What is the Role of a Mathematical Physicist?

[SpanishOmelette]

probably, I am a home-utored student(self-teaching!) and I'm seeking a little help.

While I am drawn to MANY forms of physics or mathematics, the mathematical physicist seems to be the ticket. But I am not sure.

I was just wondering if this would be a good way to go, and what exactly is the purpose of the mathematical physicist?

Blessings,
Mahmoud.

 

[CalcNerd]

Generally works for large corporation (R&D or applied mathematics) or University (teaching), unless you are gifted on the order of world class. Your statement of self-taught would generally indicate you may not survive teaching (you may end up disgusted with students who need to much help when you know with effort they could do it, after all, you did).

Where are you at in your studies? It is hard to become good at something without some interaction.

In the US, home schooling is common for up to the High school level. However, I don't believe it serves the student well much past Junior high. Many Home schooled students are superior students up to and including High School, but at the High school level, they can only progress so far. Key concepts are sometimes missing in their education, and there is no way for them to discover their shortcomings.

 

[SpanishOmelette]

Hmm ok. So, degree would be needed?

R&D sounds pretty good though. I am just inspired by both Mathematis and physics, so I though this would be the perfect match.

Thanks for quick reply.

Jsut as a side-note, where does dynamics of non-linear systems (I.E. Chaos) fit in? M. Physics or A. Mathematics?

Thankyou.
Mahmoud.

 

[Cygnus_A]

R&D can be misleadingly glamorous when you first hear about it. Here's a vague glimpse at how mathematics might be used in industry: http://www.maa.org/mathematics-and-operations-research-in-industry

At some point you will need credentials to get into either industry or academia. A simple B.S. degree in Math, Physics, or Computer Science will suffice to get you to the next level (provided that you work hard and solve problems well). I would use the time during your B.S. degree to get research experience or internship experience, starting with your 2nd year. You will usually need to become acquainted with your professors before you can get involved in their research, which means taking classes in the subjects that you are interested in and doing well in them. Take as many classes as possible in every subject that interests you; this way you will be able to refine your interests.

Keep these four questions in mind during your undergraduate experience:
1) how can I get research and/or internship experience?
2) who will write me the most effective letters of recommendation? how will I earn their respect?
3) how can I keep my grades at a top level?
4) what tests or credentials are required upon graduation in order to be admitted to grad school or to get a job?

After your bachelors degree, the next level is either an entry level position at a company (where you likely will not use very much math), or a graduate degree in one of the three subjects listed above. After either an MS or a PhD, you will have the credentials to get into a job where you might use mathematics and/or physics, though it probably will be on a very specific subject with a very specific skill-set. If you maintain a wide variety of math/physics interests, a professorship will likely allow you to study the interesting things; however, an industry job will allow you to make more money.

Jsut as a side-note, where does dynamics of non-linear systems (I.E. Chaos) fit in? M. Physics or A. Mathematics?

Nonlinear dynamics is a broad subject that is difficult to penetrate deeply. At the forefront of modern research, nonlinear dynamics can be incorporated into just about every physics subject. It requires a very strong background in physics, calculus, statistics, differential equations, and numerical methods/computation.

 

[Arsenic&Lace]

Nonlinear dynamics is actively pursued by physicists and applied mathematicians.

To address your question about what an actual mathematical physicist is, this depends upon your definition of the term, which varies from individual to individual. Some people consider theoretical physicists and mathematical physicists to be identical. I personally view them differently. Mathematical physicists are mathematicians who work on physical theories, typically with the purpose of making the underlying mathematics more rigorous. Weyl and von Neumann are famous examples of this. The focus was on the mathematics; neither Neumann or Weyl really made direct contributions to physics (that I know of, I'm no historian). Theoretical physicists are more like Einstein; Einstein worked on the physical theories themselves, which are somewhat more qualitative, and was not as interested in or as skilled in the mathematics. Special relativity arises from pondering the physics and Einstein taking the philosophical stance that the laws of physics should hold in all reference frames; much of the physics here can be characterized without any mathematics, although of course the mathematics is vital at some point. By contrast, the Hilbert space formalism arises from, among other things, questions about how one can represent mathematically the state of a quantum system (in this case as a point in Hilbert space)