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.
this post was submitted on 26 Jun 2025
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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.
the man you're thinking of is, I believe, George Boole, the inventor of Boolean algebra.
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
Shoutout to Satyendra Nath Bose who helped pioneer relativity as a theoretical physicist because he didn't want to study something useful that would benefit the British.
George Boole introduced Boolean algebra, not Charles. Charles, according to this site on the Boole family, he had a career in management of a mining company.
Was he trying to dunk on his professors?
Yes and no
So no.
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)
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.
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.
My disclaimer: I don't know what any of this means, but it might give you a direction to start your research.
First thing he came up with is Number Theory, and how they've been working on that for centuries, but they never would have imagined that it would be the basis of modern encryption. Multiplying a HUGE prime number with any other numbers is incredibly easy, but factoring the result into those same numbers is near impossible (within reasonable time constraints.)
He said something about knot theory and bacterial proteins, but it was too far above my head to even try to relay how that's relevant.
Tell him I would like to subscribe to his blog
The following aren't necessarily answers to your question, but he also mentioned these, and they are way too funny to not share:
The Hairy Ball theorem
Cox Ring
Tits Alternative
Wiener Measure
The Cox-Zucker machine (although this was in the 70s and it's rumored that Cox did most of the work and chose his partner ONLY for the name. 😂)
Origami can be used as a basis for geometry:
http://origametry.net/omfiles/geoconst.html
IIRC, you can do things that are impossible in standard Euclidean construction, such as squaring the circle. It also has more axioms than Euclidean construction, so maybe it's not a completely fair comparison.
Does this count? Because it really is wtf.
Doom absolutely counts!
Not math but the discovery of Thermus aquaticus was seemingly useless but later had profound applications in medicine. There's a good Veritasium video on it
IIRC quaternions were considered pretty useless until we started doing 3D stuff on computers and now they're used everywhere
This talk by Freya Holmer on Quarternions is awesome and worth anybody’s time that like computer graphics, computer science, or just math.
That was a cool watch. Thanks.
I wonder if complex numbers predate the discovery of electromagnetism
Yes, mathematicians first encountered equations which could only be solved with complex numbers in the 16th century.
Complex numbers. Also known as imaginary numbers. The imaginary number i is the solution to √-1. And it is really used in quantum mechanics and I think general relativity as well.
It's used extensively in electronic circuit design (where it's called "j", as "i' already meant electronic current).
Also signal processing has i or j all over it.
I’m the akshually guy here, but complex numbers are the combination of a real number and an imaginary number. Agree with you, just being pedantic.
Sure, but 1 is a real number. 😜
Yes, and 1 is also a complex number.
Of course, but 1 is the loneliest number.
Electromagnetics as well.
Non-linear equations have entered the chat.
Chaos and non-linear dynamics were treated as a toy or curiosity for a pretty long time, probably in no small part due to the complexity involved. It's almost certainly no accident that the first serious explorations of it after Poincare happen after the advent of computers.
So, one place where non-linear dynamics ended up having applications was in medicine. As I recall it from James Gleick's book Chaos, inspired by recent discussion of Chaotic behavior in non-linear systems, medical doctors came up with the idea of electrical defibrillation- a way to reset the heart to a ground state and silence chaotic activity in lethal dysrhythmias that prevented the heart from functioning correctly.
Fractals also inspired some file compression algorithms, as I recall, and they also provide a useful means of estimating the perimeters of irregular shapes.
Also, there's always work being done on turbulence, especially in the field of nuclear fusion as plasma turbulence seems to have a non-trivial impact on how efficiently a reactor can fuse plasma.
A good friend of mine from high school got his physics PhD at University of Texas and went on to work in the high energy plasma physics lab there with the Texas Petawatt laser, and a lot of the experiments it was used for involved plasma turbulence and determining what path energetic particles would take in a hypothetical fusion reactor.
Be honest, how many unofficial experiments were there?
You ever just start lasering shit for kicks?
I've read that all modern cryptography is based on an area (number theory?) that was once only considered "useful" for party tricks.
prime number factorization is the basis of assymetric cryptography. basically, if I start with two large prime numbers (DES was 56bit prime numbers iirc), and multiply them, then the only known solution to find the original prime numbers is guess-and-check. modern keys use 4096-bit keys, and there are more prime numbers in that space than there are particles in the universe. using known computation methods, there is no way to find these keys before the heat death of the universe.
DES is symmetric key cryptography. It doesn't rely on the difficulty of factorizing large semi-primes. It did use a 56-bit key, though.
Public key cryptography (DSA, RSA, Elliptic Curve) does rely on these things and yes it's a 4096-bit key these days (up from 1024 in the older days).
thank you
Donuts were basis of the math that would enable a planned economy to be more efficient than a market economy (which is a very hard linear algebra problem).
Basically using that, your smart phone is powerful enough to run a planned economy with 30 million unique products and services. An average desktop computer would be powerful enough to run a planned economy with 400 million unique products and services.
Odd that knowledge about it has been actively suppressed since it was discovered in the 1970s but actively used mega-corporations ever since…
I'd like to read up on this if you have sources
Look up Wassily Wassilyevich Leontief
That's pretty interesting. Do you happen to have any introductory material to that topic?
I mean, it might even have applications outside of running a techno-communist nation state. For example, for designing economic simulation game mechanics.
Well Wassily Wassilyevich Leontief won a Nobel prize in economics for his work on this subject that might help you get started
How do you define "pure math discovery"?