Undergrad What are some good arguments against mathematics being discovered?

[murshid_islam]

What are some good arguments against mathematics being discovered (or for it being invented)?

 

[FactChecker]

IMO, it's a mixture. On one hand, mathematicians invent methods and techniques that humans can understand. Also, many techniques are invented to apply mathematics in other subjects such as physics, astronomy, etc. On the other hand, many truths are discovered when their proofs are derived.

 

[Nugatory]

Seeing as how mathematics has already been discovered, this question is counterfactual. Compare with "What are some good arguments against the sun having risen in the east this morning?" - there aren't any.

That makes it hard to conduct a sensible discussion within the forum rules so this thread is closed. (As with any thread closure, we can reopen for further comments if someone has more to say - PM any mentor to ask).

@murshid_islam you might want to read https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

 

[jedishrfu]

In reply, this is a debate that will never be answered. We develop math from patterns we see and we develop math for some abstract problem we created. Much of math is discovered as in the pythagorean theorem but there are areas of math like topology that worlds unto themselves and later become tools in more practical matters.

Feynman had a talk (Cornell Messenger Lectures) about needing math for a 3D problem and the mathematician in his story well I have just the answer an N dimensional mathematics. Feynman would say no no no, I just want it for 3D use. Later he sheepishly goes back to the mathematician and asks for the N dimensional math.



Prof GH Hardy was proud that his work on pure mathematics had no bearing on anything military or anything practical until someone realized it could help in cryptography. He detested war.

https://en.wikipedia.org/wiki/G._H._Hardy

Here is a whole reddit thread on the debate:



and a BBC program on it:

https://www.sciencefocus.com/science/was-maths-invented-or-discovered

As well as NOVA's The Great Math Mystery