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August 8th, 2016, 09:31 PM   #1
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Is physics a subset of math?

The critical distinction I see is physical measurement mostly requiring uncertainty. Math can formulate uncertainty, or exclude it entirely.
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August 8th, 2016, 09:40 PM   #2
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Physicists make extensive use of mathematics, and some have made significant contributions to mathematics, but I don't think physics can be considered a subset of mathematics. Linguists also make use of mathematics and a few have actually contributed to it (e.g. the Chomsky hierarchy in discrete mathematics, though it's usually studied by computer scientists). But surely one wouldn't say linguistics is a subset of mathematics. The crucial difference is, I think, that physics studies the world, while mathematics is not contingent on it. Though much of mathematics has been successfully applied to the world, a lot of mathematics starts out pure (Hardy's NT, for example.)
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August 8th, 2016, 10:03 PM   #3
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There is much of physics that is outside of mathematics, not least the experimental/observation side of the discipline. Physics theories are also very different animals to mathematical theories.

Theories in physics are ideas about how the universe appears to work. There are there to be confirmed or disproved by observations. In most cases, physicists are actively looking for the flaws in the theories because that is how knowledge advances.

Mathematical theories are true. There is no expectation that anyone will find a flaw in them. And if someone did, it would be a setback to knowledge.
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August 9th, 2016, 12:59 AM   #4
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Applied Physics, AKA Engineering, has processes that have no explicit mathematical solution, although mathematics can (and does) help.

A simple example would be the construction of a road embankment.
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August 17th, 2016, 03:25 AM   #5
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Mathematics is the discipline of turning coffee into theorems.

Physics is the discipline of drinking coffee and trying not to be sidetracked by all of the pretty pictures!

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November 2nd, 2016, 07:24 PM   #6
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I don't think that physics is a subset of math. Rather, I think that those two intersects in a large area.
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November 3rd, 2016, 12:51 PM   #7
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I had read from a Russian guy at physics forums years ago that mathematics is all-inclusive when it comes to physics, that all physics is based on math theory, but that physics does not describe math.
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November 23rd, 2016, 03:00 AM   #8
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According to me, there are commonalities for sure, and some shared techniques like logic, but you cannot really say physics is a subset of mathematics.
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November 23rd, 2016, 04:55 AM   #9
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Quote:
Originally Posted by Loren View Post
I had read from a Russian guy at physics forums years ago that mathematics is all-inclusive when it comes to physics, that all physics is based on math theory, but that physics does not describe math.
I would say that that is akin to suggesting that (physical) books are a subset of the printing industry. Every book is created using techniques of the printing industry but (almost) none of them describe it.

However, if that were true, where does the content of books come from? The printing industry doesn't write stories or histories or (many) academic papers. Clearly books have more than the printing industry provides.

Similarly, mathematics provides techniques and models that physics uses to describe the universe. But physics doesn't have any point-sources of waves or point-masses. Maths doesn't have suns or planets or electrons or quarks.
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November 24th, 2016, 07:13 AM   #10
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Black holes are massive yet are called singular. Some point-like particles like fermions or bosons correspond to an antisymmetric (sine) or symmetric (cosine) wavefunction.
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