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 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.