# Mathematics path for physics?

1. Feb 16, 2016

### Devin

Hi, I wish to not only learn, but prove every theory I come across. This requires a ton of math research, and at this point, I am about to begin quantum mechanics, and general relativity after I finish up my differential geometry book. My question, I suppose, is after I finish differential geometry, and tensor calculus (assuming I've met all the prereqs for it), what mathematics and physics should I learn before I do 1) Lorentz force derivation, 2) Quantum (chromodynamics and electrodynamics)

2. Feb 16, 2016

### rootone

Your next step is whatever you think is the most interesting.

3. Feb 17, 2016

### Staff: Mentor

What does that mean? How do you "prove" a physical theory?

4. Feb 17, 2016

### Devin

I thought it to be implied that proof, and or derivation of any of the mathematical constructs involved, and for that, I apologize.

5. Feb 17, 2016

### Devin

thank you :)

6. Feb 17, 2016

### bigfooted

Gerard 't Hooft (Nobel prize physics 1999) has a long list of topics he thinks you should study if you want to become a good theoretical physicist. He also gives some subtopics and links to online lecture notes.

My opinion is that physics and mathematics knowledge should be acquired following a pyramid structure: you need a lot of general physics and mathematics (calculus, differential equations, classical mechanics) before you can move to more advanced topics. If your path toward specialist knowledge is too narrow, your fundamental understanding in certain related fields is too weak and you will not be able to fully comprehend/appreciate the theory and you will certainly not be able to contribute to the field.

7. Feb 17, 2016

### bcrowell

Staff Emeritus
None of the fancy math you describe is necessary in order to derive the Lorentz force. (Actually, it's ambiguous to say that you want to "derive the Lorentz force." It would have to be derived from some assumptions that you consider more fundamental.)

8. Feb 18, 2016