Math or physics

  • Thread starter ehrenfest
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  • #26
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That's a very arrogant and foolish thing to say. Their understanding of the material probably far exceeds yours, and I bet they could reproduce any of those derivations without much trouble. It is clear that you value memorization highly, but understanding is far more important.


I bet your wrong. I am not saying I could reproduce the derivations either ... I am not sure why you think that was arrogant or foolish. It was my assessment of their understanding.

I am also not saying I value memorization. In fact, I hated the biology and organic chemistry classes that relied so much on memorization. When you understand something like electromagnetism or classical mechanics really well, you can basically just remember the main ideas of a derivation and the details will follow. When you understand the subject poorly, you need to recall all the details to complete the derivation.
 
  • #27
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if you like proofs i can't imagine why you like physics.

Haha that's a good point. I am not saying I only like proofs though. This discussion is really rocking what I thought was a straightforward career path in theoretical physics. The consensus seems that I should go into math. I was kind of planning of just doing lots of math on the side but devoting my career to physics...but I don't know...do you think it is possible to do math "on the side" i.e. actually publish in math journals even though I would have a PhD in theoretical physics? It seems like Witten has done that quite succesfully?
 
  • #28
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OK. So I have been thinking and rethinking and rerethinking my decision of whether to go to grad school in physics or mathematics and my original plan to go to grad school in physics never seems to produce anything but hesitation and unhappiness in me. I was planning to take the physics GRE in the fall, so I kept telling myself I should start preparing for that but then I would just go read Rudin's Principles of Mathematical Analysis. So, I think I am done seesawing back and forth and will finally just decide to go to grad school in math. Almost every post here is an indication that this makes more sense. I still want to do work in mathematical physics but as everyone here has said the best way to approach that is through mathematics not physics. My research interests (string theory, general relativity, the standard model) have not really changed at all throughout this.

I guess one of my main reservations was that I am doing an REU in physics this summer and I felt like that kind of compelled me to go into physics. I wrote in my REU application that I definitely wanted to get a PhD in theoretical physics, so I kind of feel like that was one reason that they accepted me and that I would be kind of a traitor if I did not do that. This summer won't be totally wasted if I apply to math progams and say I am interested in mathematical physics, right? That is what I am scared of since an REU is a major commitment and I will be hard to stay motivated if I know that

Hopefully, I will get a math REU next summer. I think I am basically going to take 3 semesters of graduate math courses only so hopefully that will be enough to get me into one of the best grad schools.

Thanks everyone for your input. This is why I love PF: I could never have made an informed decision about this just by talking to my friends and family, almost none of who are mathematicians or physicists.

Everyone please comment liberally here about what I wrote--I spend way too much mulling and not enough time discussing my thoughts--so I need to know that what I wrote is not hogwash to other people.
 
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  • #29
I agree with the above posts as well. Job prospects are wayyyy better with a Math or Stats phD than with a theoretical physics degree. Plus math is just better. I minored in physics and I felt like there was way too much to memorize in terms of concepts/vocab/formulas (and too many damn symbols). With math, all you need are a few definitions, theorems, and you can go from there. If you enjoy Rudin, you are destined to go to Math grad school.
 
  • #30
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If you enjoy Rudin, you are destined to go to Math grad school.

Rudin is like a deity to me.
 
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  • #31
I agree with the above posts as well. Job prospects are wayyyy better with a Math or Stats phD than with a theoretical physics degree. Plus math is just better. I minored in physics and I felt like there was way too much to memorize in terms of concepts/vocab/formulas (and too many damn symbols). With math, all you need are a few definitions, theorems, and you can go from there. If you enjoy Rudin, you are destined to go to Math grad school.

On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.
 
  • #32
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On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.

I have heard that before but it really depends on what part of physics you are talking about. That is probably true for classical mechanics but it is definitely NOT true for something like condensed matter physics.
 
  • #33
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On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.

no i think it's you who hasn't studied for long enough. almost all of physics is phenomenology and by virtue of that a collection of formulas. yes someone did derive them all from one model but practicing physicists and apprentice physicists(students) don't. go ahead i dare you to derive the potential due to a sphere from gauge invariance. hence the wide use of formula sheets in physics classes.

math is no different though as far as that goes. every discipline uses reference books.

the actual difference between math and physics is that there are no contradictory theorems in math. in physics there are regions of accuracy for certain theories and outside those regions they contradict other theories.

the point is that one does not go to school to learn how to solve specific problems so the formulae themselves are irrelevant. one goes to school to learn how to learn effectively and solve general problems. of course one of the most effective problem solving techniques is to read the pertinent literature(look at the formulae).
 
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  • #34
almost all of physics is phenomenology and by virtue of that a collection of formulas.

That's extremely misleading. In theory the phenomenological results could be irreducibly complex, but that's not the case. And I never said one model, I said few.

And in the example that you brought forward to supposedly put me in my place-- what is more elegant than classical electrodynamics? How could you possibly give an example in the most elegant, concise beautiful theory in physics to show irreducible complexity?? Do you realize how absurd that even is!

Maxwell's Equations you use to derive potential due to a sphere, also the equations are manifestly gauge invariant. Two birds, one stone. There, satisfied?

You know, I'm surprised that you have to throw in more wrong headed things while you're at it. Saying that physics is filled with contradictions... it would be a contradiction if quantum mechanics was completely different from classical mechanics. Instead it is a logical extension of the theory, take the classical limit and guess what? you get back the old theory. How is that a contradiction?
 

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