This came up as a tangential in relation to whether math is a thing we're discovering, or inventing:
Suppose we meet with an alien race: their symbols, and even ways of computation might be different than ours, but putting 2 pebbles, and 1 pebble on a table will map to their concept of "3". This is because physics provides a grounding for experimentation on various theories. On the other hand, there is a lot of "fanfic" in Math -eg category theory's Monads- for which there is no such easy grounding. On the middle hand, there are things which can be mapped to the 1st category, and therefore have grounding by relation.
This question pivots mostly around the term "grounding", so for the purpose of this question, I'd define grounding as: results being convertible into physical observations (which do not, by themselves contain the computation itself -no computers re-implementing the same thing allowed!).
Using this (or if ill-defined, closest by intent) definition, what proportion of Math is grounded in Physics? To put it in the larger context, what is the lower estimate on intersection of potential common mathematical understanding between 2 alien races?
Edit: okay, this thread seem to have a problem of gravity wells. I'd like to highlight, that this is specifically not a "bring your pet theory to work" topic.
For this reason, I've added a bounty.
Bounty, and answer acceptance specifically goes for an answer, which has the following structure:
- describes a reasonable methodology (of fermi estimation, of approximation methods, of any reasonable form of method), and a list of specific assumptions it makes.
- For example: you can ask physicists of all the math they've learned what proportion do they use during their work; deduce what proportion of "all math" is being taught to physicists, and thereby reach an estimate. This is totally a thing you can do.
- works through the methodology from the specific assumptions given, to reach an estimate conclusion
- concludes with a specific number (this was the question), optionally with an upper, and lower bound.
Numerical, quantitative methods, inspired by sociology, economics, or math very much preferred; so is grounding things into numbers as much as possible; methods, or possible ways of attack will also be upvoted. Please kindly keep a firm quantitative perspective when posting in this topic. Thank you.