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For anyone wondering about the story of the numberhttps://en.m.wikipedia.org/wiki/1729_(number)

If it was invented, there could be different kinds of maths, and 2+2 could equal 5, or 1234567890, or anything we liked. Therefore, it's discovered.

OK Take the statement "the three angles of a triangle add up to 180 degrees. Is that discovered or invented?

You are confusing arithmetic with mathematics. They are not the same thing.

Arithmetic is part of mathematics.

It's discovered (with the caveat that we're talking about a triangle on a flat surface, not e.g. the surface of a sphere).

What's the difference? It's all sums ain't it?

No.

Then explain it to me.

jeremyp gave some examples in #6.

Sounds alot like splitting hairs to me.

Then you don't get it. Most of mathematics isn't about 'sums', that is, combining numbers to get a numerical answer.