uman
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I think you've got things backwards when you say we can discover new pure mathematics through string theory.
Should I Become a Mathematician?
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uman said:
I was thinking exactly the same thing lol.
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odd as it may seem, he may be right. check out the story of counting rational curves on the quintic threefold, by candelas, et al...
mathis314
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i still want to be a mathematician
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mathwonk said:
Our object wasnt in that mathematics was derived from string theory, but that the mathematics is "pure" (not applied), because it inherently can not be; it is applied in string theory.
mathis314
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Gib Z said:
Its funny, however, that sometimes epiphanies in science beg for higher mathematics.
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muppet
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Ed Witten became the first theoretical physicist to win the Fields Medal because he worked out new maths needed to tackle string theory 
That being said, I'd say that string theory is really applied rather than pure math?
That being said, I'd say that string theory is really applied rather than pure math?
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mathis314 said:
Not at all. In fact, its been like that throughout the history of science and mathematics.
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to me, counting the rational curves on a quintic threefold is about as pure as math gets.
of course you can define pure to mean it did not come from physics, but then your argument is tautological.
of course you can define pure to mean it did not come from physics, but then your argument is tautological.
uman
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Well what is pure mathematics then?
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good question, but i have no interest in answering it. its what i do, not what i philosophize about.
i guess my point is that the question answered in this case is one of pure mathematical interest, with no physical application. The answer was however obtained via insights stimulated by very theoretical physics, i.e. quantum gravity and string theory.
you will also find more than a few people who do not believe string theory is physics, but is merely pure mathematics, since it has apparently no predictive power in physics. Not only have no predictions been shown correct, but critics say it has not even produced any checkable predictions at all.
It does however have predictive power in pure mathematics, as exemplified above.
i guess my point is that the question answered in this case is one of pure mathematical interest, with no physical application. The answer was however obtained via insights stimulated by very theoretical physics, i.e. quantum gravity and string theory.
you will also find more than a few people who do not believe string theory is physics, but is merely pure mathematics, since it has apparently no predictive power in physics. Not only have no predictions been shown correct, but critics say it has not even produced any checkable predictions at all.
It does however have predictive power in pure mathematics, as exemplified above.
Darkiekurdo
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Is it weird that when I see an expression I need to simplify I don't automatically think 'Right, obviously I need to apply so-and-so rule'? Or is that something that comes with lots of practice?
RonL
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I'm not sure if Lord Kelvin has been mentioned, (1364 post) a lot to go thru, what impressed on me the need for math, was a quote by kelvin, and doing a search, produced so many variations, that i'll just use the words that are in my mind.
" Any idea, that cannot be given a numerical solution, is not worth the paper it is written on"
" Any idea, that cannot be given a numerical solution, is not worth the paper it is written on"
pivoxa15
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mathwonk said:
Just read it. Very interesting. Some of you were discussing what is pure maths. I think the mathematics done by Grothendieck is an extremely good example of pure maths. I love it when he says he doesn't like to use tricks to solve problems but using many small steps that are completely natural to crack open a problem as if by no force at all. There seems to be many similarities between him and the philosopher Ludwig Wittgenstein. For one, they both try to get to the absolute foundations of their disciplines.
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With my due respects to Lord Kelvin, he obviously was wrong on that point. The Fundamental theorem of algebra has no numerical quantities. Is it not worth the paper it is written on?
RonL
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Not sure what i have learned today, but one thing is to be more careful where i put a comment. -:)
As for the Fundamental theorem of algebra, after a quick read my brain started hurting.
It seems more of an assertion, than an idea.
I have always thought of Kelvin's statement, more in the action, reaction, physical, and mechanical world.
So much to learn.
As for the Fundamental theorem of algebra, after a quick read my brain started hurting.
It seems more of an assertion, than an idea.
I have always thought of Kelvin's statement, more in the action, reaction, physical, and mechanical world.
So much to learn.
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mathwonk,
How important is the topic of research for my master's degree? By "important", I mean, how easily will I be able to switch subject for my doc? How relevant is it to a professor that a student seeking to do a doc under him has no research experience in his field or no experience at all despite possibly one or two relevant course followed at the undergrad or grad level?
How important is the topic of research for my master's degree? By "important", I mean, how easily will I be able to switch subject for my doc? How relevant is it to a professor that a student seeking to do a doc under him has no research experience in his field or no experience at all despite possibly one or two relevant course followed at the undergrad or grad level?
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i did not do a research based masters degree myself. usually in math people go straight into the phd program. a masters thesis is often an expository paper on a topic one has learned, involving no original research.
this may be changing now, as even undergraduates are often involved in some research, frequently involving computers, where one does not need a great deal of technical expertise.
this may be changing now, as even undergraduates are often involved in some research, frequently involving computers, where one does not need a great deal of technical expertise.
proton
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i have a question about applied math grad school admissions:
what do the top grad schools look for in applicants? are gpa, letters of rec and gre scores the main factors? do research, REUs, etc matter?
what do the top grad schools look for in applicants? are gpa, letters of rec and gre scores the main factors? do research, REUs, etc matter?
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i do not know about applied math in particular, but i know about all grad programs in general. what is sought is sheer mathematical strength and tenacity, creativity and potential to do good research.
it is assumed that the best candidates will also have high scores of most every sort, but the really distinguished candidates will have impressed someone personally, who will say so in a letter.
it is assumed that the best candidates will also have high scores of most every sort, but the really distinguished candidates will have impressed someone personally, who will say so in a letter.
proton
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oh yeah, i had 1 more question about grad schools:
do they only really care about your major gpa? like if you majored in physics and math and apply to math grad school program, do they only care about your math gpa? not your physics gpa?
do they only really care about your major gpa? like if you majored in physics and math and apply to math grad school program, do they only care about your math gpa? not your physics gpa?
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i think i answered this above.
eastside00_99
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mathwonk said:
oh my god! I waiting to hear from the schools I applied too; this sounds really intimidating.
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well that's what we want. but there are not a lot of those, so we'll take what we can get.
torquerotates
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Hey, guys. I'm new to this forum. I have been interested in math for a while now, but have now decided to major in. I face a major concern. I'm currently a community college student intending to transfer to a top school. I have great grades and straight A's in math courses up to differential equations and am currently expecting an A in linear algebra. But I'm afraid that all this will not prepare me for upper div work at the 4yr. We've covered all the standards that the AP covers, i.e computing derivatives and integrals etc. But we lack rigor completely. I fact I haven't even seen proofs until linear algebra. I'm transferring next fall. Is there still time to catch up? If so what should I do?
PowerIso
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I wouldn't worry to much. You might want to work on some of your proof writing, since the courses after linear algebra are pretty heavy into it. Especially if your university requires math majors to take a calculus proof based class. If you want to get a good idea on general proof ideas and terminology you can read:
"A transition to Advanced Mathematics" by Chartrand. It isn't a long book, but it gives you a good overview on the type of proofs out there and how to attack certain problems.
"A transition to Advanced Mathematics" by Chartrand. It isn't a long book, but it gives you a good overview on the type of proofs out there and how to attack certain problems.
aXiom_dt
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How does co-op work for a (undergraduate) pure math program? Is there a way to get some kind of research related job?
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eastside00_99
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mathwonk said:
Its amazing! I got an acceptance letter today from U of ill in urbana. I didn't see that coming; this was the highest ranked school I applied to.
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Congratulations! 
Evariste
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Is it always best to read one subject at a time?