What are some good arguments against mathematics being discovered?

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Discussion Overview

The discussion centers on the philosophical debate regarding whether mathematics is discovered or invented. Participants explore various arguments and perspectives related to this question, touching on the nature of mathematical truths, the development of mathematical techniques, and the implications of these views in different contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that mathematics is a mixture of invention and discovery, where methods are invented for human understanding and application, while certain truths are discovered through proofs.
  • One participant argues that the question itself is counterfactual, suggesting that since mathematics has already been discovered, discussing arguments against this notion is nonsensical.
  • Another viewpoint emphasizes that mathematics is developed from observed patterns and abstract problems, indicating that while some areas of math are discovered (like the Pythagorean theorem), others (like topology) may be more about invention until they find practical applications.
  • References to historical figures such as Feynman and Hardy illustrate the complexity of the relationship between pure mathematics and its applications, with Hardy's work initially seen as non-practical until it found relevance in cryptography.

Areas of Agreement / Disagreement

Participants express differing views on the nature of mathematics, with no consensus reached on whether it is primarily discovered or invented. The discussion remains unresolved, reflecting a range of opinions and interpretations.

Contextual Notes

Some arguments depend on specific definitions of "discovered" and "invented," and the discussion does not resolve the implications of these definitions on the debate.

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

 
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