Should I Become a Mathematician?

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  • #1,776
mathwonk
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good question, and one I seem to have stopped short of answering in my general discussion. real world survival is very tough. with all the shortcomings the attractiveness of doing math research for a living is so appealing to many very bright people here and abroad that the job situation is often difficult. perhaps that will change as my generation of baby boomers retires beginning now and continuing for some time. but there are many emigres looking for these jobs too and they are very well trained.


i myself wrote a decent thesis and had a very fine advisor with some contacts, and I had several offers of temporary jobs, including one at columbia. However I myself generated another offer, the very tenure track offer i have tenure in now at UGA, and preferred it to the others because with a family, tenure track seemed very attractive.

however the shortcoming was there was no one else strictly in my field although at least one person was interested in it. having no one to learn from or work with, my future development was hindered. so i went to work and obtained an nsf grant for a regional conference headed by the famous phillip griffiths, and this brought a large number of outstanding people to my school for me to make contact with.

professor griffiths also said if i would come to harvard to visit i could have some fun doing algebraic geometry with his team, so my university gave me leave to do this. i also met david mumford and heisuke hironaka there, learned from all of them, and wound up staying 18 months.
thus i survived by doing things backwards, tenure track first, then postdoc.

others no doubt have different stories.
 
  • #1,777
mathwonk
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for more on my career path and related matters, go back and read posts 166 and 177-186.
 
  • #1,778
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Hello again,

Now that I've started college, I've had some time to think about my Math career. Right now I'm absolutely loving my current math course (a theoretical treatment of multivariable calculus that uses linear algebra and differential forms) even though we haven't gotten very far. The rigor of the course is very stimulating.

I'm at the U of MN - Twin Cities campus right now. How is the U of MN PhD program in Pure math? Applied? Or does it really matter that much what university I obtain my PhD from?
 
  • #1,779
mathwonk
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minnesota seems an excellent place, but it is usual to go somewhere else from your undergraduate school for a phd. please go see my friend joel roberts for more advice. tell him roy smith sent you.
 
  • #1,780
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i wanna become a good theorotical physicist how far pure maths is useful for that????
 
  • #1,781
mathwonk
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well witten, who seems to me a fine theoretical physicist is a fields medalist in math. so the two are certainly related. i have also mnyself been a guest lecturer in math at the ictp in trieste lecturing on riemann surfaces to physicists and mathematicians. as far as i know physicists are often interested in learning as much math as possible e.g. group representations, operator theory differentiable manifolds, and riemann surfaces, for application to quantum mechanics, string theory, relativity,.....
 
  • #1,782
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I want to do theoretical physics, so I decided to do half of my degree in maths-the best courses my universty offers on GR or quantum field theory are taught by the maths department. The reason Witten got a fields medal is because the maths he needed to use didn't exist... so he invented it :biggrin:
 
  • #1,783


Hey mathwonk. I am taking a year of complex analysis now. Its good stuff!
 
  • #1,784
mathwonk
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Great!! are you enjoying a particular book you think others might like too? and would you like to give your prof a plug?
 
  • #1,785


Well, its only the first semester so we started out with Complex Analysis Lars V. Ahlfors, secondary sources are Theory of Functions by Knopp and Hyperbolic Geometry from a Local Viewpoint by my teacher Linda Keen.
 
  • #1,786
thrill3rnit3
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I'm just wondering, did I do the right thing in not skipping geometry? I had the choice of testing out of it, but I decided not to and instead I took it freshman year (high school). I should say I didn't really regret it, since my geometry teacher was like the only math teacher in our school who knows his stuff (plus probably the AP "Calc" teacher)

Now I'm a soph, and I'm on Alg. II/Trig Honors class (nevermind the honors label. It's not really "honors", if you know what I mean). I'm thinking about doing Precalculus over the summer (which would cost me - no, my parents - a painstaking 800 bucks), so that I can take 2 years of AP "Calc" (AB and BC) to add to my college application.

Am I doing the right thing??
 
  • #1,787
symbolipoint
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Skipping Geometry might or might not mean much now; in any case, you already studied it instead of skipping it and it probably helped you at least a little bit, certainly did not hurt you. PreCalculus in the summer might be rough going - not always enough time for some people.

If you are truely interested in Mathematics then you shoud definitely study Geometry. You may see how some things are obtained with Calculus while those same things can also be developed in Geometry without resorting to Calculus.
 
  • #1,788
thrill3rnit3
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I'm doing self-studying so I'll probably be almost if not finished with PreCalc by next summer. I'll take the course just to refreshen my memory, ask some questions, and because my school puts PreCalc as a prerequisite for AP Calc.
 
  • #1,789
mathwonk
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i do not know what your geometry course was like, but i seem to recall no one was allowed to enter plato's academy who was ignorant of geometry. the same should hold for college entrance today in my opinion. just today i have been reading archimedes, for more insight on his anticipation of basic facts now considered a part of integral calculus. euclid is also superb training.
 
