Difference between Physics and Mathematics

[Office_Shredder]

I thhink that a difference may be articulated as: doing Physics specifically requires Mathematics, while doing Mathematics has only the general dependencies on facts of Physics that doing anything has.

I think this is missing the point that doing physics is *not* doing mathematics. It uses mathematics as a communication tool, but there are plenty of examples where a physicist says 'then I do xyz and get a prediction", and the mathematicians say 'well wait that computation wasn't valid', and then the physicist does an experiment and what do you know their prediction was correct.

A lot of physics is taking a situation where calculation is infeasible, asserting things must be true because come on, physics, and then solving the remaining math problem. I think it does physics a great disservice to think the thing in the middle is irrelevant, and the bulk of the field is the first and third step.

Like, if Albert Einstein *only* speculated that the speed of light was the same for all observers, and asked someone else to do the math, we would still know all about special relativity. Identifying the new axiom was the interesting part, the rest was just verification. You don't even really need to do any math to get a decent number of interesting predictions from this idea.

 

[symbolipoint]

Isn't that a bit like the difference between Literature and Language, in the sense the latter is necessary foundation for the former, and the former eventually influences the latter?

Mathematics is a type of language used to quantify (or measure) things, and also map out relationships of/among things, and it's a way to communicate quantitatively about the world we observe. Physics is like literature in which we describe the world we observe, and sometime invoke mathematics to quantitatively describe on observation, like one would use a sentence (collection of words) to qualitatively describe an observation.

I wasn't very good at analogies on those standardized tests like the SAT.

You picked a very helpful analogy, in this case.

 

[sysprog]

One perhaps noteworthy difference is that I've seen where the OP in this thread, @fresh_42, said "I am no physicist", but I think that he would never say 'I am no mathematician', and if he did, he'd be wrong.

 

[Buzz Bloom]

I confess I did not read all of the 38 preceding posts, but I did scan them looking to see if the point I make below was preciously discussed. I failed to find any, so I proceed.

The difference between mathematics and physics is that a proved theorem in math may reasonably be believed to be true with 100% certainty, while there is no physics statement for which it is reasonable to believe it is true with 100% certainty.

In math the truth is based on the definitions of the concepts being discussed, rather than what is in the physical world. There is no need for any physical evidence to conclude a theorem proof is correct. On the other hand belief in the correctness of descriptions of physical phenomena is based on the degree of experimental evidence supporting the description's correctness. The reason this is never 100% certainty is that there is always a possibility that future experiments may find a flaw in the correctness of the descriptions of physical phenomena.

 

[fresh_42]

Isn't that a bit like the difference between Literature and Language, in the sense the latter is necessary foundation for the former, and the former eventually influences the latter?

This is the physicist's point of view. Mathematics is more than the language for physicists. It is a different mindset.