I'm majoring physics, but really interested in mathematics.

I liked physics since it was really beautiful to have an analysis on a nature with mathematical tool. However, the more i study, the more it seems like physics is not like what i thought it was. It's not because physics don't use mathematics, but because professors don't teach mathematics. Mathematical physics is an example. One can check that it's not precise at all.

Many physicists say that "Physics is totally different from mathematics" and don't like to treat physics as an application of mathematics. (Mathematicians too don't like people treating mathematics as a tool for physics. Aren't you?) I agree both, but i believe one could influence on another. Who is the inventor of calculus? and Who thinks Lorentz is nothing compared to Einstein? Hilbert said, "Physics is too hard for physicists".

Anyway, I haven't decided yet, but i think I'm going to major theoretical physics (I even have some mind to change my major to mathematics) and i have a great interest in set theory. However, i see there are only few set theoriest relative to other branches of mathematics professors. One day, i visit a topology professor and asked some questions about set theory. I was so surprised that he doesn't even know what is ZFC, and he suggested me to study another mathematics rather than set theory which is 'tedious' to do. Well, I think it's not tedious at all, but it's something fundamental.

However, there is a problem. It's going to take a really long time to study proper set theory. To make it clear, 'I'm not interested in sets, but interested in precisely studying mathematic starting from ZF or ZFC'. It's almost impossible for me to study both physics and mathematics..(Maybe possible! If i study really hard.. Any experience?). Should i change my major to mathematics to be a mathematical theoretic physicist?

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    $\begingroup$ If I were you I would do it $\endgroup$ – Seyhmus Güngören Nov 12 '12 at 23:22
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    $\begingroup$ Yes, there aren't many things more infuriating than a physicist (or god forbid, an engineer) tells me that "mathematics has no intrinsic content, it is only a tool for physics". $\endgroup$ – Asaf Karagila Nov 12 '12 at 23:31
  • $\begingroup$ Most mathematicians don't care much about axiomatic set theory. It's like most novelists don't care much about linguistics. $\endgroup$ – Makoto Kato Nov 13 '12 at 0:04
  • $\begingroup$ @Makoto: that is a pretty strong claim. Can you back it up somehow? $\endgroup$ – Asaf Karagila Nov 13 '12 at 5:35
  • $\begingroup$ @AsafKaragila OK. It seems. They usually don't get into axiomatic set theory in their papers or textbooks. $\endgroup$ – Makoto Kato Nov 13 '12 at 16:20

The first thing I must remark is that all things take a long time to master. It takes somewhere between seven to ten years to truly master something. So time should not be a factor if you enjoy something.

The second thing I must remark is that many topologists today are doing algebraic topology or dimension theory and have nothing to do with the axioms of ZFC. For them set theory can be very tedious, and depending on their personality they will either cancel it or just appreciate it from afar. There are, however, people who do set theoretical topology and they will agree that set theory has its merits (but still might recommend that you learn more).

I'm biased, really biased, in favour of set theory. I believe that if you feel that you are interested in it then you should definitely go for it. In particular axiom of choice stuff. There is so much open, and the mathematics can be very beautiful.

However I should also add that set theory, and mathematics in general, is not always what it seems to be. You should study more than just set theory on a more than superficial level, because someday you might find yourself bored with set theory and you might want to do something else. Of course these things could come up naturally (e.g. if you work on testing mathematical objects without the axiom of choice, you will invariably have to learn more about vector spaces; if you apply infinitary combinatorics to groups, you will have learn about group theory; and so on).

To sum up, I am biased but I think that you should go for it. Set theory can be fun!

(As a historical side remark I should probably add that until the 1950's or so there was only a vague distinction between mathematicians and physicists, and before the 1800's there was hardly any distinction at all.)


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