Pure Mathematics vs Physics

[Akzis]

For privacy reasons, I'll abstain from posting my college/professors/programs, etc.

I've recently decided to switch trains and head from the murky waters of biology into the beautiful world of mathematics. I'm already set on a major in math, but I was going to try and get into med school afterwords.

So, which one of the forementioned should I [try to] get a PhD in? Theoretical mathematics or theoretical physics? One constrained by a harsh mistress -- nature -- which may or may not respond, the other only by it's own good logic.

[Toad]

Theoretical physics is a harsh route to go down. Research the post doc on it and look into how most people live. I don't have any links at the moment (can't find them), but I know that you really have to love it to get a PhD in it.

[Monte314]

I faced this same choice, and I found the decision boiled down to a matter of "precision".

I began my undergraduate studies in Physics, and found that I had a terrible time figuring out when to make simplifying approximations (e.g., small-angle approximation for a simple pendulum). This is an essential skill that becomes more important the farther you go into the subject. Virtually all modern physics is grounded in the characterization of boundary value systems (piles of differential equations with initial conditions), or other methods involving limiting processes that are intractable by direct methods, and have no closed-form solutions.

When I realized this, I switched to mathematics, which I find to be much more "precise" and satisfying (it is a lot more versatile, too, which is nice in a tough job market). I often still function as a "bridge technologist", standing in the gap between physical theory and practical engineering applications; this satisfies my occassional desire for "tangibility". And, along the way, I've learned when to make simplifying approximations!;)

[ScottH]

In my 40's now, I know what I would choose in your shoes: mathematics.

My reasoning is similar to Monte's, though I've not his experience (I'm a CS guy).

It seems to me if you want to have a long, satisfying career with many options open to you, you can't go wrong with mathematics. If, on the other hand, you want to roll the dice at that once in a life time discovery of something no other human has found, physics is a great choice, but more than 99% of them find no such reward.

[Anemoi]

I think Mathematics is your best choice. If you still like biology, you can explore different areas (computational biology for example).

I like physics too so I was reviewing the admissions requirements for Physics MS/PhD and they're very harsh. Prospective students have to pass through a lot of exams in very narrow topics in Physics making it almost impossible for example, to an engineering major to apply and be considered for admission.

Have you considered Biomedical Engineering? It contains biology (not the murky part) and a rigorous formation in mathematics.

[Asocialkat]

I had an acquaintance in college whose parents did NOT accept her desired math degree. Apparently, it is the "liberal arts" of the sciences. :p