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I have been interested in philosophy for a while and I was just curious on what you guys thought about this question. On one hand you have a science that is able to (basically) relate all the bodies in this reality in terms of quantity and space with rigorous proofs. On the other you have a science that is trying to describe the universe, but it lacks the rigor that math has.

user13772496
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    Physics is math+experiments – Mauro ALLEGRANZA Jun 19 '20 at 05:59
  • As Mauro said, physics uses math. – Cotton Headed Ninnymuggins Jun 19 '20 at 06:03
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    *Pure* math can not explain anything real, it is a collection of detached abstractions. Once they are corresponded to something real the math is no longer pure, it is applied and a tool of science. And such correspondence is never "rigorous", it is a limited model. The choice you speak of does not exist. "*As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality*", Einstein. – Conifold Jun 19 '20 at 13:41
  • Physics is a specific kind of math + experiments. And the math it uses is specifically "engineered" to apply to the reality as much as we can make it. – rus9384 Jun 19 '20 at 15:44
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    Neither, it's your mind trying to explaining reality (assuming it exists *and* accessible for mind to make sense)... – Double Knot Aug 26 '22 at 06:22
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    "Mathematics is the art of giving the same name to different things."-Henri Poincare. See The Unreasonable Ineffectiveness of Mathematics in most sciences https://philosophy.stackexchange.com/questions/92058/the-unreasonable-ineffectiveness-of-mathematics-in-most-sciences/92064#92064 Also 'How the laws of physics lie' by Nancy Cartwright https://joelvelasco.net/teaching/120/cartwright-How_the_Laws_of_Physics_Lie.pdf – CriglCragl Aug 26 '22 at 09:41
  • Neither one explains anything at all. Nothing that humans do gives an explanation. – Scott Rowe Aug 26 '22 at 12:11

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Physics, and in general science, is all about developing "models" that we hope fit to physical reality as much as possible. Fitting criteria are explanation of current observation (that is not necessarily the pure reality in its essence as the observation might well be restricted by not only the instruments but also the current paradigm and theories of the science branch) with least amount of assumptions and desirably with simpler models, and at least a little bit prediction power broadening our current view of the physical world.

The models central to this endeavor is heavily math oriented/based/expressed-in but they usually are more than this. Beside the strong math involvement in the models, they include certain presuppositions resembling axioms of mathematics (but not being the same) or principles. Contrary to mathematical axioms they are quite open to change or complete disposal and typically extending.

Despite its central role in physical world model development, math itself alone is not about real world explanations in its pure form.

mami
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Mathematics can be used to model all possible universes, but it does not tell us which one is the one we inhabit. Physicists can choose one of these models and experimentally determine whether or not it correctly describes the particular universe we inhabit.

niels nielsen
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  • As an example, mathematics has the [surreal numbers](https://en.wikipedia.org/wiki/Surreal_number), which is a very large number system. It shows up in things like game theory. Is it applicable to reality? Well, we do indeed use it to describe games, but current mainstream scientific belief is that all systems in reality can be described using only real numbers, which are *much* smaller than the set of surreal numbers. Whether there is something in "reality" that cannot be explained with these real numbers is an open question, but currently we choose models with reals. – Cort Ammon Aug 26 '22 at 14:52
  • @CortAmmon, yes, agree, thanks for your comment. -NN – niels nielsen Aug 26 '22 at 15:55
  • what a lovely answer. –  Aug 27 '22 at 00:33
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Math is sort of a thought experiment, if certain assumptions were to be true what would happen. However in reality we don't know whether these assumptions are true, we only assume that.

Pure math isn't bothered by that, if they are true then it describes the real world, if they aren't then it describes a world different from reality. Whereas physics is highly bothered by that because it's interested in what the real world looks like. So physics makes heavy use of math to build models and run simulations and thought experiments, but crucially relies on experiments and observations in order to verify them, while math doesn't care if they are true.

So unless pure math just happens to be completely based on true assumptions there's a good chance that it will need some updates sooner or later to correct the course and better describe the real world and the process of conceiving these "updates" would be called science.

haxor789
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