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?
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 shit 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.
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.
You can, they map, but complex numbers are much much easier to deal with
In quantum mechanics, there are times you divide two different complex numbers, and complex multiplication/division is the thing two real numbers can’t really replicate. That’s how the Bloch 2-sphere in 3D space is constructed from two complex dimensions (which maps to 4 real ones).
It’s peripheral, though. Nothing in the guts of the theory needs it AFAIK - the Bloch sphere doesn’t generalise much and is more of a visualisation. So, jury’s still out on if it’s us or if it’s nature that likes seeing it that way.