Why did you choose math over physics or vice versa?

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In summary: I am currently in the process of introspection and reflection in order to determine whether I will apply to graduate school in physics or mathematics. I, like dkotschessaa, also view mathematics as more "pure" and more "perfect" than physics. On the one hand, there is physics which appears more superficially interesting and inspired, and on the other is mathematics, which to me, follows in the tradition of Plato's world of forms-something that transcends reality, something that transcends physics. Mathematics seems to me to be a truly sublime and magnificent edifice, beautiful and deep, yet elusive. Physics comes a lot more naturally to me, not to say that it is easy which it certainly isn't,
  • #1
Orson
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For a major or This could be related to career as well.
 
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  • #2
I like to think that Physics is math with a story. The two go hand-in-hand. You cannot study math without knowledge of physics and you cannot study physics without math.

I chose physics because I was curious on why and how things work in the universe.
 
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  • #3
Dopplershift said:
You cannot study math without knowledge of physics
I doubt that.
 
  • #4
The tutorial in physics had been scheduled at 8 a.m.
 
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  • #5
the possibly apocryphal quote of Feynman's relating physics to math as sex is to masturbation comes to mind.
 
  • #6
I chose math because it felt "perfect" to me. Physics felt kind of messy. Even within mathematics I prefer discrete type stuff. I do not like calculus/analysis or anything like that (the kind of math, incidentally, you do in physics).

I also liked the fact that it doesn't rely on experimentation but on pure reasoning, so you can do math or think about it anytime any where.
 
  • #7
Dopplershift said:
You cannot study math without knowledge of physics

blue_leaf77 said:
I doubt that.
As do I. There are many areas of mathematics that have no connection to physics.
 
  • #8
I enjoyed physics more.
 
  • #9
Mark44 said:
As do I. There are many areas of mathematics that have no connection to physics.
Physics is a basic scientific area in which the Mathematics you study really becomes alive. This is why "Physics is good for you", even if you don't really need it for Mathematics.
 
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  • #10
Physics in my opinion falls into the gap of being too pure to be useful but too applied to be beautiful, the end result is a field which is neither applied nor clean. I went from math to engineering, I never gave physics a thought because I always felt it was kind of a train wreck.
 
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  • #11
Crek said:
Physics in my opinion falls into the gap of being too pure to be useful but too applied to be beautiful, the end result is a field which is neither applied nor clean. I went from math to engineering, I never gave physics a thought because I always felt it was kind of a train wreck.

I always thought engineering looked more difficult than math or physics, because not only do you need to know math and physics, but you have to be able to do something useful with it. Whenever I saw the engineering majors at work, it looked like a lot of..well..work!

-Dave K
 
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  • #12
dkotschessaa said:
I always thought engineering looked more difficult than math or physics, because not only do you need to know math and physics, but you have to be able to do something useful with it. Whenever I saw the engineering majors at work, it looked like a lot of..well..work!

-Dave K

Engineering is based upon the principle of abstraction. Make good enough approximations, internal functioning doesn't really matter. Example: I don't know anything about semiconductor physics or semiconductor manufacturing but I make circuits using transistors because there exists a simplified abstract model which describes the device under the range of conditions I am interested in.

I would say engineering is closer to mathematics then physics actually.
 
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  • #13
I had always looked at math as a means to and end, what can I use it for.
 
  • #14
blue_leaf77 said:
I doubt that.

Have you ever taken a mathematical modeling course. The laws of physics apply there when modeling physical applications.
 
  • #15
Dopplershift said:
Have you ever taken a mathematical modeling course.
No I have not, but mathematics is not only about modelling physical phenomena, is it? Logic and algebra for instance, they need only a fine reasoning to work.
 
  • #16
Dopplershift said:
You cannot study math without knowledge of physics

This is not true.
 
  • #17
George Jones said:
This is not true.

Indeed it is not, and I stand as a living testament to this fact, as do numerous mathematicians.

Curious what @Dopplershift means by the statement. Probably something different than what he is actually saying.
 
  • #18
I am currently in the process of introspection and reflection in order to determine whether I will apply to graduate school in physics or mathematics. I, like dkotschessaa, also view mathematics as more "pure" and more "perfect" than physics. On the one hand, there is physics which appears more superficially interesting and inspired, and on the other is mathematics, which to me, follows in the tradition of Plato's world of forms-something that transcends reality, something that transcends physics. Mathematics seems to me to be a truly sublime and magnificent edifice, beautiful and deep, yet elusive. Physics comes a lot more naturally to me, not to say that it is easy which it certainly isn't, but it seems to suit my mode of thought more than does mathematics. Although I agree once again with
dkotschessaa about physics being messy, there is also a certain beauty in finding the patterns nested deep inside the mess.
 
