Mathematical purity vs real world understanding

[Klockan3]

Klockan, the problem is you are assuming the stance of the opposition in the argument, ergo you are arguing with yourself. It is frustrating to the people having a discussion, when you do not even read their points. I am not saying you always do, but you just admitted yourself you assume things about the opposition, well in this case they were non trivial.

Maybe you misunderstood, they assume just as much about me as I assume about them. You can't have a discussion without assumptions, as I said. Maybe the assumption I made in this topic was a bad one, but after a few posts I almost always agree with my opponent. As I said, I do not discuss to try to sway people to my cause but to further my understanding, I have no problem with losing arguments. I do however try to argue till my opponent shows his point clearly, the best way to do that is to attack the holes which I don't see how he would fill. Then if he fills them I have learned something new. In this case I wanted to make sure that we used the same definitions, talking like he did it wasn't obvious.

Also, unless you have a fields medal hidden away, i would not be ready to assume that either you or what your learning style has led to, are very different from everyone else.

I managed to take courses for a dual masters + the necessary undergrad courses in 4 years with barely any studying outside of classes. I can bet quite a lot that you and most others who study these subjects won't manage to do the same, but that would solve all your problems if you could, right?
Why do I need to have a fields medal by the way, can't I discuss things relevant for education without one? Then, considering that it is just 4 years since I took my first college course requiring a fields medal would seem a bit excessive for anything at all considering that none have ever gotten one that quick. I probably won't ever get one, but considering that at most one per year gets one it isn't that strange.

Lastly, unless you have managed to do anything noteworthy at all I would advice you to take a softer approach with your replies. What we know of you so far is that you haven't even started with your higher education and it shows.

I was providing a hyperbole to convey my point. You brought this back up, and i explained why the failure to reach an eternal truth does not forgo approximate ones. I did not claim that the Liberal arts were worthless or inferior in general to science, i claimed that they do not study subjects of interest to me and that their attempt at discrediting science as just another postmodern theory is baseless. I did refer to them as junk, but it was the process i was speaking of, not the content. I do not see any reason for you to be offended. This is a Physics board, maybe a literature one would be more to your liking.

You are aware of the fact that mathematics and theoretical physics are parts of liberal arts? And that there are philosophy classes which are more rigorous than any mathematics class will ever be? Liberal arts is more than book reviews and political discussions.

 

[Functor97]

Maybe you misunderstood, they assume just as much about me as I assume about them. You can't have a discussion without assumptions, as I said. Maybe the assumption I made in this topic was a bad one, but after a few posts I almost always agree with my opponent. As I said, I do not discuss to try to sway people to my cause but to further my understanding, I have no problem with losing arguments. I do however try to argue till my opponent shows his point clearly, the best way to do that is to attack the holes which I don't see how he would fill. Then if he fills them I have learned something new. In this case I wanted to make sure that we used the same definitions, talking like he did it wasn't obvious.

I managed to take courses for a dual masters + the necessary undergrad courses in 4 years with barely any studying outside of classes. I can bet quite a lot that you and most others who study these subjects won't manage to do the same, but that would solve all your problems if you could, right?
Why do I need to have a fields medal by the way, can't I discuss things relevant for education without one? Then, considering that it is just 4 years since I took my first college course requiring a fields medal would seem a bit excessive for anything at all considering that none have ever gotten one that quick. I probably won't ever get one, but considering that at most one per year gets one it isn't that strange.

Lastly, unless you have managed to do anything noteworthy at all I would advice you to take a softer approach with your replies. What we know of you so far is that you haven't even started with your higher education and it shows.

You are aware of the fact that mathematics and theoretical physics are parts of liberal arts? And that there are philosophy classes which are more rigorous than any mathematics class will ever be? Liberal arts is more than book reviews and political discussions.

Klock, i do appreciate the fact that you responded to my thread, but your attitude has impacted my view upon some of your points. I understand your English is not the best, so maybe you are coming off as more arrogant than you really are.
I have looked through most of your posts and your responses seemed to be reserved for fairly trivial areas. By that i mean general topics, and fairly basic undergrad questions, there are very few graduate mathematics or physics topics you engage in. If you really are the prodigy you claim to be, i am sure many on this site would appreciate the guidance from someone so talented. Instead i see you making a goose out of yourself in many threads, mostly because you have resorted to ad hominem attacks or baseless ones.
Anyone can claim to be anything on the Internet, and i would question how experienced you are with the broader mathematical or physics community, if you are so quick to place yourself above others. If your masters courses were at a prominent research university such as Harvard, Princeton, caltech or say Cambridge in Britain, i would be more inclined to take your claims seriously. I do not deny it is possible, i simply doubt that you are all you claim to be.
Yes i am only an undergraduate, i try not to take myself too seriously, we are all human, and for the sake of good conversation it helps to act a tad modest.

