Do Physics Majors Need to Love Pure Math?

[torquemada]

I am a physics major and I seem to find that I just enjoy the math insomuch as it helps me to understand physics and the laws of nature. Do I need to enjoy math for the sake of pure math? For example, when things get abstract and there is less physical application, I tend to groan. Is a change in attitude in order? Will it hurt me in the long run, say in grad school or a career in something physics related, if I don't have a paradigm shift in my view of things? Or is this something that is ok? Thanks

 

[Clever-Name]

The more you get into physics the more it's just abstract math so I have to say you need to enjoy it at least a little.. What level of physics are you currently at?

 

[Timo]

As long as you are capable of doing the calculations needed in your work you are usually fine. A real understanding of the math or a passion for it are not required, as far as I see. To quote a colleague of mine: "Most theoretical physicists don't even know Calculus 1 properly".

 

[Functor97]

There comes a point when the physical explanation IS pure mathematics.

 

[micromass]

Pure math (= math for the sake of math) surely exists, but not in the undergraduate level. I claim that (almost) all of the mathematics there has some kind of physical application. So the thing you should do is to research what the physical application is, perhaps this will motivate you in grasping the material.

 

[wisvuze]

I think physics and math really have the same attitude when it comes to how it is studied. The only difference is that math is a step further in the "abstraction process"

 

[Visceral]

There comes a point when the physical explanation IS pure mathematics.

no, its applied math.

 

[deRham]

I agree with Visceral. There is quite a difference between the two. If it were just pure mathematics, then a pure mathematician would have done it already. ;) Yes, there are cases where physicists explain a phenomenon in mathematics using deep physical motivation, but that's quite the exception. Usually the mathematicians have developed the mathematics independently, and that really is how it should be!

 

[deRham]

For example, when things get abstract and there is less physical application, I tend to groan.

You are probably not alone, and I don't think you have to worry. But I do mathematics, not physics.

You should definitely know, however, that advanced physics will use quite a lot of mathematics. But that is because mathematics is the language. You should at every opportunity try to convert your mathematical knowledge to physical intuition. Then, everything will remain interesting to learn for you.

 

[Functor97]

no, its applied math.

Maybe you should read some string theory papers.
Physical explanations disappeared with quantum mechanics. We do not use a Newtonian intuition, but a mathematical one, that is how theoretical physics is carried out these days.

 

[Functor97]

You are probably not alone, and I don't think you have to worry. But I do mathematics, not physics.

You should definitely know, however, that advanced physics will use quite a lot of mathematics. But that is because mathematics is the language. You should at every opportunity try to convert your mathematical knowledge to physical intuition. Then, everything will remain interesting to learn for you.

Interesting. What area of mathematics do you work in deRham?

 

[deRham]

^ Still not quite set on that, but I guess my comment was not based on any advanced knowledge of physics, although I do think I know a thing or two about what mathematics it requires, based on having done some perusing.

It also comes from my experience talking to people either interested in physics as mathematicians or the other way around, and who are not afraid of either discipline.

I don't tend to think in terms of physical intuition, however, myself.

 

[Functor97]

^ Still not quite set on that, but I guess my comment was not based on any advanced knowledge of physics, although I do think I know a thing or two about what mathematics it requires, based on having done some perusing.

It also comes from my experience talking to people either interested in physics as mathematicians or the other way around, and who are not afraid of either discipline.

I don't tend to think in terms of physical intuition, however, myself.

What is physical intuition though? Our basic physical intuition is Newtonian (Einstein's thought experiments with trains). But that intuition breaks down at the quantum level (Hence Einstein's dislike of many quantum results?) and seems to be replaced by a mathematical one. The age of thought experiments seems to have passed. Now we seem to simply create the mathematical model that fits our experiments, which imo is the way it should be, as thought experiments tend to presuppose certain constraints which are problematic.

 

[deRham]

I think I meant physical intuition in a less restrictive sense - i.e. sensing in the mathematics the physical meaning, as given by the experiments like you said.

 

[Visceral]

Maybe you should read some string theory papers.
Physical explanations disappeared with quantum mechanics. We do not use a Newtonian intuition, but a mathematical one, that is how theoretical physics is carried out these days.

Theoretical physics isn't pure math. Why do you insist on this? Its obviously applied math because the math is being used for a reason other than math itself. Physical explanations still exist in physics.

You have a bias towards mathematics. I have read your other threads and I can't understand why you keep insisting that physics is a sub-field of mathematics, and that mathematics is pure truth, and that studying mathematics is the best way to understand reality.

I wait, yes I do understand. You want these things to be true. Just because you wish something to be true doesn't mean it is, btw.

 

[Dembadon]

I am a physics major and I seem to find that I just enjoy the math insomuch as it helps me to understand physics and the laws of nature. Do I need to enjoy math for the sake of pure math? For example, when things get abstract and there is less physical application, I tend to groan. Is a change in attitude in order? Will it hurt me in the long run, say in grad school or a career in something physics related, if I don't have a paradigm shift in my view of things? Or is this something that is ok? Thanks

I'm not a physics graduate student, so I'm not sure how much pure mathematics will be used in your graduate courses. However, this might be something worth considering: How will a change in attitude affect your enjoyment of something? I can see an attitude adjustment affecting your ability to finish something you don't like, but I'm not sure that it always has the power to change your interests.

In other words, enjoyment isn't a prerequisite for a positive attitude. An attitude adjustment might help you endure, but a change in interest will ensure that you'll enjoy.

