Question

Different Perspectives of Numbers: layman vs mathman

Answer 1

Saving this post just to see the dumpster fire in the comments over the number theory remark

Answer 2

_harmonic anal_

Answer 3

I'm surprised you say topologists don't need more than the natural numbers. \mathbb{R} and [0,1] are two of the most importabt topological spaces. How do you find an n-dimensional manifold without reference to \mathbb{R}^n?

Answer 4

Differential geometry:

0 means I've just applied Stokes' theorem.

1 I don't care about.

2 is useful.

2pi means I'm making something an integer.

3 and 4 are cool, but 4 is too hard.

1/n! means I've messed up a summation convention or computed a volume.

No other numbers exist.

Answer 5

Some things you‘re saying are just utterly wrong.

Answer 6

I too search for counterexamples to the CH. That dang independence result usually gets in the way, however...

Answer 7

(Some) applied mathematicians: the only numbers are floating point numbers

Answer 8

Category theorists: scared of numbers

Answer 9

**Number Theory**

Numbers? Oh, you mean the most complicated and intricate geometric landscape in the entirety of math?

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Also,

>The set theorist is probably the first person to come to mind when thinking about numbers.

Out of everything even in the "Number Theory" portion, this is the most triggering.

Answer 10

We also use Z to index the homotopy groups in stable homotopy theory