My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge.
[1] https://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf
Gauss's notes and margins is riddled with proofs he didn't bother to publish - he was wild.
Not sure if true, but allegedy he insisted his son not go into maths, as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths :'D
When I interned at Chevron someone said they (or some other oil company) were using Fourier transforms in the 1950's for seismic analysis but kept it a secret for obvious reasons. I think you couldn't (can't?) patent math equations.
Gauss is gonna Gauss.
How was Gauss so productive with 6 children?
There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.