- #1

Ishida52134

- 139

- 0

thanks for the advice.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Schools
- Thread starter Ishida52134
- Start date

In summary: Algebra and Geometry were the first fields to be formalized in mathematics, and it's not surprising that they are the pillars. However, the rest of math is just as important, and mathematicians will tell you that there is no "pure" math anymore. The fields you mention are all important and have deep connections to other fields. For example, combinatorics is used in theoretical computer science, and probability theory is used in statistics and financial mathematics. Dynamical systems are used in physics and engineering. So don't let the label of "pure" math discourage you from pursuing those fields.In summary, the conversation discussed the dilemma of choosing between pure mathematics and theoretical physics for graduate school. The individual is equally interested in both fields and

- #1

Ishida52134

- 139

- 0

thanks for the advice.

Physics news on Phys.org

- #2

Hypersphere

- 191

- 8

That said, mathematical physicists is often taken to mean the people that try to put parts of theoretical physics on a rigorous (i.e. acceptable to mathematicians) foundation. That might be right for you (hard to tell), but certainly doesn't imply taking an equal number of physics and mathematics grad courses.

- #3

Ishida52134

- 139

- 0

By taking an equal number of courses in both areas, I just mean that I am equally interested in both fields. And also, I have participated in both theoretical physics and pure math research groups before, so I still don't really know yet.

Then again, exactly what areas are considered theoretical physics and pure mathematics? Is nuclear physics theory and condensed matter theory considered theoretical physics, and is research in combinatorics, probability theory, and dynamical systems considered pure math?

I always thought that the main pillars of theoretical physics were quantum mechanics and relativity, and mathematics were algebra, analysis, and geometry. How exactly do those other topics fall in?

Then again, exactly what areas are considered theoretical physics and pure mathematics? Is nuclear physics theory and condensed matter theory considered theoretical physics, and is research in combinatorics, probability theory, and dynamical systems considered pure math?

I always thought that the main pillars of theoretical physics were quantum mechanics and relativity, and mathematics were algebra, analysis, and geometry. How exactly do those other topics fall in?

Last edited:

- #4

SophusLies

- 222

- 0

Ishida52134 said:For people like me, who like pure mathematics like algebra and analysis, as well as theoretical physics like quantum mechanics, general relativity, and elementary particle physics, would pursuing mathematical physics be the most reasonable path?

I'm assuming that you're a senior. As a math/physics person, I can that the best thing right now is talk to professors in each field, math and physics, and see the actual research. I spent a quarter as an undergrad working on a math research project, by the end of the quarter I knew that I didn't think like a mathematician enough to produce much. I also did the same, although many more quarters in physics research. Physics seemed much more natural for me to think of ideas and apply principles. For grad school, I applied to both math and physics departments but ended up choosing physics because of my affinity for it.

To be blunt, I've seen a lot of people that claim they can do both math and physics but in almost all cases they have strengths in only one. Experiencing the research of each subject should quickly show your decision.

- #5

Hypersphere

- 191

- 8

Ishida52134 said:By taking an equal number of courses in both areas, I just mean that I am equally interested in both fields. And also, I have participated in both theoretical physics and pure math research groups before, so I still don't really know yet.

Maybe SophusLies has the right approach then: which field are you better at and can hope to be more successful in?

If there is truly no way for you to decide, you might want to take a chance or use a random decision method. It's usually not entirely impossible to switch programs,and it's quite possible to work with a professor in the other department (at least within reason). Until then, there is certainly time to look more into research.

Ishida52134 said:BThen again, exactly what areas are considered theoretical physics and pure mathematics?

That is a classification issue which is ultimately down to subjective opinion and different choices of definitions. Essentially, some people consider "theoretical" an adjective, in which case theoretical physics is just a way to distinguish it from experimental physics, while others (mainly the public, apparently) seems to consider "Theoretical Physics" a proper noun encompassing the parts of physics cool enough to be the subject of TV documentaries. Actually, few physicists talk about "theoretical physics" if they get a chance to say "subfield X theory".

You might get a better idea by reading the relevant wikipedia pages, but there isn't really a final word on any of these.

Theoretical physics

Mathematical physics

Fields of mathematics

Pure mathematics

In the end, classification issues shouldn't matter that much. Early Jag Panzer might be considered a speed metal band, a (US) power metal band or a heavy metal band but the choice of genre doesn't change the sound of their music. The essence matters, not the label. (Feel free to replace this example by any other cultural entity without a clear genre.)

Ishida52134 said:Is nuclear physics theory and condensed matter theory considered theoretical physics, and is research in combinatorics, probability theory, and dynamical systems considered pure math?

Not always (see above). That is why you should try to find an area that interests you, without paying attention to how it's classified.

Ishida52134 said:I always thought that the main pillars of theoretical physics were quantum mechanics and relativity, and mathematics were algebra, analysis, and geometry. How exactly do those other topics fall in?

If quantum physics is considered a pillar, it would encompass condensed matter - at least the solid variety; as well as all of nuclear physics, particle physics, quantum information and so on. Quantum mechanics (and QFT) is more of a framework than a current research field (neglecting the associated challenges for mathematical physicists, that is). Basically, if you count QM and GR as pillars of theoretical physics, you are only leaving out the fields which use essentially classical physics, i.e. fluid mechanics, plasma, lots of accelerator physics etc. These fields can also be

As for math, the whole idea of "purity" as an ideal to strive for annoys me a bit. Anyway, combinatorics would usually be called pure I guess. According to the wikipedia link above, dynamical systems is considered part of pure mathematics too. Probability theory is a tricky one, as it is used throughout statistics and analysis (look up stochastic analysis) as well as number theory.

There are several important factors to consider when choosing a field of study for graduate school. These include your interests and passions, career goals, job market demand, potential for research and publication opportunities, and availability of funding and scholarships. It's important to carefully weigh all of these factors before making a decision.

To determine if a specific field of study is a good fit for you, it's important to do thorough research. This can include talking to current students and professors in the field, attending conferences and workshops, reading academic journals and publications, and even taking relevant courses as an undergraduate. It's also important to consider your strengths and weaknesses and how they align with the requirements and expectations of the field.

There is no one-size-fits-all answer to this question. It's important to find a balance between your interests and the job market demand. If you are passionate about a particular field, you are more likely to excel and find job satisfaction. However, it's also important to consider the job market and potential for employment after graduation. It may be helpful to speak with career counselors or professionals in the field to get a better understanding of the job market demand.

This ultimately depends on your career goals and personal preferences. A broad field of study may provide a more diverse range of job opportunities, while a specialized field may lead to more focused and in-depth knowledge. It's important to research the job market demand and potential career paths for both options before making a decision.

It is possible to switch fields of study in graduate school, but it may require additional time and effort. Some programs may allow you to transfer some credits, while others may require you to start from the beginning. It's important to carefully consider the implications of switching fields, such as the impact on your graduation timeline and availability of funding. It's also important to talk to advisors and professors in the new field to ensure it is a good fit for your interests and career goals.

Admissions
Advice to enhance my profile for grad school

- Replies
- 2

- Views
- 495

- Replies
- 20

- Views
- 851

- Replies
- 32

- Views
- 1K

Admissions
Graduate school admission chances

- Replies
- 7

- Views
- 2K

- Replies
- 3

- Views
- 599

- Replies
- 6

- Views
- 2K

- Replies
- 10

- Views
- 2K

- Replies
- 11

- Views
- 686

- Replies
- 24

- Views
- 3K

- Replies
- 7

- Views
- 1K

Share: