Should a physicist learn math proofs?

[pivoxa15]

You need to know the tools, and how to use those tools correctly. This is true no matter if you're a theorist or an experimentalist. You don't, however, in most cases need to know how to make those tools. Of course there are exceptions to the case, but the question that was asked was not about "exceptions" was it?

Zz.

But for me, knowing the tools and knowing how to use it is not easy when the mathematics get complicated. It seem the only way to fully know the tools and know how to use it is by knowing how the tools work from first principles. i.e in second year QM, they start solving the equations of the Hydrogen atom with some fancy mathematics like Legedrel polynomials and I felt i didn't know what was going on. Even though I could use it on face value and do some calculations (i.e differentiations) to solve some basic problems. Without knowing the maths (i.e knowing the mathematics ground up) I felt I didn't understand the physics either although it was QM which makes things even more fuzzier.

 

[^_^physicist]

I am similar with pivoxa15, in that although I can use the tool, and in many cases figure out which tool to use without much refereance, I do not feel confindent in the rule unless I have either seen where the tool itself was proved (and can then I proceed to also go through the proof myself). And it isn't because I don't trust the mathematicians that came up with the tools; it is just a personal thing. I don't "know" the "tool" until I have seen where it comes froml, and have had a chance to fittle with the mathematical conclusions gained from it.

Take for instance, taking the derivitive of some function; I have no problem actually preforming the task, but I could not form a concept of how differenation worked or even how I it could be of any real use to physics, until I took an advanced calculus/intro to real anylsis course, which had nothing to do with physics. I guess my brain is just wired that way, but hey I go with what makes it easiest for myself to learn the tool

Granted, from a professional prespective (which I am just gauging a guess), the concept of working through the proof for the usage of a tool could, (and I would guess in many cases would) become quite cumbersome.

Being that I am still a student, what I may state could be utter nonesense; however, I feel the discouragement of learning proofs does a diservace to physics students; as it both artifically distances physics from mathematics and discourages the development of possible new uses of "old tools."

Of course that's just my revised 2-cents on the subject.

 

[ZapperZ]

But for me, knowing the tools and knowing how to use it is not easy when the mathematics get complicated. It seem the only way to fully know the tools and know how to use it is by knowing how the tools work from first principles. i.e in second year QM, they start solving the equations of the Hydrogen atom with some fancy mathematics like Legedrel polynomials and I felt i didn't know what was going on. Even though I could use it on face value and do some calculations (i.e differentiations) to solve some basic problems. Without knowing the maths (i.e knowing the mathematics ground up) I felt I didn't understand the physics either although it was QM which makes things even more fuzzier.

There seems to be some confusion here in terms of "knowing mathematics" and "using in the workings of a typical physicist". I was tackling the latter.

The FACT that you have to take math classes as an undergrad means that you have to know how some of these mathematical idea came from. There's a pedagogical reason for that. It allows you to have a flavor of how such things came into existence. No one here, and certainly not me, would tell you not to study such a thing.

But the ORIGINAL question, if you recall, wasn't this! It is on whether, someone who is a physicist and have gone through years of education (and necessary studying), would need to know mathematical proofs to be able to perform his/her job as a physicist. I believe that I should not have to repeat everything I have said here already in answering that question.

Zz.

 

[pivoxa15]

There seems to be some confusion here in terms of "knowing mathematics" and "using in the workings of a typical physicist". I was tackling the latter.

The FACT that you have to take math classes as an undergrad means that you have to know how some of these mathematical idea came from. There's a pedagogical reason for that. It allows you to have a flavor of how such things came into existence. No one here, and certainly not me, would tell you not to study such a thing.

But the ORIGINAL question, if you recall, wasn't this! It is on whether, someone who is a physicist and have gone through years of education (and necessary studying), would need to know mathematical proofs to be able to perform his/her job as a physicist. I believe that I should not have to repeat everything I have said here already in answering that question.

Zz.

Good point, I should get back to study...

 

[Werg22]

It depends, I would say. Some physicist are mathematically inclined while others are "chemically" inclined.

 

[pivoxa15]

It depends, I would say. Some physicist are mathematically inclined while others are "chemically" inclined.

"chemically" as in more experimental or "chemically" as in more hand waving? Although the two go hand in hand at times because the real world is so complex.

 

[Werg22]

Go figure . I, for one, get very bothered by the idea of using a mathematical concept without knowing it's substance, which includes proofs. It's the satisfaction of mastery, I guess.

 

[pivoxa15]

Go figure . I, for one, get very bothered by the idea of using a mathematical concept without knowing it's substance, which includes proofs. It's the satisfaction of mastery, I guess.

Same as me, that is why I am leaning towards the mathematician road although I find nature extremely fascinating and exciting as well.

 

[tim_lou]

Well, in general, a physicist probably wouldn't care about something like the proof of a derivative using delta and epsilon... Just like in my mechanics class. When we see differential equations, he usually says... let's try a solution of the form... bla bla bla... while in my calc 4 class, my prof. goes over operators and such and derive the solution from scratch instead of "trying" solutions.
My guess is many physicist just get a sense (a justification) of what is probably right about the tools they use.

 

[mathwonk]

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.

 

[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.