Science

The Fast Fourier Transform (FFT) is a modern algorithm to compute the Fourier coefficients of a finite sequence. Fourier will forever be known by his assertion in 1807 that any function could be expressed as a linear combination of sines and cosines, its Fourier series. "Any" was a little ambitious, counter-examples coming to the fore in due time. A fair amount of mathematics from that time to this has been devoted to refining Fourier's insight and studying trigonometric series, a subject that led Georg Cantor to founding set theory. Piecewise smoothness is sufficient for pointwise convergence on $[-\pi, \pi]$:

$$f(x) = {a_0 \over 2} + \sum_{j=1}^\infty \left( a_j \cos jx + b_j \sin jx \right),$$

My original calendar program was on the Casio fx-3600p calculator in 1980 or so - my first programming venue and exercised partly in spare moments when driving truck out on the route; a precursor mobile device you could say. My buddy Dave got me started. I might have scarred myself permanently though. The transition from math to software engineering is always tricky, considering that there are many commonalities, but just as important differences to snag the self-taught and perhaps obstinate and all-too-confident mathematician (perish the thought). The 3600 had this bizarre little macro language providing for a trade-off between memory and program size. You could have (say) fifty memory locations and 400 instructions or twenty locations and 600 instructions. They're really variables of course, but the memory locations were designated K0 through K19 or something.