Mathematics: is it discovered or invented? TV Documentary

[SteveH]

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.

[Stranger]

For anyone wondering about the story of the number


https://en.m.wikipedia.org/wiki/1729_(number)

And here's the link that isn't broken by the trailing bracket: https://en.m.wikipedia.org/wiki/1729_(number)

[Harrowby Hall]

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.

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

[Stranger]

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.

I'm inclined to agree but things like complex numbers (involving the the square root of -1) seem to be invented. Then again, they seem to play a crucial role in quantum mechanics - but they were discovered/invented long before that.

IIRC Hannah Fry came to the conclusion of discovered in the program I referred to in the OP - I was rather irritated with the last episode, though, because she perpetuated some often used but totally inaccurate popularisations of science.

[jeremyp]

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?

[SteveH]

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

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). The size of a degree is of course invented: if we'd decided that a circle contained 500 degrees, then a triangle's internal angles would equal 250 degrees. What degrees measure, though, isn't invented.

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

Arithmetic is part of mathematics.

[Harrowby Hall]

Arithmetic is part of mathematics.

Indeed it is, but it is a minor part of mathematics dealing with rather mechanistic numerical activities. Your earlier post implies that mathematics is an extension of arithmetic. If instead of "and 2+2" you had written "for example 2 + 2" the implication would have been different.

I do admit that my relation with mathematics was not deep - I did study (decades ago) differential and integral calculus, complex numbers and matrix algebra and cannot recall much about them - but my recollection is that within these areas concepts and logic are paramount not just ordinal, interval and ratio relationships.

[jeremyp]

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).

But the "axiom" that makes it true was invented as were the alternative axioms that makes it not true.

[ad_orientem]

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

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

[Stranger]

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

No.

[ad_orientem]

No.

Then explain it to me.

[Stranger]

Then explain it to me.

jeremyp gave some examples in #6.

[ad_orientem]

jeremyp gave some examples in #6.

Sounds alot like splitting hairs to me.

[Stranger]

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.

[ad_orientem]

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

I suppose I don't.

[jeremyp]

Sounds alot like splitting hairs to me.

Is the difference between knowing howe to drive a car and knowing how to design and make a car splitting hairs? Because the relationship between a car driver and a car designer is roughly analogous.