How Important Is Physics to a Mathematician?

In summary, there is a common belief that physics provides a fertile ground for new ideas in mathematics, as seen in historical examples such as Newton inventing calculus to solve physics problems and Fourier inventing Fourier analysis to solve engineering problems. Today, it is often said that particle physics, QFT, and string theory offer numerous ideas for mathematicians to research. While some universities require math students to take a course in general physics, the connection between physics and mathematics is not always clear. It ultimately depends on the career a mathematician wishes to pursue, with some areas of mathematics, such as geometry and topology, having more connections to modern physics than others. However, there is no clear consensus on the importance of physics to mathematicians, with some like
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I was just wondering about this, because I've heard it quite often that physics is fertile ground for new ideas in mathematics, historically and currently. In the past we can think of Newton inventing calculus to solve physics problems, Fourier inventing Fourier analysis (now that sounds odd; I doubt he named it after himself, but way to go if he did!)-- or what mathematicians today call Harmonic Analysis-- to solve engineering problems and so on. Today, I've often heard it said that particle physics, QFT, string theory etc. provide many ideas for research for mathematicians. How true is this?

How much physics should the mathematician and a mathematics student know? I am reading Peter Woit's book Not Even Wrong and he's convinced me phyics is very important to the research mathematician. Woit received his PhD in physics, but then moved to mathematics. I've also heard this opinion expressed a countless number of other times, from Witten, Atiyah (an admirer of Witten, btw), Bott, Hermann Weyl and many others, to pick on the famous people (I have forgetten most of the places I have heard this). Even in http://www.math.ohiou.edu/~shen/calculus/chen1.pdf" .

Most universities require math students to have at least a course in general physics, so appearently they think there is some worth in learning physics. How much should you know? I myself have taken courses in EM, QM and classical mechanics, but I have never seen anything I found usefull in any of my mathematics courses, since the only math that ever seems necessary is vector calculus and differential equations, not particularly interesting areas of mathematics in my opinion.

Any thoughts?
 
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It depends very much on the career you want to pursue. If you want to go into applied math you need to know something about the area of application, such as physics, engineering, statistics, economics, etc. On the other hand you could use Hardy or Erdos as a model and just work in pure mathematics, presumably as a teacher.
 
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To most mathematicians, physics is no more "important" than to any other person- which is a good reason for university students to take a physics course. But very very few research fields in mathematics have any connection to physics.
 
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HallsofIvy said:
To most mathematicians, physics is no more "important" than to any other person- which is a good reason for university students to take a physics course. But very very few research fields in mathematics have any connection to physics.

That's not what Sir Michael Atiyah thinks:
http://www.wlap.org/umich/phys/colloq/2002/winter/atiyah/

Apparently Raoul Bott was influenced greatly by Edward Witten's work too.
http://www.crm.umontreal.ca/Bott08/index_e.shtml

Also check out:
www.pnas.org/content/85/22/8371.full.pdf
http://www.cgtp.duke.edu/

It seems that mainly geometry and topology have connections to modern physics.
 
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It seems that mainly geometry and topology have connections to modern physics.
That is too narrow. Quantum theory relies heavily on probability theory. Group theory is important also in quantum theory. Calculus, diff. eq., complex variables, etc. are widely used also.
 
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I did not have to take a physics class when I was an undergrad. I probably wouldn't see much of a connection since I did a lot of discrete math (which is obviously the best field within mathematics).
 
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Dragonfall said:
I did not have to take a physics class when I was an undergrad. I probably wouldn't see much of a connection since I did a lot of discrete math (which is obviously the best field within mathematics).

Mathematicians do not need to learn any physics unless they want to do applied math in physics. Physicists, on the other hand, must have a good background in mathematics.

Why is discrete math the best field? To me, whatever your field is, it is a matter of taste more than anything else.
 
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Indeed it is a personal preference. I just like it very much.
 
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I am a mathematician studying algebraic topology and I have no interest in physics. However, this is very subjective. One could argue that physics propells mathematical research. I disagree; in fact, I spend much of my time at work setting young physics and engineering students in the right path as far as the mathematics they are doing. But to do real mathematics, one doesn't need any knowledge of physics to be successful. The intuition one may think they have after doing some physics may even be a detriment. In practice, it is usually the case that the mathematics is developed first and only later are applications found by scientists.
 
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Related to How Important Is Physics to a Mathematician?

What is the relationship between physics and mathematics?

Physics and mathematics are closely related fields, as both involve the study of patterns and relationships in the natural world. Mathematics provides the language and tools for understanding and describing physical phenomena, while physics uses mathematical principles to build models and theories that explain the behavior of the physical world.

How does physics benefit a mathematician?

Studying physics can benefit a mathematician in several ways. It can provide them with real-world applications and examples for the abstract concepts they learn in mathematics. It can also help them develop critical thinking and problem-solving skills, as well as an appreciation for the beauty and elegance of mathematical principles in action.

Can a mathematician become a physicist?

While there are many mathematicians who also have a strong understanding of physics, the two fields require different sets of skills and approaches. It is possible for a mathematician to transition into studying physics, but they would need to gain a thorough understanding of the fundamental concepts and principles of physics.

What specific areas of physics are most relevant to mathematicians?

There are several areas of physics that are particularly relevant to mathematicians, including classical mechanics, electromagnetics, and quantum mechanics. These fields involve complex mathematical concepts and principles, making them of interest to mathematicians who enjoy solving challenging problems.

Is a background in physics necessary for a mathematician?

A background in physics is not necessary for a mathematician, as the two fields are distinct and can be pursued separately. However, having some knowledge of physics can enhance a mathematician's understanding and appreciation of mathematical concepts and their real-world applications.

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