 

[Klockan3]

Klock, i do appreciate the fact that you responded to my thread, but your attitude has impacted my view upon some of your points. I understand your English is not the best, so maybe you are coming off as more arrogant than you really are.

I am tired, I really shouldn't have reacted like that.

I have looked through most of your posts and your responses seemed to be reserved for fairly trivial areas. By that i mean general topics, and fairly basic undergrad questions, there are very few graduate mathematics or physics topics you engage in. If you really are the prodigy you claim to be, i am sure many on this site would appreciate the guidance from someone so talented. Instead i see you making a goose out of yourself in many threads, mostly because you have resorted to ad hominem attacks or baseless ones.

Look through my arguments with jostpuur in this thread, it was 1 year ago:
https://www.physicsforums.com/showthread.php?t=360250&page=3
And these ones were 2 years ago:
https://www.physicsforums.com/showthread.php?t=318507
https://www.physicsforums.com/showthread.php?t=340886&page=2
Not much but something. But your post I was responding to was an ad hominem as well. An ad hominem is not a bad thing in all occasions, especially when discussing things strongly related to peoples own experiences.

Anyone can claim to be anything on the Internet, and i would question how experienced you are with the broader mathematical or physics community, if you are so quick to place yourself above others.

I don't place myself above others, there is probably plenty of people out there who had it much easier than myself although I haven't met them. But I am certain that my time have been much easier than for a majority out there and that is what is important, I might not have been to Harvard but I have studied with the best students of my country. I'd like to think that others could do the same thing or at least get closer to what I do if they just changed some of their habits.

And I don't claim to have mastered many things, I have a quite rudimentary understanding of several of the courses I have taken. I have a really hard time motivating myself, can barely keep a book open for minutes most of the time. I learn most of the things in the classrooms, so to get as much lecture time as possible I took many extra courses but that gives several holes since I miss things, I often manage to repair many of them afterwards but I don't know many things as well as I would have liked. As I said before a reason for me to discuss things is to fill in holes like that, although I don't really go searching for discussions pertaining directly to those subjects, I prefer discussing things like education and learning processes.

 

[MathematicalPhysicist]

And I don't claim to have mastered many things, I have a quite rudimentary understanding of several of the courses I have taken. I have a really hard time motivating myself, can barely keep a book open for minutes most of the time. I learn most of the things in the classrooms, so to get as much lecture time as possible I took many extra courses but that gives several holes since I miss things, I often manage to repair many of them afterwards but I don't know many things as well as I would have liked. As I said before a reason for me to discuss things is to fill in holes like that, although I don't really go searching for discussions pertaining directly to those subjects, I prefer discussing things like education and learning processes.

This has a huge drawback, cause coursework are usually short in scope, so if you want to broaden your horizons, this will hold you back.

 

[lostcauses10x]

Interesting thread.
Yet it does come back to personal choice of were the original poster goes with their career.
One of the most basic questions that should be being asked is simply: Which will get you further in the world the way, and what you want from it?

Again the question of mathematics and physics is brought up.
Again I go with mathematics is unto itself a study of itself.
How mathematics fits into the study of the physical universe we live in, is still a good question. Still so far math has managed to keep ahead of the physics so it can be used in the physics world.

In math so many times discoveries are made that have been said to be only of interest to the mathematician. Of course later situations arose in the real world, that such can be used for have arisen. It would not be unreasonable to expect the same still occurring today.

Again concerning the original question this thread asks, does come to a personal choice.
As also been stated, to go with one subject, and still perusing the other is an option.
Not an easy one per say, but if a person is motivated, well it has been done.
Again personal choice and personal limitations.
The question comes down to: Were do you want to be, and what do you want??

 

[deRham]

But with that definition all acts of memorization would be called intuition. Would you call it intuition when someone solves a second order polynomial equation by using the standard formula?