  • #19
Crek said:
Engineering is based upon the principle of abstraction.
That is what all scientific discipline based upon. When a physicist solves a simple Atwood machine problem, he doesn't reason from first principles (even if his knows them - a beginning physicist does not - that would be downright madness), he reasons with high-level abstractions. And those high-level abstractions are built on the whole hierarchy of abstractions that go all the way down to the most basic, most fundamental physics theories. And the first principles that await us at the bottom of this hierarchy ladder... is just another bunch of abstractions.
 
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  • #20
Dopplershift said:
[...] You cannot study math without knowledge of physics and [...]
blue_leaf77 said:
I doubt that.
George Jones said:
This is not true.
dkotschessaa said:
Indeed it is not, and I stand as a living testament to this fact, as do numerous mathematicians.

Perhaps we can agree that at least from a historical point of view, mathematics and physics have some considerable overlap when it comes to their incremental discoveries/inventions. Some mathematical discoveries/inventions were made in the process of investigating physical phenomena (e.g. Newton's calculus), and some physical theories emerged by examining the underlying mathematics (e.g. Dirac's antimatter).

Heck, there is also some overlap between engineering and mathematics in certain mathematical discoveries/inventions. The mathematical fields of Information Theory and Digital Signal Processing fall into the realm of mathematics from start to finish, but it was and is engineering behind the driving force of their discoveries/inventions. (These fields are often taught and researched in the Engineering departments in universities, even though the fields are technically, purely mathematical.)

Of course it goes without saying that engineering and physics have some overlap. No need to say more on that.

[Edit: Corrected a quotation (I had copied and pasted the wrong part of the original quote).]
 
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  • #21
collinsmark said:
Perhaps we can agree that at least from a historical point of view, mathematics and physics have some considerable overlap when it comes to their incremental discoveries/inventions. Some mathematical discoveries/inventions were made in the process of investigating physical phenomena (e.g. Newton's calculus), and some physical theories emerged by examining the underlying mathematics (e.g. Dirac's antimatter).

And this is probably what @Dopplershift mean. Unfortunately it is not what he said.

And actually, I cold argue, if I wanted to, that the way math research is conducted these days is really Greek in flavor. But I won't. :D

-Dave K
 
  • #22
Elvis 123456789 said:
dkotschessaa about physics being messy, there is also a certain beauty in finding the patterns nested deep inside the mess.

I have no doubt there is, and I have it is clear that my characterization of messiness is an aesthetic one, i.e. one of taste, and not meant as a categorical statement.

I did some work in mathematical biology where we used differential equations to model tumor growth. Talk about messy. But I have to admit that the more I stared at the equations the more they kind of grew on me and I came to consider them beautiful ways of describing this particular system. So I imagine much of physics can be like that.

(Although I think I can do it better with cellular automata!)

-Dave K
 
  • #23
I think the discussion has deviated from what the OP wished.
Alright, to initiate the return to the original question, I will start by providing my answer. In my case, I was suggested by my mother to enter physics department on the ground that someone in our family had previously went to this department and now is having a prosperous life - she wanted me to follow his path. Although now our field of expertise is entirely different, he is in oil exploration while I am in atomic physics. My own choice at that time was not physics, I was inclined more towards either engineering or graphics and design. Math was not even among those I considered to enroll to. Despite not being my honest decision, being in physics major is fun. In physics you can get the access to both theory and experiment (I guess in pure math, no one ever talks about experiment). One of the joys, to me, is when seeing two curves one from experiment another from theoretical model that exhibits very good agreement. All the more if I were the one who produce both curves.
 
  • #24
Elvis 123456789 said:
I am currently in the process of introspection and reflection in order to determine whether I will apply to graduate school in physics or mathematics. I, like dkotschessaa, also view mathematics as more "pure" and more "perfect" than physics. On the one hand, there is physics which appears more superficially interesting and inspired, and on the other is mathematics, which to me, follows in the tradition of Plato's world of forms-something that transcends reality, something that transcends physics. Mathematics seems to me to be a truly sublime and magnificent edifice, beautiful and deep, yet elusive. Physics comes a lot more naturally to me, not to say that it is easy which it certainly isn't, but it seems to suit my mode of thought more than does mathematics. Although I agree once again with
dkotschessaa about physics being messy, there is also a certain beauty in finding the patterns nested deep inside the mess.
can't you have your cake and eat it too by becoming a mathematical physicist?
 
