’s crazy how engaging and well done Veritasium videos are and they’re just free to watch on YouTube.

[–] saimen@feddit.org 1 points 4 hours ago

And on spotify nowadays

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