# Is theoretical physics pure or applied math

## General respect level: physics or math?

- Thread startergaloiauss
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## Main Question or Discussion Point

Just wondering, what is the general consensus on whether physics or math is a more respectable and "harder" intellectual field. I'm a mathematician, and I know both can be very hard, but just wanted to know on a simple level. I'm asking this in the same light as how people usually rank the sciences in terms of their difficulty/pureness/respect level (eg. bio< chem < ...)

## Answers and Replies

There is a joke which says: 'Chemists think they're physicians; physicians think they're mathematicians; mathematicians think they're gods.'

Joke aside, I don't think one can draw conclusions about that in general. Of course, for example, knowing a lot math makes it easier for one to learn some physics, but that means nothing.

Joke aside, I don't think one can draw conclusions about that in general. Of course, for example, knowing a lot math makes it easier for one to learn some physics, but that means nothing.

A physician is a doctor, as in medical doctor. I think you might have meant physicist.

Yes, I meant physicist, thanks.A physician is a doctor, as in medical doctor. I think you might have meant physicist.

Well considering the focus of western medicine to fix everything will a pill..There is a joke which says: 'Chemists think they're physicians; ....

From my undergradate experiences, I'd consider the levels of difficulty from most to least: experimental physics<pure maths<theoretical physics<applied maths

I put experimental physics at the top due to my lack of experience with experimental science and low level of kowledge of general physics (i.e. how things work) and the huge amount of vaguenss that occurs in undergrad lab classes which really puts me off.

From observing other students I have noticed that good at maths => good at physics but not always the other way around. I feel that physics always takes small sections of maths and combine many applications with it. So in this way physics is a branch of maths and so maths is more general. General things are considered harder than special things, in general. As Dyson said, Mathematicans are like birds flying across the field whereas physicists are like frogs leaping around in the same field but being able to see it more closely but obviously not as far.

From observation from academics in both departments I conclude that mathematicians are 'smarter' than physicists. Although the word smart is subjective. Maybe its the fact that mathematics is precise which makes the arguments made by mathematicans to be more solid or less hand waving. And nothing beats elegant maths proofs because not only is it 100% correct, its also delivered in an efficient manner. Just reading these things can make one smarter.

The more maths a physicist uses, the smarter they seem. i.e Witten. And people like Witten are considered the best physicists. A mathematician knowing more physics dosen't neccessiarly make them better mathematicians but a physicst who knows more maths will definitely make them better physicists so in this way (and the other reasons given), maths is more respectable.

Although having said all this here is a thread that might give some different views.

https://www.physicsforums.com/showthread.php?t=80027

I put experimental physics at the top due to my lack of experience with experimental science and low level of kowledge of general physics (i.e. how things work) and the huge amount of vaguenss that occurs in undergrad lab classes which really puts me off.

From observing other students I have noticed that good at maths => good at physics but not always the other way around. I feel that physics always takes small sections of maths and combine many applications with it. So in this way physics is a branch of maths and so maths is more general. General things are considered harder than special things, in general. As Dyson said, Mathematicans are like birds flying across the field whereas physicists are like frogs leaping around in the same field but being able to see it more closely but obviously not as far.

From observation from academics in both departments I conclude that mathematicians are 'smarter' than physicists. Although the word smart is subjective. Maybe its the fact that mathematics is precise which makes the arguments made by mathematicans to be more solid or less hand waving. And nothing beats elegant maths proofs because not only is it 100% correct, its also delivered in an efficient manner. Just reading these things can make one smarter.

The more maths a physicist uses, the smarter they seem. i.e Witten. And people like Witten are considered the best physicists. A mathematician knowing more physics dosen't neccessiarly make them better mathematicians but a physicst who knows more maths will definitely make them better physicists so in this way (and the other reasons given), maths is more respectable.

Although having said all this here is a thread that might give some different views.

https://www.physicsforums.com/showthread.php?t=80027

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I think that by asking this in a math forum you're going to get a lot of responses biased in that direction.

For my part, I tend to agree with pivoxa15 -- and have had the same experience with math professors vs. other professors in terms of general intelligence. Of course its all very subjective.

For my part, I tend to agree with pivoxa15 -- and have had the same experience with math professors vs. other professors in terms of general intelligence. Of course its all very subjective.

Alkatran

The question you're actually asking here is "Is math/physics preference correlated with IQ?" If they aren't correlated, then we expect people of the same intelligence to go in both fields and cover all the 'low hanging fruit' at their level.

There should be some sort of study done.

... Yes, I know IQ is a bad measure of intelligence.

There should be some sort of study done.

... Yes, I know IQ is a bad measure of intelligence.

You could also look at this problem from the perspective of which field of study can be learnt by self study most easily.

At first one thinks that maths can more easily learnt than (theoretical) physics because it is purely a priori. But from experience it is not the case because a priori doesn't mean it is easier to learn. It takes a lot of training and effort to see these a priori truths. With physics, one has an intuitive feel more so than maths and plus the hardest things in physics are usually the maths. In this way, maths is harder to self learn than physics.

At first one thinks that maths can more easily learnt than (theoretical) physics because it is purely a priori. But from experience it is not the case because a priori doesn't mean it is easier to learn. It takes a lot of training and effort to see these a priori truths. With physics, one has an intuitive feel more so than maths and plus the hardest things in physics are usually the maths. In this way, maths is harder to self learn than physics.

