[jdblair]

The book "Where Mathematics Comes From"[1] by Lakoff and Núñez makes a lengthy, detailed argument that numeracy is evolved, not universal. I didn't find myself agreeing with everything in it, but I no longer take it for granted that math is a universal concept.

[1] https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From

[barrkel]

Can you explain what you mean by evolved as opposed to universal?

Because from my perspective, they mean the same thing when applied to this context. That is, if numeracy is evolved, everyone is fundamentally numerate at some level. And if numeracy is universal, then everybody is fundamentally numerate. They're both nature, not nurture.

What do you mean by those words?

(Personally, I think that numbers are mostly learned, but that the brain has an evolved aptitude for symbolic systems, mathematics being just one of many. I don't think any innate concept of number goes much beyond order of magnitude (i.e. logarithmic) relative differences.)

[jdblair]

I mean, universal across the universe. There is a common assumption that mathematics is a common language that we could use to communicate with aliens. The notion is that, for example, the concept of prime numbers would be discovered everywhere in the universe just as an intelligence would discover that hydrogen is the simplest atom.

To go further, the Mathematical Universe Hypothesis formalizes the notion that the universe itself is math, and that we are just discovering the math of the universe as we develop mathematics.

I'm personally agnostic on the universality of mathematics. Math is a tremendous tool for describing the universe, but I am willing to consider that a different intelligence might invent some accurate and non-mathematical predictive model.

[beojan]

> The notion is that, for example, the concept of prime numbers would be discovered everywhere in the universe just as an intelligence would discover that hydrogen is the simplest atom.

The concept of prime numbers is a lot more fundamental than hydrogen being the simplest atom. You could conceivably have a universe where every element is an elementary particle, but you couldn't have a universe where you can put two and two together and get five. Nor could you possibly have a universe where you can take five of something, and divide it into equal sized groups, unless each group has one item or you only have one group.

[theoh]

This is a fine lecture by John Stillwell on the question of alien mathematics, and what might constrain it: https://youtu.be/9MV65airaPA