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Mathematics Without Numbers (1959)

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75 points measurablefunc | 1 comments | 02 Dec 25 01:08 UTC | HN request time: 0.3s | source
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jbandela1 ◴[06 Dec 25 23:31 UTC] No.46177607[source]▶
I think the biggest mistake people make when thinking about mathematics is that it is fundamentally about numbers.

It’s not.

Mathematics is fundamentally about relations. Even numbers are just a type of relation (see Peano numbers).

It gives us a formal and well-studied way to find, describe, and reason about relation.

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1. somewhereoutth ◴[07 Dec 25 00:53 UTC] No.46178210[source]▶
The most commonly used/accepted foundation for mathematics is set theory, specifically ZFC. Relations are modeled as sets [of pairs, which are in turn modeled as sets].

A logician / formalist would argue that mathematics is principally (entirely?) about proving derivations from axioms - theorems. A game of logic with finite strings of symbols drawn from a finite alphabet.

An intuitionist might argue that there is something more behind this, and we are describing some deeper truth with this symbolic logic.