A Math Student's Dilemma: To Pursue Physics or Pure Mathematics?

[Group_Complex]

Hello guys. Some of you might remember my posts regarding the talent required to become a pure mathematician. I have done much introspection as of late, and I keep coming to the conclusion that I am not enjoying "Pure" mathematics as much as I thought I would. I originally became interested in science by thinking about physics and the nature of reality (I could not stop asking "why" as a child). In high school however, I developed a sense of mathematical elitism, I was good at mathematics (at least I thought I was at that stage) and came to believe that mathematics was the highest form of knowledge. This was in no doubt also a result of reading the writings of G.H Hardy, Bell and other mathematians who have admonished the applied aspects of mathematics.

Though I find developing a physicial intuition challenging, I am finding theoretical physics much more enjoyable than my Purer courses (Real+ Complex Analysis, Group theory). I do enjoy pure mathematics, but sometimes I find myself sitting with an abstract mathematical text infront of me, wondering "why am I doing this?". I find mathematics beautiful, but I am not sure if I could devote my life to working in Pure Mathematics. I still feel that going into theoretical physics is taking the easy way out, that Mathematicians will scoff at me for the rest of my life (There is a certain elitism amonst even Pure Math undergraduates). I also feel that a Mathematician will understand more Physics than a Theoretical Physicist will understand Pure Mathematics (I am not sure if this is correct, but It is a fear of mine). Edward Witten is very mathematical for instance, and I would like to work in a similar field, but I fear that this would result in me ending up in a mathematics department working in pure mathematical fields.

I want to go into the field which gives me the most "understanding", or the ability to ask "why?" as much as I can. I feel that Theoretical Physics is a field which interests me, but that it is also only applied mathematics, using tools developed by mathematicians, whereas the mathematician is the one who "Understands" what is going on. I feel like going down the Physics path would turn me into a hack who simply calculates using equations developed by mathematicians... If Physics is the science that models the universe, is not mathematics the field which explains Physics?

Sorry for the ramble. Any help would be appreciated.

 

[Steely Dan]

If Physics is the science that models the universe, is not mathematics the field which explains Physics?

The answer to this question always varies depending on who answers it, but the statement that "mathematics is the field that explains physics" is most certainly incorrect, for nothing about mathematics serves to explain what we see around us. All we physicists do is make models to help explain what we observe. I am fairly certain in saying that we can understand what properties an electron has without having a mathematical equation defining the electron (for example). Mathematics is indeed intimately tied to this; we could not have made our models nearly as precise as we have done so far, without the mathematical grounding. But nothing says that studying pure mathematics gives one the ability to reason in the same way a physicist would. Also, most of theoretical physics does not require more advanced mathematical tools than one would learn at the undergraduate or graduate level (it is only people like Ed Witten who do, in fact, use that information on a regular basis -- there are theoretical physicists who don't do string theory or cosmology, as it happens ;P).

But I think the much more important issue here is that the whole point of obtaining an education and receiving an education is to study what you enjoy. Quite frankly, you shouldn't be concerned at all with whether someone in a different field than you understands the material better than you do (a proposition which I find quite unlikely to begin with). The point of studying physics or mathematics is not to prove to anyone else that you have superior conceptual knowledge of either subject. We do this because we enjoy discovering new things about the nature of our world, and you have to practice before you can do that. So my advice is to think not about what preparation you want to have accomplished, but what you want to do with said preparation. And then take the route which most directly allows you to achieve that goal. If what you really want to do with all the knowledge you will obtain in your studies is to uncover new facts about the physical universe, then be a physicist. There's absolutely no shame in that. Maybe some or most pure mathematicians do have what it takes to do research in physics, but that's not the route they have chosen. That shouldn't influence your own choice.

And never forget that the labels are arbitrary to begin with. We are all working to improve our collective understanding of the world, and we all play a role.

