Should a physicist learn math proofs?

[complexPHILOSOPHY]

absolutely, a physicist who does not learn math proofs, his belly button falls off. and chikldren laugh at him when he walks down the street with his best girl.

Fantastic! That sounds like something you say when you are tripping. Or atleast something i'd say.

I love you.

 

[Moridin]

The mathematics part of physics shouldn't be just to learn how input the right values and find the magical answer. Some level of understanding is crucial, even though it might not be full proofs, but a general or brief knowledge of the area in terms of derivation. Does a rock climber need to understand his gear to be a successful rock climber? Not really, but if he does, it might come in handy.

 

[andytoh]

We've gotten a lot of mixed opinions. I believe the following is the MINIMUM mathematical rigour requirement of all physicists who use mathematical tools on a regular basis:

A physicist needs not study the proofs of mathematical theorems that he uses, but he MUST be able to (better yet, actually do it) prove the basic properties of each mathematical tool that he uses.

For example, if a physicist uses Lie groups, he must be able to prove that GL(n,R), C-{0}, products of Lie groups, etc... are indeed Lie groups. If he uses homotopic functions, he must know how to prove that homotopic functions form equivalence classes, that compositions of homotopic functions are homotopic, that the fundamental group is in fact a group under composition of homotopy equivalence classes, etc...

These elementary results are not difficult and by being able to prove them, the physicist will get a stronger feel for what the mathematical tool really is and how it works. This is the minimum proving requirement for physicists in my opinion, and such basic proving skills will make the physicist better in his usage of the mathematical tools.

 

[mathwonk]

complex philosophy, i get the impression we may be kindred spirits. or perhaps that you are holed up in a conservative religious school where rampant lunacy is outlawed. hang in there buddy, there is fun to be had in math land. as to tripping, this is not recommended by artificial means, math provides many outlandishly delightful journeys.