## The Should I Become a Mathematician? Thread

Recently I encountered a book "Mathematical problem solving methods" written by L.C.Larson. There are many problems from the Putnam competition.
My question is: how important is it for a physicist (mathematician) to be able to solve this kind of problems.

 Recognitions: Homework Help Science Advisor well it is not essential, but it can't hurt. I myself have never solved a Putnam problem, and did not aprticipate in the contest in college, but really bright, quick people who do well on them may also be outstanding mathematicians. My feeling from reading a few of them is they do not much resemble real research problems, since they can presumably be done in a few hours as opposed to a few months or years. E.g. the famous fermat problem was solevd in several stages. first peoiple tried a lot of sepcial cases, i.e. special values of the exponent. None of these methods ever yielded enough insight to even prove it in an infinite number of cases. Then finally Gerhartd Frey thought of loinking the problem with elliptic curves, by asking what kind of elliptic curve would arise from the usual equation y^2 = (x-a)(x-b)(x-c) if a,b,c, were constructed ina simple way from three solutions to fermat's problem. he conjectured that the elliptic curve could not be "modular". this was indeed proved by ribet I believe, and then finally andrew wiles felt there was enough guidance and motivation there to be worth a long hard attempt on the problem via the question of modularity. Then he succeeded finally, after a famous well publicized error, and some corrective help from a student, at solving the requisite modularity problem. He had to invent and upgrade lots of new techniques for the task and it took him over 7 years. I am guessing a Putnam problem is a complicated question that may through sufficient cleverness be solved by also linking it with some simpler insight, but seldom requires any huge amount of theory. However any ropqactice at all in thinking up ways to simplify problems, apply old ideas to new situations, etc, or just compute hard quantities, is useful. I would do a few and see if they become fun. If not I would not punish myself.
 Recognitions: Homework Help Science Advisor you could start a putnam thread here perhaps if people want to talk about these problems and get some first hand knowledge. but in research the smartest people, although they often do best on these tests, do not always do the deepest research. that requires something else, like taste, courage, persistence, luck and inspiration. One of my better results coincided with the birth if one of my children. Hironaka (a famous fields medalist) once told me, somewhat tongue in cheek, that others had noticed a correlation between making discoveries and getting married, and "some of do this more than once for that reason". I have noticed that success in research is in the long run, related to long hard consistent work. I.e. if you keep at it faithfully, doing what you have noticed works, you will have some success. Don't be afraid to make mistakes, or to make lengthy calculations that may not go anywhere. And talk to people about it. This can be embarrassing, but after giving a talk on work that was still somewhat half baked, I have usually finished it off satisfactorily. Here is an example that may be relevant: Marilyn Vos Savant seems to be an intelligent person, who embarrassed many well educated mathematicians a few years back with a simple probability problem published in a magazine. But she not only cannot do any research in the subject without further training, but even does not understand much of what she has read about mathematics. Still she has parlayed her fame into a newspaper column and some books. The great Grothendieck, so deep a mathematician that his work discouraged Rene Thom from even attempting to advance algebraic geometry, once proposed 57 as an example of a prime number. But he made all of us begin to realize that to understand geometry, and also algebra, one must always study not just individual objects or spaces, but mappings between those objects. This is called category theory. that is why the first few chapters of hartshorne are about various types of maps, proper maps, finite maps, flat maps, etale maps, smooth maps, birational maps, generically finite maps, affine maps, etc....
 If someone wanted to get a Ph.D in mathematical physics should you pursue an undergrad degree in math or physics. I would like to eventually like to do research in M theory but as a Mathematical physicist. Thanks in advance for your reply.

 Quote by courtrigrad Do most people major just in math? Or do they have a minor in something else? ... What are some good combinations?
i didn't minor in anything else but a subject where math is used heavily might be not hurt. physics, economics or computer science combined with math are somewhat obvious choices. statistics and computer science would be a good combination if you're interested in raking in far more $$than any engineering, comp sci or business student. depending on your interests, statistics and biology (biostatistician=$$\$), statistics and economics, statistics and another social science (psych, soc, etc) might be good combinations.

 It depends on where you go to college what minors and majors will be available to you. At the college I go to, as part of the applied mathematics curriculum, we're required to get at least a minor in some other field, and as it is a tech school, the options are limited to mostly engineering and science fields.
 Recognitions: Homework Help Science Advisor we need input from some mathematical physicists here. my acquaintances who were mathematical physicists seem to have majored in physics and then learned as much math as possible. on the other hand some lecturers at math/physics meetings seem to be mathematicians, but i do not elarn as much ffrom them sinbce i want to understand the ophysicists point of view and i already nuderstand the amth. i would major in physics if i wanted to be any kind of physicist and learn as much math as possible to use it there.

 Quote by fournier17 If someone wanted to get a Ph.D in mathematical physics should you pursue an undergrad degree in math or physics. I would like to eventually like to do research in M theory but as a Mathematical physicist. Thanks in advance for your reply.
you could do an undergraduate degree in combined maths & physics, and afterwards you can pursue with a phd in theoretical physics (synonymous with mathematical physics).

 Recognitions: Homework Help Science Advisor from pmb phy: pmb_phy pmb_phy is Online: Posts: 1,682 Quote: Originally Posted by mathwonk by the way pete, if you are a mathematical physicist, some posters in the thread "who wants to be a mathematician" under academic guidance, have been asking whether they should major in math or physicts to become one. what do you advise? I had two majors in college, physics and math. Most of what I do when I'm working in physics is only mathematical so in that sense I guess you could say that I'm a mathematical physicist. I recommend to your friend that he double major in physics and math as I did. This way if he wants to be a mathematician he can utilize his physics when he's working on mathematical problems. E.g. its nice to have solid examples of the math one is working with, especially in GR. Pete