 

[Group_Complex]

The answer to this question always varies depending on who answers it, but the statement that "mathematics is the field that explains physics" is most certainly incorrect, for nothing about mathematics serves to explain what we see around us. All we physicists do is make models to help explain what we observe. I am fairly certain in saying that we can understand what properties an electron has without having a mathematical equation defining the electron (for example). Mathematics is indeed intimately tied to this; we could not have made our models nearly as precise as we have done so far, without the mathematical grounding. But nothing says that studying pure mathematics gives one the ability to reason in the same way a physicist would. Also, most of theoretical physics does not require more advanced mathematical tools than one would learn at the undergraduate or graduate level (it is only people like Ed Witten who do, in fact, use that information on a regular basis -- there are theoretical physicists who don't do string theory or cosmology, as it happens ;P).

But I think the much more important issue here is that the whole point of obtaining an education and receiving an education is to study what you enjoy. Quite frankly, you shouldn't be concerned at all with whether someone in a different field than you understands the material better than you do (a proposition which I find quite unlikely to begin with). The point of studying physics or mathematics is not to prove to anyone else that you have superior conceptual knowledge of either subject. We do this because we enjoy discovering new things about the nature of our world, and you have to practice before you can do that. So my advice is to think not about what preparation you want to have accomplished, but what you want to do with said preparation. And then take the route which most directly allows you to achieve that goal. If what you really want to do with all the knowledge you will obtain in your studies is to uncover new facts about the physical universe, then be a physicist. There's absolutely no shame in that. Maybe some or most pure mathematicians do have what it takes to do research in physics, but that's not the route they have chosen. That shouldn't influence your own choice.

And never forget that the labels are arbitrary to begin with. We are all working to improve our collective understanding of the world, and we all play a role.

Thank you for the reply.

I just can't shake the feeling that if I go down the Physics path, I will have to rely upon mathematicians to show me why things are true, with my sole function being to convey experimental ideas to the mathematicians.

 

[Diracula]

I just can't shake the feeling that if I go down the Physics path, I will have to rely upon mathematicians to show me why things are true, with my sole function being to convey experimental ideas to the mathematicians.

Seems like you want to work in mathematical physics? Why not specialize in this area? I think this field is generally in physics departments, but is also sometimes in math departments.

It seems like you are just saying you don't want to be an experimentalist or a phenomenologist. There are more areas of physics than ones that "convey experimental ideas to the mathematicians". In fact pure mathematicians don't even touch physics by definition. They occasionally work on things that are found to apply to physics problems, but that is generally by accident with no immediate physical motivation and is discovered much later (by physicists).

 

[Matrix0]

I can understand your dilemma and the conflicting thoughts you are experiencing. Both physics and pure mathematics are fascinating fields with their own unique challenges and rewards. It is natural to feel torn between the two and to question which path will lead to a deeper understanding of the universe.

Firstly, I want to assure you that there is no "easy way out" when it comes to pursuing a career in science. Both physics and pure mathematics require hard work, dedication, and a strong passion for the subject. It is important to choose a field that truly interests and motivates you, rather than basing your decision on external factors such as societal perceptions or expectations.

Secondly, I want to challenge the notion that theoretical physics is only applied mathematics. While mathematics certainly plays a crucial role in understanding and describing physical phenomena, it is not the only aspect of theoretical physics. Theoretical physicists also use creativity, intuition, and conceptual thinking to develop theories and models that explain the natural world. In fact, many groundbreaking theories in physics have come from individuals with backgrounds in both mathematics and physics.

Furthermore, I believe that the relationship between mathematics and physics is symbiotic. While mathematics can provide a framework for understanding physical laws, it is also deeply influenced and inspired by the discoveries and questions posed by physics. Both fields constantly push each other forward, leading to new insights and developments.

Ultimately, the decision between pursuing physics or pure mathematics should be based on your personal interests and strengths. If you find yourself more drawn to the conceptual and theoretical aspects of physics, then pursuing a career in theoretical physics may be the right path for you. However, if you have a strong passion for abstract mathematical concepts and enjoy solving complex problems, then pure mathematics may be a better fit.

In either case, I encourage you to continue exploring both fields and to keep an open mind. It is possible to combine elements of both physics and pure mathematics in your research and career, and there is no right or wrong answer. What matters most is that you find fulfillment and satisfaction in your chosen path.