EPTWhy math? - Page 3
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EternaLLegacy
United States410 Posts
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Iranon
United States983 Posts
Most people, even many people who extol the virtues of mathematics up and down, seem to be under the delusion that mathematics is a science. As such, it seems only natural that attention to and funding for mathematics research be allocated according to how useful it is -- a return on an investment. But mathematics is not a science; it's an art. The occasional applications of math to practical matters are not the purpose of math, they are byproducts and happy accidents. People who question the usefulness of pure math don't really understand what mathematics is, and people who leap to the defense of pure math with "it builds the foundation for later applications" are sort of missing the point, good intentions aside. | ||
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Lebesgue
4542 Posts
On January 19 2012 17:32 Muirhead wrote: But could Einstein have expressed enough of his ideas that physicists could have developed a language like Riemannian geometry themselves? Certainly it would have been a lot slower than having a ready-made language in place! But does the existence of the occasional ready-made language really justify the work on mathematics that could be spent working on other things? You know the phrase "Dwarfs standing on the shoulders of giants ". It's because it is So MUCH easier to further progress something that was discovered earlier. Even if it was in completely different setting, ineffective. maybe not even correct. You don't really appreciate that fact till you do research at the frontier yourself (believe me, I also didn't appreciate till I started doing research). Einstein maybe could have developed Riemanian Geometry himself (though Riemann was one of the greatest mathematicians of all time and a genius himself) but I doubt he would be able to develop both Riemanian Geometry and Relativity Theory. He wasn't almighty and there is a limit (even for the greatest of minds) to how much one can think of. Moreover, a lot of progress is not done by huge discoveries but is incremental. For that incremental process you need past work. It would be a huge impediment not being able to use advance mathematics in any field that applies mathematical techniques. And developing these techniques was non-trivial. As someone said it took years before they became applicable in practical progress. If you read history of math you will see how people struggled for decades to understand the notion of integral, define notion of continuity or understand the notion of cardinality. Tools from mathematics become wildly used with long delay. Measure Theory and Functional Analysis also seemed too abstract even in eyes of mathematicians that witnessed their development and now are basic tools used everywhere. And finally, your arguments against research in mathematics can be applied to anything. The rule of research is that bright minds pursue what they find interesting. And no one can tell if what they discover will or will not be useful in the future. These people have passion and talent for doing that. | ||
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Lebesgue
4542 Posts
"Malliavin calculus were introduce by Paul Malliavin (..) as an infinite-dimensional integration by parts technique.For several years there was only one known application. Therefore, since the theory was considered quite complicated by many, Malliavin calculus stayed relative unknown theory also among mathematicians for some time. Many mathematicians simply considered the theory too complicated compared to the results it produced." And now it is used all over sophisticated finance. So here we have a contemporary example were even mathematicians themselves and since mid 1990s it's been applied extensively. | ||
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Cascade
Australia5405 Posts
Will there ever be any practical applications from TeV scale particle collisions? Meh, not sure. Not out of the question. Is the science connected to physical reality? Most definitely yes. Will there be applications coming out from the technical constructions of the LHC? Probably yes. Will there be applications on the existence/non existence of the Higgs? Not anytime soon for sure, maybe never. When I saw the title I first open it with the intent to troll ("lol no use for math wtf srsly? i never use math and I do fine!!") but I found a kindof serious well thought through OP, so I though I could actually share some inside info, but then I read the replies and I see several people in the trade already has done so. Now there is not much for me to do here more than comment on the other comments.  The "art" argument is ridiculous. If the only reason to study math would be it's own beauty, then I'd strongly urge every government to cut all funding to mathematics... It'd be like any other art, only that you would have to spend years and years to understand it. 99.9% of the people would have no chance to understand it. Then please spend that money on sorting out the starving situation in Africa instead please. Cutting funding completely for everything except engineering and trust the engineers to themselves find the mathematics. Well, as some people have said, some engineers would be more focused on actual use, and would not grasp the maths well enough to really advance maths. It would have to be the more math-type engineers to think about how math could be advanced to further engineering. Why not call those math-type engineers "mathematicians"?  There has to be a balance for how much funding is spent on applications, and on theory. Imo, there is a bit too much spent on theory atm. While I have not a good idea of how much is spent on non-application mathematics, I know that quite a lot is spent on particle physics, not least due to LHC. I have the feeling that there could have been better things done for that money. Then string theory...  now THAT is a talent sink. So many smart masters students that get fascinated by string theory and waste their career on this thing existing only in their minds... I know, because I was very close to be one of those myself. I went to italy to do my master project, and essentially went there and picked the most abstract theoretical subject I could find for my master project (supergravity). I was young and enthusiastic about exploring and pushing the front of physics and understanding. I got offered to stay for PhD there, but decided to go back to sweden for personal reasons. In sweden I presented my master project and afterwards I got some questions from the audience, one of which was "Can you measure any of this?". I don't see myself as stupid or narrow minded or anything, but during the year working on this project in italy, not one time had that though crossed my mind. Measure? What? :o I ended up taking a PhD in particle physics phenomenology in sweden instead, doing things that you actually can measure, somehow exploring nature if you want, although I don't see how my work will ever be of public use. So yeah, we should definitely keep funding research on theory, even without applications in sight, but in moderations. Theory with possible or even probably application, short or long term, deserve much more funding ofc. Not always easy to tell the difference though. Particle physics for example, and specially string theory for example is overfunded imo. There is a continuous scale - from engineering that is of clear public use (combustion physics) - through physics that is barely generating things of public use (advanced quantum mechanics, GR) - through physics that may be of use (particle physics) - through physics that is very far from any applications (strings) - to pure mathematics without any current applications in physics. these should be funded less the further down the list, but it's not easy to place a specific area on this scale, and not clear exactly how much decreasing it should be. and OP: do you know that groups are used A LOT in particle physics? Not sure exactly what groups you work on, but I think any work on groups and their classification is of potential use in particle physics. E_8 is the master group in string theory for example, who could have guessed when they first classified the lie groups and found some stupid exceptional group of very high dimension that didn't really fit into their system. | ||
