PyCryptoing on the Physics Maths Border

Studies of nonlinearity often bring us to the badlands between physics and mathematics. 

One such exponent is Professor Pierre Raphael who specializes in the study of nonlinear waves.

Pierre Raphael joined Cambridge's Department of Pure Mathematics and Mathematical Statistics (DPMMS) in 2019. He has a PhD from Cergy Pontoise (since January 2020 known as CY Cergy Paris university).

At Cambridge, PR is the Herchel Smith Professor of Pure Mathematics (named after organic chemist Herchel Smith who was an undergraduate at Emmanuel College, Cambridge).

"The Most Important Noog of Our Time" - Gilbert Strang

Gilbert Strang described the Fast Fourier Transform as "the most important numerical algorithm of our time".

The FFT samples a signal over time and divides it into its frequency components.

Cooley and Tukey are credited with the development of the FFT in its modern form although Gauss had developed his own methods in an unpublished work from 1805 (using it to interpolate the orbit of asteroids).

John Tukey was an American statistician who coined the term "bit"(a short form for "binary digit"). He and Cooley developed the FFT algo in 1965 while working at IBM.

Manchester-born Frank Yates (graduate of St John's College Cambridge and one of the pioneers of 20th Century statistics, known to A-level students for Yates Continuity Correction) also created something similar in 1932 which he called the interaction algorithm.

Modern FFT was developed in the context of processing sensor data and has become a leading algorithm in the art of digital signal processing.

Mathematician Marcus du Sautoy (Fellow of New College Oxford) also talks about it in his podcast on Fourier, on the BBC's podcast series A Brief History of Mathematics.