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This is going to sound insane but... would it not be nice, if there was no need for numbers (except for counting like in subscripts)? Mathematicians talk about eliminating the Axiom of Choice, because of the craziness of the Banach-Tarski Paradox. But the paradoxes numbers create are even crazier.

  1. It is possible to create a numerical function called the Busy Beaver function that lets you prove the Goldbach conjecture (a statement about an infinite set of numbers) by testing it on every number from 1..BB(n) (a finite, although very large, set of numbers).
  2. Gödel's theorems require arithmetic in order to construct the true-but-unprovable sentences. No numbers and such sentences cannot be made.
  3. Numbers give rise to Berry's paradox (there is nothing analogous to it without numbers), which in turn gives rise to the undefinability of an information compression algorithm, even though humans rely on being able to calculate the Kolmogorov complexity of information in day-to-day life.

Has some eccentric mathematician talked about moving maths beyond numbers just like how some mathematicians talked about moving beyond sets in order to define the field of one element?

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closed as primarily opinion-based by Alex2006, puppetsock, Roger, Mołot, Morris The Cat Aug 20 at 14:54

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Slightly confused about this - do you mean "Math without the specific symbolic representation we now call 'numbers'" (i.e. could we have come up with a different symbolic representation), "Math without any symbolic representation", or "math without symbolic manipulation"? $\endgroup$ – LinkBerest Aug 20 at 3:52
  • $\begingroup$ Also do you mean "high-level" mathematics or everyday math like counting (which we definitely did way before symbols were introduced)? $\endgroup$ – LinkBerest Aug 20 at 3:58
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    $\begingroup$ Finally, how is this involved in building a world? If it is not you might be better off asking on Math.SE - though expect more comments like mine seeking clarification. $\endgroup$ – LinkBerest Aug 20 at 4:04
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    $\begingroup$ This sound more about math philosophy than world building. And it would be nice if you provided some explanation of each thing you mentioned, for those who didn't grow up with bread and math. $\endgroup$ – L.Dutch Aug 20 at 4:28
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    $\begingroup$ Urdula K. Le Guin is one of the greatest scifi writers ever and she describes an alien race that did just that in one of her books. Also this may be relevant, though not a duplicate: worldbuilding.stackexchange.com/a/52386/21222 $\endgroup$ – Renan Aug 20 at 14:26
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Doing that would cripple mathematics and sciences.

Imagine a world where accountants and engineers do arithmetic, and mathematician do theoretical work on geometry and the like. But something keeps the two groups from talking to each other in a systematic way.

No calculus for engineers. No statistics for epidemiologists. No trigonometry for surveyors.

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  • $\begingroup$ Perhaps there's a better concept that is superior to numbers. The concept of average is outclassed by the concept of distribution, for instance. $\endgroup$ – BalancedTryteOperators Aug 20 at 20:00
  • $\begingroup$ @BalancedTryteOperators, I don't see that. You need numbers to talk about statistics. $\endgroup$ – o.m. Aug 21 at 4:33

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