Well, in a sense yes. It depends what the nature of the solving involved. As another poster stated, when presented with an unfamiliar situation, being able to reduce it to a familiar situation by remembering the formula or something would be an act of using intuition.

As you yourself said - there are assumptions to be made always. One kind of assumption is what we take for granted when doing mathematics. Just because the intuition relies somewhat more on symbol recognition doesn't mean it's not intuition - simply a different kind.

I think your problem with the limits example was that you wanted to say intuition should involve some degree of greater understanding. But I think that is clearly unnecessary - in fact, when studying advanced material, it is customary to not fully understand what is going on in a full sense, but have a good idea relative to some reference point that is not yet well understood?

At least, this is all my reading of what we're struggling with in these later parts of the thread.

 

[The_Brain]

Finally, how is it that physicists such as Edward Witten and Clifford Taubes become so talented as mathematicians? I heave heard it said that Witten for instance relies on intuition and does not often provide proofs, and that is often devisive amongst the pure mathematics community, but Taubes for instance got a phd in physics and now seems quite the pure mathematician. Someone like witten is what i aspire to be, or at least the area of research, but i have trouble telling if he is more mathematician than physicist, imo most of his results have been derived from pure mathematics, in a fashion similar to Dirac, rather then in physical ponderings in the fashion Einstein.

I was an ambitious undergraduate who took several graduate courses in physics. I didn't have quite the same dilemma as you because I knew I didn't want to go into pure mathematics. Still, I once emailed Ed Witten and asked if I should continue taking graduate level physics courses or math courses, as I was interested in string theory and mathematical physics. His response was along the lines of suggesting to take as many physics classes as possible and that I would or could learn the mathematics I didn't know along the way. This suggestion has been confirmed by a couple of other prominent high energy and string theorists since.

 

[Functor97]

I was an ambitious undergraduate who took several graduate courses in physics. I didn't have quite the same dilemma as you because I knew I didn't want to go into pure mathematics. Still, I once emailed Ed Witten and asked if I should continue taking graduate level physics courses or math courses, as I was interested in string theory and mathematical physics. His response was along the lines of suggesting to take as many physics classes as possible and that I would or could learn the mathematics I didn't know along the way. This suggestion has been confirmed by a couple of other prominent high energy and string theorists since.

That is quite interesting, if this really is true advice. I mean imagine how much you impacted modern physics by sending that email, how much more could witten have done? That is a joke of course, its good advice!

I would like to know how strong witten is at the rigor side of pure mathematics, does he have the skill to think intuitivley and rigorously? If he has not taken any graduate pure mathematics courses, then that makes his accomplishments all the more impressive.

From my point of view, i am going to wait a bit longer before getting set on one path or another. I would love to do both, but we are all human.

 

[deRham]

I what Witten meant is that if you want to understand physics and are intelligent enough, you can learn the requisite mathematical language on your own.

Mathematics courses are not to learn the formalism only - presumably, they expose you to how you can move forward with mathematics itself, but that's not of primary interest to the physicist.

Whereas for physics, I doubt you need more than the language. Which, to someone as brilliant as Witten, is child's play to pick up - so he was probably saying to learn the real content, if interested in the physics.

Whereas to do mathematics, you need much more than the language - after all, if someone can pick up your work very easily and guess half the results themselves, you're not going to get a job as a mathematician really.

 

[Hughesy]

To functor97; I am getting an impression that you are very extrinsically motivated. For example, I feel that you are too inclined to base your personal decisions on what people think and say about particular things. You are very driven to become someone great, like Edward. For me, since I do physics, the thing with such extrinsic motivations is that you lose sight of what is important in the sense that you subordinate your intimacy with what you love to superficial things like receiving recognition for what you do or fear of repugnance. I just have an opinion that these extrinsic motivations are harmful to endeavours in fields such as physics, and this sort of mentality is common as muck in areas such as sport where there is so much empahsis on being the best.

And here is the most important and simplest thing I want to point out: You do things because you love to. You do physics to not become like Einstein, but you do physics because it appeals to you. You do not need to consider its applications, its practicality, its usefulness, its purity or even its general importance. Just do it because its damn fun. You do not need to impress everyone and be the greatest physicist to have a motivation for a deep appreciation of nature. For me, the joy of physics is always enough. You are irresponsible of the prejudice and expectations of other people just as much as you are responsible for your own prejudices and expectations.