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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 – Mauro ALLEGRANZA Jun 19 at 5:59
  • As Mauro said, physics uses math. – Cotton Headed Ninnymuggins Jun 19 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 Jun 19 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 at 15:44
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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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