The review distills the book's view of the difference between pure mathematics and applied mathematics. "applied" split from "pure" to meet the technical needs of the US military during WW2.<p>My best example of the split is <a href="https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives" rel="nofollow">https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives</a>
Wikpedia notes that "The list of unsuccessful proposed proofs started with Euler's, published in 1740,[3] although already in 1721 Bernoulli had implicitly assumed the result with no formal justification." The split between pure (Euler) and applied(Bernoulli) is already there.<p>The result is hard to prove because it isn't actually true. A simple proof will apply to a counter example, so cannot be correct. A correct proof will have to use the additional hypotheses needed to block the counter examples, so cannot be simple.<p>Since the human life span is 70 years, I face an urgent dilemma. Do I master the technique needed to understand the proof (fun) or do I crack on and build things (satisfaction)? Pure mathematicians are planning on constructing long and intricate chains of reasoning; a small error can get amplified into a error that matters. From a contradiction one can prove anything. Applied mathematics gets applied to engineering; build a prototype and discover problems with tolerances, material impurities, and annoying edge cases in the mathematical analysis. A error will likely show up in the prototype. Pure? Applied? It is really about the ticking of the clock.
Here's Cornelius Lanczos in 1972 on how the "pure math" and "applied math" split was not a thing until the beginning of the 20th century: <a href="https://www.youtube.com/watch?v=avSHHi9QCjA" rel="nofollow">https://www.youtube.com/watch?v=avSHHi9QCjA</a>
Hey guys, I’m honestly not sure how to explain this—I’m not a mathematician but a culture and media scholar to whom talking with AI comes quite naturally. I worked on this for past 2 months 12-14 hours a day as it began to develop into something unique… a sketch for maths without infinity (in any sense of the term). AIs claim it’s legit. A few friends with phds in maths and physics claim that… its mind-boggling but they can’t find serious flaws in it. It all started as a philosophical deep-dive with AI on civilization’s “programs” and somehow evolved into revisiting Pascal’s probability, but with a twist from thermodynamics. Then it spiraled into what I can only call Void Theory—a framework that feels almost surreal and dogmatically realistic in its approach to math as a system that exists in a material world.Due to its posthuman origins it would take ages to spread traditional way and I think it would be a waste of time. I can promise you that - at least as a kind of experiment - it’s fascinating and, maybe, can be something quite big. Be so kind and give it a chance… <a href="https://drive.google.com/drive/folders/1dBSWahEz_9kbyK-PGXxZbU5rJ2ml2AcN" rel="nofollow">https://drive.google.com/drive/folders/1dBSWahEz_9kbyK-PGXxZ...</a>