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The closing sentence > But once I learned about infinite series, I could no longer see math as a tower. Nor is it a tree, as another metaphor would have it. It
by auggierose 5y ago
The closing sentence
> But once I learned about infinite series, I could no longer see math as a tower. Nor is it a tree, as another metaphor would have it. Its different parts are not branches that split off and go their separate ways. No — math is a web. All its parts connect to and support each other. No part of math is split off from the rest. It’s a network, a bit like a nervous system — or, better yet, a brain.
is also something I recently read in similar form in Saunders Mac Lane's "Mathematics: Form and Function":
> We cannot realistically constrain Mathematics to be a single formal system; instead we view Mathematics as an elaborate tightly connected network of formal systems, axiom systems, rules, and connections. The network is tied to many sources in human activities and scientific questions.
- refset 5y agoAlso reminiscent of Stephen Wolfram's recent thinking about the "Ruliad"[0], which I initially heard him discussing during the keynote at the recent re:Clojure conference: https://www.youtube.com/watch?v=FzbWAiu50MU&t=3200s https://www.youtube.com/watch?v=FzbWAiu50MU&t=3200s [0] https://writings.stephenwolfram.com/2021/11/the-concept-of-the-ruliad/ https://writings.stephenwolfram.com/2021/11/the-concept-of-t...
- auggierose 5y agoInteresting read. Why I am not sure about "Ruliads" :-), it led me to a previous post of his [0], where he talks about how he found the minimal axiom system for classical propositional logic. [0] https://writings.stephenwolfram.com/2018/11/logic-explainability-and-the-future-of-understanding/ https://writings.stephenwolfram.com/2018/11/logic-explainabi...
- zmgsabst 5y ago