An introduction to functional analysis for science and engineering

A new tutorial paper tries to do something almost heroic: make a notoriously intimidating corner of higher math feel readable for scientists and engineers. In plain English, it’s a guide to the math used to handle big real-world problems like waves and continuous systems, showing how people turn scary infinite problems into workable approximations. The author promises a self-contained path from basic number sequences all the way to tools for studying operators, eigenfunctions, and singular value decomposition—while shoving longer proofs off to a separate section to keep the main story moving. That alone should have earned applause. Instead, the comments immediately did what comments do best: made it about everything else.

The hottest mini-drama? Formatting snobbery versus content purity. One drive-by grenade—“Not LaTeX...” —instantly set the mood, only for another commenter to step in with the internet’s version of a reality check: if it’s clear and correct, who cares what it was written in? Then came the academic side-eye: one user noted the paper is from 2019 and has no exercises, which in textbook-land is basically being accused of showing up to the gym with no weights. Others were kinder, praising it as “compact” and readable, with one commenter dropping a dad joke so inevitable it practically wrote itself. And then, the classic comments-section finishing move: someone argued an older book by Kreyszig already does this job better, with more applications and actual practice problems. So yes, the paper is about making hard math accessible—but the real show was the crowd debating whether readability beats tradition, and whether a tutorial counts if it doesn’t make you do the homework.