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?
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.
I am pretty sure that the first thing you mentioned (multiplying being easy and factoring being hard) is the basis of public key cryptography which is how HTTPS works.
Somewhat related fun fact: One of the most concrete applications for quantum computers so far is breaking some encryption algorithms.
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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. 😂)