Does Math Require Types

On this wiki there are pages such as DoesRelationalRequireTypes and ThereAreNoTypes.

Saying ThereAreNoTypes is like saying ThereIsNoMath? or ThereAreNoPeople?. What is the point of such silly pages?

This page was created because programming is very mathematical, and in math we find types very useful. Therefore logically it follows that in programming, we should also find types very useful.

Examples of types in math: http://www.purplemath.com/modules/numtypes.htm

Does math require types? Is that a silly question to be asking? Yes.

Worded differently, are types useful for humans, in math? If so, why not also in programming?

Some people, oddly, think types are not that useful in programs. Why? Programs are mathematical. The relational model is mathematical. So obviously types are very useful for humans, in both math and in programming.

If math students and teachers find types to be useful in math, what is the big problem with programmers finding types useful?

Note that I never claimed ThereAreNoTypes. Somebody else created that topic. My beef is that the definition of "types" is vague, yet some claim it's clear and use this claim to bully others on type-related topics. I believe that types are in the head, and every head may have a different model of them. Most people carry a general notion of types around in their head, just like we have a notion of "love", but that is not sufficient to solve borderline or controversial cases of "type-ness". --top