 

[deRham]

@Visceral I think you might be slightly overstating - I don't think he believes mathematics is the best way to understand reality. In fact, he made a thread specifically about what to do given interest in both fields, and feeling that a lot of people even in mathematical physics seem to be more concerned with where their understanding of mathematics fits in, rather than the actual physics.

I think it is a slight blur, and I would even go as far as saying a lot of people don't really seem to be giving what I'd call the real reason mathematics is distinct.

The idea of "understanding reality" is fine and dandy, but it can mean almost anything. By some definition, understanding logic is the road to understanding "reality" - I think if one TRULY understood any single thing to the fullest, that would be understanding reality in the sense sought. But we all know that's realistically not happening.The problem I find with linking physics and mathematics too closely is that one clearly concerns itself with modeling something via mathematics, and that just isn't mathematics - it's applied mathematics.

But I feel like sometimes people are too quick to dismiss something as not leading to "higher truth" just because it was called applied. No, I'm not saying what you're doing is crunching numbers. Or just mindless use of formulas.

You can use tons and tons of advanced mathematics in your work, and be completely unafraid of PhD level work in mathematics, but still be a physicist if what you are interested in are physical questions. Yes, I understand Modern Physics often is severely based upon mathematics, rather than our everyday intuition, but physical intuition and everyday intuition (and mathematical intuition, for that matter) are all distinct enough things that I feel it's worth acknowledging.

Mathematics is not about describing something using mathematical structures - it is about studying mathematical structures. A mixture of mathematics, experiment, and many things is required to do physics. You may even have to invent new mathematics the way a mathematician does at times - I'm sure some of the great physicists have done exactly this. So yes, they contributed to the body of mathematics.Again, I should be very clear - just because one is studying a model constructed in the mind doesn't mean it's mathematics, unless one is studying the mathematical structure underlying the model in its own right. The pursuits lead to significantly different paths (i.e. where the questions day by day that you might be asking yourself and focusing on are different enough) that I can't say physics is just a part of pure mathematics.

In fact, it was said in a prior thread itself that Mathematical Physicists are more interested in messing around with Differential Equations, perhaps, than with understanding physics. Which is why they are traditionally put under mathematics departments.

 

[deRham]

Maybe you should read some string theory papers.

That's the whole thing - string theory is a strange in between. It can't be used as the standard for comparison really. Perhaps some people don't even consider it physics. But I still do, because it still aims to answer an issue posed by physics (and all I know is the vague statement that we want to relate GR and QM or something). Yet, I would agree there is sufficient argument to say it is mathematics too, because my understanding is the theory can be quite purely mathematical, and in some sense may not be modeling reality so much as providing a mathematically consistent link.

But really I think the best way would be to call string theory exactly what it's called - string theory. It seems to have highly immodest aims, and perhaps one can come at it with different perspectives, making it belong neither strictly belonging in one camp nor another.

I also admit freely that my understanding of it is so insignificant that what I say may be taken with a grain of salt for this particular matter.

 

[Functor97]

Theoretical physics isn't pure math. Why do you insist on this? Its obviously applied math because the math is being used for a reason other than math itself. Physical explanations still exist in physics.

You have a bias towards mathematics. I have read your other threads and I can't understand why you keep insisting that physics is a sub-field of mathematics, and that mathematics is pure truth, and that studying mathematics is the best way to understand reality.

I wait, yes I do understand. You want these things to be true. Just because you wish something to be true doesn't mean it is, btw.

If anything i started off being biased towards physics. I used to believe that pure mathematicians were droll number crunchers, who just forged the tools that the theoretical physicists would yield in their battle for eternal truth. The more I have thought about it, from a philosophical standpoint, the more i believe i was mistaken.
You seem to be claiming that application makes an abstract entity distinct from its original foundation. I understand your point, but I do not like where it leads. It begs the question of what is application? What is use? Is something ever trivially useful?
I do think that mathematics is as close to "pure truth" as we can come. Why? Because that is the mathematical method, we use axioms in mathematics, but postulates in physics. String theory, Loop quantum gravity all of high energy physics aims at a pure mathematical model where uncertainty is eliminated. As humans i believe the philosophical questions generated by a empiricalist standpoint are unanswerable or unfalsifiable, we should instead embrace a mathematical platonic philosophy, as that is the only way, which i believe, maximises the faith of our scientific reasoning, in effect removing our need for philosophical ponderings (or garbage if you prefer). The question of who is right, is a needless one.

Also, i am well aware of the irony of this being a philosophical discussion

 

[deRham]

I think it is great to develop purely mathematical theories, but it begs the question what one wants to describe, and what one aims to understand. Clearly pure mathematicians believe what they work on to be important knowledge. But I would hardly say they care in the least about understanding reality! Often they develop new perspectives and tools on mathematical structures. Sure, it is believed it will lead to some higher truth.

I agree mathematical precision should be aimed for wherever possible.

I think the distinction lies in what is sought to be achieved - developing a knowledge of the structures and tools used to understand those, or employing them as models.

What if one reduces understanding reality to understanding some mathematical problem? The mathematician probably would still want to see what significance that problem has for mathematics and its development.

 

[sciillit]

no, its applied math.

Tell that to the stringy people. ;)

 

[Functor97]

Tell that to the stringy people. ;)

The stringy people love to think they are doing applied mathematics. They are criticized by other physicists for doing pure mathematics.