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Btw, in my opinion, IQ (measured as it is) is a factor related only to the speed and time of study, mostly, under assumption that the person is average (orThe question you're actually asking here is "Is math/physics preference correlated with IQ?" If they aren't correlated, then we expect people of the same intelligence to go in both fields and cover all the 'low hanging fruit' at their level.

There should be some sort of study done.

... Yes, I know IQ is a bad measure of intelligence.

*slightly*below).

mathwonk

i think math must be the easiest of all fields, as it is the only one i could ever understand anything in.

Lol hilarious mathwonk. Personally, I think mathematicians are the most respectable, at least between them and physicists. Physicists are smart, but not as much so as mathematicians. Albert Einstein piggybacked on Riemann with General Relativity, but not as many people know who Riemann is. Mathematicians will be able to do a physicists job for a day and won't be too bad, maybe even better. A physicist will cry at a mathematicians, unless its a string theorist, then they may fair alright. I like to think of physics as applied math, which makes me think math is more pure. Math is the language of physics.

Another example, Gauss was an excellent mathematician, and did physics as a hobby and still made contributions the average physics student would be dreaming to achieve.

Another example, Gauss was an excellent mathematician, and did physics as a hobby and still made contributions the average physics student would be dreaming to achieve.

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Fair point Gib Z. Theoretical physicists are just like applied mathematicians although less rigorous.

How many physicists who started out as pure mathematicians? A few.

How many pure mathematicians started out as physicists? I can't think of any.

How many physicists who started out as pure mathematicians? A few.

How many pure mathematicians started out as physicists? I can't think of any.

I can see how this impression comes about. I think it is hard to learn maths but once you have learnt it, you think how easy it is because it should be self evident truths. Whereas with the other subjects, most deal with empirical objects that are naturally not well defined so the concepts may be easier and learning it for the first time may be quicker and easier than maths but one can never 'understand' those empirical subjects - at least not in the way one could 'understand' mathematics.i think math must be the easiest of all fields, as it is the only one i could ever understand anything in.

Nothing prevents a physicist from being a very strong mathematician. The opposite is also true.

To specialize in, say, superstring theory, you have to learn mountains of mathematics, as well as know all the basic physics topics as well as the difficult specialized topics like relativity and quantum field theory. But a mathematician does not need to learn any physics at all. A mathematical physicist is capable of earning two different PhDs, one in math and one in physics. On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch). This is why I admire mathematical physicists like Hawking and Penrose.

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At my university, you could potentially do a Phd in mathematical physics without having done any undergraduate physics. So when these people (who haven't done any undergrad physics) become mathematical physicists in the maths department , I am not sure they can study a second Phd in the physics department straight away?To specialize in, say, superstring theory, you have to learn mountains of mathematics, as well as know all the basic physics topics as well as the difficult specialized topics like relativity and quantum field theory. But a mathematician does not need to learn any physics at all. A mathematical physicist is capable of earning two different PhDs, one in math and one in physics. On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch). This is why I admire mathematical physicists like Hawking and Penrose.

I'm not sure you'll find that is true. At least no more true than the next quote:A mathematical physicist is capable of earning two different PhDs, one in math and one in physics.

is true. Not least because your favoured area of string theory is very likely to be studied by a pure mathematician. In fact I know very few applied people, or those with a physical background who do string theory, and many pure mathematicians.On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch).

I would also like to point out that plenty of pure mathematicians have a more than average working knowledge of relativity and quantum mechanics - they are after all undergraduate course. I even know some people who did these subjects for personal interest during Part III and are very pure mathematicians. Just as there are plenty of applied people who have a working knowledge of representation theory, say. The pure mathematics of string theory (that wouldn't be assumed from, say, relativity) and are essectial to the beginner can be summed up as:

essential: Riemann surfaces

useful: category theory, algebraic topology/geometry

all but category theory can be, and is, learnt to reasonable level as an undergraduate course. Category theory might be taught, but is often overlooked. To be honest, outside of Baez's n-categorical viewpoint, I'm not sure how useful this really is. The student may end up knowing some highly specialized stuff (in some sense) like chern classes, and poincare duality, or McKay correspondence but it is by no means assured. At the last conference I attended dealing with such matters I don't think I saw a PhD student there, and only a handful of people on post-docs like me. And, no, I'm not a mathematical physicist.

I think it very misleading to imply that a recently qualified Maths Phys PhD is somehow a demigod of both subjects, and knows enough to do research in either. They don't. They certainly ought to know enough to do research in Maths Phys, but that is the only thing nearing a certainty you can say. You start learning the real stuff after the PhD, apparently. If I were you, I'd check out some PhD theses from maths phys students before saying what it is they have to know, and what it is they do at this stage.

This is why I admire mathematical physicists like Hawking and Penrose.

They are certainly admirable names. But an average mathematical physicist is no more or less able than an average mathematician/physicist. They just happen to work at a very fluid boundary.

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mathwonk

i think it depends who you ask. i.e. in some circles mathematicians are regarded as hopeless knuckle draggers, and physicists the height of sophisticted intellectuals.

e.g this position is often heard forwarded in meetings of the flat earth society, or of the kansas school board.

e.g this position is often heard forwarded in meetings of the flat earth society, or of the kansas school board.

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