God created the real numbers

Isn't this article conflating our formalism of a given abstract entity (like real numbers or integers) with the abstract entity itself? Surely quantities existed long before humans (e.g. there was a quantity of stars in the Milky Way 1 million years ago). And surely ordinals existed long before humans (e.g. there was a most massive star in the Milky Way 1 million years ago).

The article's claim seems to be about the mathematical formalisms humans have invented for integers and real numbers. And I agree that our formalism of integers is simpler and more elegant than our formalism of real numbers. But that could just be because we've done a worse job formalizing real numbers!

> And I agree that our formalism of integers is simpler and more elegant than our formalism of real numbers. But that could just be because we've done a worse job formalizing real numbers!

Everything you can express in integers you can express in reals, but there are many things expressable in reals not possible in integers. It would be surprising if the formalism for a thing that completely supersets another thing had an equally simple formalism

> [...] but there are many things expressible in reals not possible in integers

Are you sure there is anything we can express in the Reals that isn't an integer in disguise?

The first answer might be the sqrt(2) or pi, but we can write a finite program to spit out digits of those forever (assuming a Turing machine with integer positions on a countably infinite length tape). The binary encoding of the program represents the number, and it only needs to be finite, not even an integer at infinity.

Then you might say Chaitin's constant, but that's just a name for one value we don't know and can't figure out. You can approximate it to some number of digits, but that doesn't seem good enough to express it. You can prove a program can't emit all the digits indefinitely. And even if you could, is giving one Real number a name enough? Names are countable, and again arguably finite.

It seems to me we can prove there are more Reals than there are Integer or Computable numbers, but we can't "express" more than a finite number of those which aren't computable. Integers in disguise.

It seems like you're suggesting that mathematicians replace the reals with the computables. This is a reasonable thing to try, and is likely of particular interest to constructivists. There's even this whole field:

https://en.wikipedia.org/wiki/Computable_analysis