  • #1,790
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i do not know what your geometry course was like, but i seem to recall no one was allowed to enter plato's academy who was ignorant of geometry. the same should hold for college entrance today in my opinion. just today i have been reading archimedes, for more insight on his anticipation of basic facts now considered a part of integral calculus. euclid is also superb training.

my geometry teacher emphasized proofs and my dad told me that mastering geometry would be really helpful in the long run, I guess what he says is true...
 
  • #1,791


Pure mathematics is the way to the underground. I don't get it all but I do know that if you understand how you are doing it and WHY you are doing it- in every way!- then you are able to understand why everything is so- i mean everything. Pure math is what people do not see, it is the foundation. I want to see like them, not just do what they thought of. ahhh that is the beauty of mathematics. :) they see things others do not-
 
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  • #1,792
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I want to be a mathematician (sort of), but I don't know if math would still want me. I am more than 15 years removed from undergrad, no major or minor in math/science/engineering. I have taken some math courses for last 3 years, and I am doing research with a Prof this year; I think I have a minor extension of a minor result. But to go into PhD, I would have to quit work (in my good earning years), get through exams (probably not a big deal), get an advisor (may be a big deal) and write a thesis (probably a big deal). Still, I am applying this year.

Unlike the young students here, I don't expect to solve a major problem - that is like picking the best apple from the top of the tree. But in just the little research I have done, I have started to see so many little apples lying on the ground ready to be picked up - like the little problem I am working on. I don't know, meybe this is because my work crosses over with CompSci, and maybe those problems are more accessible.
 
  • #1,793
mathwonk
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although very different, the last two messages seem more insightful than many. best wishes and good luck to you both.
 
  • #1,794
JasonRox
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Pure mathematics is the way to the underground. I don't get it all but I do know that if you understand how you are doing it and WHY you are doing it- in every way!- then you are able to understand why everything is so- i mean everything. Pure math is what people do not see, it is the foundation. I want to see like them, not just do what they thought of. ahhh that is the beauty of mathematics. :) they see things others do not-

I don't see what your point is, or how that is special.

There are many things others do SEE and mathematicians DO not.

There is no advantage to seeing one thing over another. It's all subjective.
 
  • #1,795


It was an opinion.
I did not say that mathematicians were the only people who see things differently. I just said some do.
Between applied and pure mathematics, which was the topic, a pure mathematician is most likely going to understand the concepts more in depth than the person who just uses a formula without questioning what you are really doing. I am not knocking applied math- I would much rather do that any day than proof writing!
I agree, everything is subjective based on our perceptions- that was just my opinion.
 
  • #1,796
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mathwonk, I was just wondering your opinion (should one exist) on Calculus by Hughes-Hallett et al (required text for my university). It seems to have poor ratings, though quite a few do. Should I get another book to learn from and just use this for problem sets? I find it strange that they would use a book that is so bad but the department at my university seems pretty good.
 
  • #1,797


Unlike the young students here, I don't expect to solve a major problem - that is like picking the best apple from the top of the tree. But in just the little research I have done, I have started to see so many little apples lying on the ground ready to be picked up.

Wow! I really like your apple analogy. It's very poetic.




And Helical, I used Hughes-Hallet for Calc I, II, and III and I absolutely hated it. Fortunately, I had some really good teachers. I recommend picking up another text to supplement your studies. Try browsing a used bookstore. You'd be surprised what kind of gems you can pick up if you look hard enough.
 
  • #1,798
JasonRox
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It was an opinion.
I did not say that mathematicians were the only people who see things differently. I just said some do.
Between applied and pure mathematics, which was the topic, a pure mathematician is most likely going to understand the concepts more in depth than the person who just uses a formula without questioning what you are really doing. I am not knocking applied math- I would much rather do that any day than proof writing!
I agree, everything is subjective based on our perceptions- that was just my opinion.

That's not true either. Where do you get this from?

A biologists will understand things mathematics will not. I said what I said in a general term. As in, don't try and feel superior or believe something is superior because one is seeing something others do not. There will always be something you don't see and someone else does.

My comment had nothing to do with applied vs. pure either.
 
  • #1,799


I did not knock anyone or what they think or how they think it-
I am not disputing an opinion that is mine alone with people that are rude.
I am a grad student and a new mom- Not a philosophy major- you twist my words around- I never said that a 'biologist' wouldn't see things that a mathematician would or whatever trivial example you want to say- all i was implying is that if one has a clearer sense of why you are doing something you are more likely to understand the outcome better.
I came here to read proofs and refresh- not to argue about deductive logic.
If you want to reply to my thoughts please refrain from things such as- well this makes no sense- or what is your point- this is rude. Otherwise feel free to say what you like- just be respectful bc I know I am not hurting anyone here by voicing my opinion-
oh and my comment did have something to do with applied vs pure mathematics- someone brought it up- which one was better to do- so sorry you are so worked over my comment!
 
  • #1,800
mathwonk
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i have not studied hughes hallet's book but she is not even a mathematician as far as i know, so why would anyone use a book by her?
 

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