August 8th, 2016, 09:31 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 257 Thanks: 23 Math Focus: Number theory  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.

August 8th, 2016, 09:40 PM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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.)

August 8th, 2016, 10:03 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra 
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. 
August 9th, 2016, 12:59 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 644 Thanks: 184 
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. 
August 17th, 2016, 03:25 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,037 Thanks: 674 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
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! 
November 2nd, 2016, 07:24 PM  #6 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,251 Thanks: 112 
I don't think that physics is a subset of math. Rather, I think that those two intersects in a large area.

November 3rd, 2016, 12:51 PM  #7 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 257 Thanks: 23 Math Focus: Number theory 
I had read from a Russian guy at physics forums years ago that mathematics is allinclusive when it comes to physics, that all physics is based on math theory, but that physics does not describe math.

November 23rd, 2016, 02:00 AM  #8 
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4 
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.

November 23rd, 2016, 03:55 AM  #9  
Math Team Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra  Quote:
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 pointsources of waves or pointmasses. Maths doesn't have suns or planets or electrons or quarks.  
November 24th, 2016, 06:13 AM  #10 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 257 Thanks: 23 Math Focus: Number theory 
Black holes are massive yet are called singular. Some pointlike particles like fermions or bosons correspond to an antisymmetric (sine) or symmetric (cosine) wavefunction.


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