Science
In reply to the discussion: Quantum Biology and the Puzzle of Coherence [View all]Joseph8th
(228 posts)... "has inspired many mathematical developments"
... "the development of quantum mechanics and some aspects of functional analysis parallel each other in many ways"
... "Use of geometry and topology plays an important role in string theory."
Yeah. That's what I said. I'm sorry if you're embarrassed, but I'm not wrong. Physical theories are comprised of models, which use math that is proven in theorems. But pure mathematics is NOT an empirical science. What physicists do with math is up to them, and I've already said that some cool physics has inspired some groovy math (calculus springs to mind), but we write proofs. When we want to prove Pythagoras' Theorem (triangle inequality), we don't measure the sides of the triangle and compare the numbers. That doesn't prove squat. We resort to abstract logic, completely divorced from 'reality' or empirical data.
If physicists then use the triangle inequality in their effort to explain, i.e., elliptical orbits, and need some sort of method to sum infinitesimal areas, inventing calculus in the process, it doesn't obviate the need to prove the Fundamental Theorem of Calculus mathematically -- that is, without recourse to empirical data or specific examples.
Even the definition of "mathematical physics" hints at the long-simmering animosity between pure and applied mathematics, and modern efforts to bridge that gap. My pure math profs still complain about all the "hand-waving" that applied math & physics profs use to make short cuts. My applied & physics profs don't disagree. I think most physicists would like to "put physical theories on a mathematically rigorous footing", but when you're trying to keep a rocket in space, it's less important to understand FTC than it is to be an equation monkey.
It still doesn't change the fact that it's a mistake to suggest that math is 'real' in nature, or that mathematics is a science. All my pure math profs call it the art of writing elegant logical proofs. Or as my number theory prof exclaimed, "I HATE numerals!"