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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.

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    Physics is math+experiments Commented Jun 19, 2020 at 5:59
  • As Mauro said, physics uses math. Commented Jun 19, 2020 at 6:03
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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
    Commented Jun 19, 2020 at 13:41
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    Neither, it's your mind trying to explaining reality (assuming it exists and accessible for mind to make sense)... Commented Aug 26, 2022 at 6:22
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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 philosophy.stackexchange.com/questions/92058/… Also 'How the laws of physics lie' by Nancy Cartwright joelvelasco.net/teaching/120/…
    – CriglCragl
    Commented Aug 26, 2022 at 9:41

3 Answers 3

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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.

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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.

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  • As an example, mathematics has the surreal numbers, 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
    Commented Aug 26, 2022 at 14:52
  • @CortAmmon, yes, agree, thanks for your comment. -NN Commented Aug 26, 2022 at 15:55
  • what a lovely answer.
    – user62233
    Commented Aug 27, 2022 at 0:33
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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.

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