Why did you choose math over physics or vice versa?

What i have heard is that if you see beauty in the way nature works, do physics. If you see beauty in the way logic works, do math.

Can you guys expand on that?

fresh_42
Mentor
What i have heard is that if you see beauty in the way nature works, do physics. If you see beauty in the way logic works, do math.

Can you guys expand on that?
Well, I think one could write complete books dedicated to this question. I find an easy answer is the following:
What do we commonly regard as beautiful?
Let's start with a subject that is innocuous: music. Sooner or later we will end up with cadences, which are patterns of symmetry and repetition. And both can be physically as well as mathematically described by the same means: symmetries and repetitions. They might be called interference, frequency or symmetry group, but this only changes language, not the underlying principle. And I think it generally pleases us, if we somehow recognize those patterns, whether intuitively with our ears or intellectually by mind.

Orson
Well, I think one could write complete books dedicated to this question. I find an easy answer is the following:
What do we commonly regard as beautiful?
Let's start with a subject that is innocuous: music. Sooner or later we will end up with cadences, which are patterns of symmetry and repetition. And both can be physically as well as mathematically described by the same means: symmetries and repetitions. They might be called interference, frequency or symmetry group, but this only changes language, not the underlying principle. And I think it generally pleases us, if we somehow recognize those patterns, whether intuitively with our ears or intellectually by mind.
Before I got into math I was a music major (ran out of money for that years ago). I played jazz guitar for 10 years, then 10 years of classical guitar. Then I didn't play as much and got into math. So really I consider myself a musician, but I do it without the notes now. :)

vela
Staff Emeritus
Homework Helper
What i have heard is that if you see beauty in the way nature works, do physics. If you see beauty in the way logic works, do math.

Can you guys expand on that?
I think that describes how I ended up pursuing physics in the end over math. When I was an undergrad, I read many books on physics and math. One thing I noticed was I just didn't identify with the joy mathematicians seemed to find in their subject, whereas I was really drawn to the the ideas and concepts of physics, particularly in particle physics and cosmology. I was driven to learn about physics at a more technical level whereas I never felt that way about most topics in math. That said, I've really enjoyed and found interesting almost all of the math classes I've taken. I would hope you don't see it really as an either-or choice, but as two subjects that complement each other.

I doubt that.
I think Mathematics was discovered/invented because of the study of the world. If we hadn't studied and observed the world first, I doubt if we would get to mathematics. There is no defined frontier between Mathematics & Physics. "For some results or discoveries, it is difficult to say to which area they belong: to the mathematics or to physics" (https://en.wikipedia.org/wiki/Relationship_between_mathematics_and_physics#Philosophical_problems).

"At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" —Albert Einstein, in Geometry and Experience (1921). I'm not suggesting that Mathematics is a branch of Physics, of course not, but, Mathematics and Physics and its relationship are not clearly defined, and I'm sure that some aspects of, for example, Superstring Theory may belong to mathematics. But, this is just my opinion.

I think Mathematics was discovered/invented because of the study of the world.
Almost. Much like early writing, math's origins are in the exceedingly dull and practical world of counting and measuring for property and taxation. Early societies didn't have the luxury of doing science, but they did want land and money (in the form form of livestock and such). The Egyptians and Babylonians did figure out that math could be fun and put a few recreational problems in their teaching material, but mostly it was the Greeks who took it to the next level of abstraction.

-Dave K

symbolipoint, Logical Dog and fresh_42
Aufbauwerk 2045
I thought briefly about becoming a math major. But I decided to major in physics because I liked science fiction when I was growing up, and I was fascinated by space travel, radioactivity, nuclear power, lasers, SETI, gravity, relativity, particle accelerators, time travel, warp drives, transporters, antimatter, electron microscopes, holography, and so on.

I saw that physicists got to build and work with amazing devices. I love the way physics allows us to uncover nature's secrets so that the world is no longer so mysterious, and we can control it to some extent. By the time I was at university I also hoped that physics would answer the whole "meaning of life" question or at least enable us to contact aliens who know more than we do.

As for the whole beauty thing, that is not my motivation, but I do admit I am attracted to equations that can explain nature and in fact even looking at equations is a bit of an emotional experience. Consider Maxwell's equations, for example. Even the symbols are beautiful. Writing them is such a pleasure. I particularly like calculus and differential equations. This is one reason I don't like working with computers even though I must at times. I miss that hands-on experience of writing equations or drawing diagrams with a pen or pencil.

I enjoy pure math to some extent, but I really only care about math because it is the language of physics. I don't like solving puzzles just as an intellectual exercise. In other words in physics I get the thrill that comes from knowledge, but not just any knowledge. It's the knowledge that leads to nuclear power, for example.

To sum up, I want to understand how nature works and at least to some extent get control over it and bend it to my will.

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Logical Dog
blue_leaf77
Homework Helper
I think Mathematics was discovered/invented because of the study of the world.
I am not well informed about such history but even if that's true, it doesn't change the fact that today you can study math without knowing physics.

fresh_42
I am not well informed about such history but even if that's true, it doesn't change the fact that today you can study math without knowing physics.
As I said, math was invented for accounting. Fortunately you can study math without that too. :D

-Dave K

fresh_42
Mentor
As I said, math was invented for accounting. Fortunately you can study math without that too. :D

-Dave K
My personal understatement of the day!

dkotschessaa
As I said, math was invented for accounting. Fortunately you can study math without that too. :D

-Dave K
Indeed hahah. But remember Physics is an excellent source of inspiration for Mathematics. You can study Mathematics without Physics, of course, but the study of Physics lead to branches such as Calculus, many contributions in Topology, etc...

Quoting Pierre Bergé, Des rythmes au chaos: " For some results or discoveries, it is difficult to say to which area they belong: to the Mathematics or to physics." If a mathematician finds a result that could belong to Physics, but has no prior knowledge on it, well, he/she may mix both areas, and some Physics may be required.

For studying Mathematics you don't need Physics at all, but for every Mathematician, I'll encourage to have the very basics of Physics while doing research. You don't know what you can find...