Integration.
this post was submitted on 26 Jun 2025
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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.
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?
I'm studying EE in university, and have been surprised by just how much imaginary numbers are used
EE is absolutely fascinating for applications of calculus in general.
I didn't give a shkt about calculus and then EE just kept blowing my mind.
I was gonna ask how imaginary numbers are often used but then you reminded me of EE applications and that's totally true.
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.
Huge in 3d graphics and AI.
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
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.
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.
12 is the most based number in that respect IMO.
But then...hey, we use that for hours!
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.
It’s crazy how engaging and well done Veritasium videos are and they’re just free to watch on YouTube.
And on spotify nowadays
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.
Same thing with early studies on prime numbers
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.
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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)
freaking freaky little Russian outpost that one is. Bridges galore
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.
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.
This won't make any sense to any of you right now, but: E = md^3^
That's a perfect example of a typical interaction between a Technology Management Consultant and somebody from a STEM area.
Techies with an Engineering background who are in Tech and Tech-adjacent companies are often in the receiving end of similar techno-bollocks which makes no sense from such "Technology" Management Consultants, but it's seldom quite as public as this one.
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