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Daimai
Sweden762 Posts
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darkmighty
Brazil48 Posts
On January 19 2012 17:32 Muirhead wrote: But could Einstein have expressed enough of his ideas that physicists could have developed a language like Riemannian geometry themselves? Certainly it would have been a lot slower than having a ready-made language in place! But does the existence of the occasional ready-made language really justify the work on mathematics that could be spent working on other things? /\ That and the whole assumption of this thread is wrong. The OP thinks a enormous amount is spent on math research, which isn't true (compare it to other sciences or engineering at it's laughable). Also, he thinks mathematicians do pure research 100% of the time, and disregards consulting work, like providing tools/assistance to other sciences/research groups, and all that jazz. Also, don't forget computer science is largely pure math. Without modern CS work in what position do you think we would be? Seriously, if you take the toll benefit of mathematical research on the long run and the toll that was spent on research, it is ridiculous to think, imo. I just agree that math shouldn't be overpopulated with students who lack real commitment to their research, but preventing that is the job of people who analyse research grants anyways. Btw, I'm not a mathematician, I'm an undergraduate electrical engineer on my 2nd year in uni. | ||
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Mr. Black
United States470 Posts
On January 19 2012 19:45 Plexa wrote: As a masters student in pure math, we study math in the hopes that one day someone discovers a use for it. At the end of the day, computer science is just math, economics is math, engineering is math, physics is math, there's math involved with some areas of genetics and protein folding, there's some math involved in chemistry etc. Math provides the framework for all of these ares to use and so their own progress isn't hindered by a lack of understanding. Without the rigor of maths then the method of 'developing things as we go' wouldn't yield the same results. Some of the results in math are very technical and rely on the rigorous framework that math provides. Sure, physicists might have 'guessed' that the theorem was true based on experiments/trial and error but they probably would have guessed some things which weren't true as well. Yeah, no. The people studying math generally aren't people who are 'egg heads' and we certainly won't 'wilt like flowers'. Most of us are multi-talented and could easily transfer to any math related field. I've also seen some very talented mathematicians choose not to study math and instead pursue another field with success. You are absolutely correct and I framed my statement poorly. I did not mean to say that a math person could not apply his intellect to a successful career elsewhere--I would not say that it is a matter of ability. Rather, my point is, if what a person wants to do more than anything else is to push the boundaries of theoretical or pure math, and that person was shamed or forced into giving this up to do something "practical," a part of their spirit is sacrificed and you won't be getting that person's best effort. Of course if a talented mathematician decides on his own to pursue something else, the ability to think systematically and logically (even creatively in a way?) will serve him well in almost any field. By 'egghead' I meant "smart person pursuing an academic (rather than commercial) field." It is a term that carries a negative connotation though, and my point was hindered by using it. To be clear, I do not think of mathematicians as particularly frail or unadaptable. By 'wilt like flowers' I mean to the extent that any passionate person is lessened when they are deprived of the thing that drives them. I admire math and mathematicians, as well as all those who pursue "pure science" type fields of study -- I can think of no more merit-based system than highly advanced math. I got up to differential equations before I accepted that I lacked the attention to detail (and other important qualities) to progress further in math. Rather than be angry that I struggled through so much math that I don't use (a common response), I am more sad that I was not more successful, and insecure about what it says about me that I have performance issues with math. I then made a choice to go in another direction and have achieved a measure of success. But thankfully no one with power has ever said to me, "You know what, you are no longer allowed to do [insert things that I love] because it is not useful to society." I would wilt like a flower in my new, "practical" job. | ||
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blankspace
United States292 Posts
1) Mathematics has had tremendous success as a tool in the sciences 2) Many people who do mathematics finding it appealing on a intellectual or artistic level. The unexpected power of new formulations or approaches can be mind boggling (galois theory, complex analysis, cantor's theory of the infinite). Non-mathematicians that use mathematics in their profession often see 1) but not much of 2). Therefore they have trouble understanding people who prioritize 2) to 1). Moreover, they aren't completely distinct things. Value in 1) may contribute to 2) and vice-versa. Mathematicians like to do math. Why make them unhappy by restricting the scope of their investigations to the applied? I certainly do not think it is a waste of time for a mathematician to indulge in highly abstract subjects even if they have no clear application. What would your friend have them do instead? Go spend his life working in charitable organizations? In terms of social value, it is probably better, he may even help save lives of homeless people. But it's foolish to have such a "utility" based short-sighted view. People aren't robots, and we have passions for various things. For some mathematicians it may be the search for truth and structure, chess players love to play chess, physicists want to learn more about how our physical world operates. I know the american culture has very little appreciation or understanding of mathematics. One could attribute this to the lack of general aptitude, but I don't think that's the case. Part of it is the sad curriculum and AP calculus based approaches to things like multivariable calculus, differential equations and linear algebra, which completely extract the philosophy that the subjects are based on. The other aspect is that mathematics requires patience and careful reflection, difficult for children and nowadays many adults as well. | ||
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