> numbers as the gateway to quantitative thinking

That's a historical artifcat, not an innate property. (Math was first invented in the Bronze Age for accounting and architecture.)

There's a theoretical parallel universe with a mathematics where numbers aren't first on the ladder but down there around number five. (Ironically computers are an example of that. Figuring out how to do numbers when all you have is finite sequences from an alphabet is advanced CS.)

Firstly are you so very sure he claimed that is an innate property? That Numbers are a gateway to quantitative reasoning seems a perfectly reasonable claim either way.

Secondly there are lots of mathematical objects that significantly predate the bronze age (eg https://en.wikipedia.org/wiki/Ishango_bone but there are others) and because these objects are so old we have no idea why math was first invented.

Thirdly I have no idea what relevance the theoretical “late numbers “ parallel universe but Tthis thread is about a book in this one.

> That Numbers are a gateway to quantitative reasoning seems a perfectly reasonable claim either way

This isn't true though. It's not supported by anything except Bronze Age tradition.

I.e., when teaching kids advanced math at an early age it's often better to skip numbers altogether and start with set theory or logic. Many kids find that a much easier gateway.

> I.e., when teaching kids advanced math at an early age it's often better to skip numbers altogether and start with set theory or logic.

What do you mean by "often better". Has it even ever been tried out?

I belive this is what was attemped in France (they taught set teory in an abstract way in elementary school), but with poor results and abandoned this approach after some time.

> Has it even ever been tried out?

Of course, and it's standard practice in some places.

P.S. I'm talking about extracurricular math clubs/circles. School curriculum is a separate thing that's divorced from actual math.

Math club for set theory before 1st grade and numbers? Do you have a link?

Set theory and logic stay below numbers, but they do not belong to quantitative thinking.

By definition, quantities, either discrete or continuous, as already classified by Aristotle, are the properties that can be expressed by numeric values, as a result of counting for discrete quantities, or as a result of measuring for continuous quantities.

Properties that are not quantities, but which can be compared, to determine which is greater or less, or if they are equal, are qualities.

The simplest numbers, i.e. cardinal numbers a.k.a. natural numbers, are equivalence classes of sets, so indeed the theory of numbers is built upon that of sets (a.k.a. multitudes in older language), but this does not contradict in any way the title from the book, because quantitative thinking refers to only a part of mathematics, not to all of ite.

Super interesting that geometry is about going beyond what we can see since in my limited world view it is more specifically that which we can see..

That's where geometry starts -- in the same way as numbers start by counting on fingers. When you run out of fingers, numbers keep going. When you run out of visible dimensions, geometry keeps going too.