  • #25
What beauty do you see in proofs?
 
  • #26
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?
 
  • #27
Orson said:
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.
 
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  • #28
fresh_42 said:
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. :)
 
  • #29
Orson said:
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.
 
  • #30
blue_leaf77 said:
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.
 
  • #31
Wastrophysicist said:
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
 
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  • #32
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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  • #33
Wastrophysicist said:
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.
 
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  • #34
blue_leaf77 said:
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
 
  • #35
dkotschessaa said:
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!
 
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<h2>1. Why did you choose math over physics or vice versa?</h2><p>This is a common question that I get asked a lot. I actually have a background in both math and physics, but ultimately decided to pursue a career in math. I found that I enjoyed the abstract and logical thinking involved in math, and I was fascinated by the endless possibilities and applications of mathematical concepts. However, I still have a strong interest in physics and often use mathematical principles to solve physical problems.</p><h2>2. What are the main differences between math and physics?</h2><p>While both math and physics involve a lot of problem-solving and critical thinking, there are some key differences between the two fields. Math is primarily focused on abstract concepts and theories, while physics is more focused on applying those concepts to understand the physical world. Additionally, math tends to be more theoretical and proof-based, while physics involves experimentation and observation.</p><h2>3. Did you find one subject more challenging than the other?</h2><p>Both math and physics have their own unique challenges. In math, I often had to wrap my head around complex abstract concepts and think outside the box to solve problems. In physics, I had to apply mathematical principles to real-world scenarios and make sense of the data collected from experiments. Overall, I would say that both subjects require a lot of critical thinking and problem-solving skills.</p><h2>4. How do math and physics intersect or overlap?</h2><p>Math and physics are closely related and often intersect in many ways. In fact, physics is often described as the "language of math" because it heavily relies on mathematical principles to explain and predict physical phenomena. Many mathematical concepts, such as calculus and linear algebra, have been developed specifically for use in physics. On the other hand, physics also provides real-world applications for many abstract mathematical theories.</p><h2>5. Can you give an example of how you have used math in a physics context?</h2><p>One example of how I have used math in a physics context is when I was studying the motion of a projectile. By using mathematical equations, I was able to calculate the trajectory, velocity, and acceleration of the projectile. This allowed me to make predictions about its motion and understand the factors that affect its path. Without a strong understanding of mathematical concepts, it would have been much more difficult to analyze and understand the projectile's motion.</p>

1. Why did you choose math over physics or vice versa?

This is a common question that I get asked a lot. I actually have a background in both math and physics, but ultimately decided to pursue a career in math. I found that I enjoyed the abstract and logical thinking involved in math, and I was fascinated by the endless possibilities and applications of mathematical concepts. However, I still have a strong interest in physics and often use mathematical principles to solve physical problems.

2. What are the main differences between math and physics?

While both math and physics involve a lot of problem-solving and critical thinking, there are some key differences between the two fields. Math is primarily focused on abstract concepts and theories, while physics is more focused on applying those concepts to understand the physical world. Additionally, math tends to be more theoretical and proof-based, while physics involves experimentation and observation.

3. Did you find one subject more challenging than the other?

Both math and physics have their own unique challenges. In math, I often had to wrap my head around complex abstract concepts and think outside the box to solve problems. In physics, I had to apply mathematical principles to real-world scenarios and make sense of the data collected from experiments. Overall, I would say that both subjects require a lot of critical thinking and problem-solving skills.

4. How do math and physics intersect or overlap?

Math and physics are closely related and often intersect in many ways. In fact, physics is often described as the "language of math" because it heavily relies on mathematical principles to explain and predict physical phenomena. Many mathematical concepts, such as calculus and linear algebra, have been developed specifically for use in physics. On the other hand, physics also provides real-world applications for many abstract mathematical theories.

5. Can you give an example of how you have used math in a physics context?

One example of how I have used math in a physics context is when I was studying the motion of a projectile. By using mathematical equations, I was able to calculate the trajectory, velocity, and acceleration of the projectile. This allowed me to make predictions about its motion and understand the factors that affect its path. Without a strong understanding of mathematical concepts, it would have been much more difficult to analyze and understand the projectile's motion.

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