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Pure Math, Pure Joy
e271828 writes "The New York Times is carrying a nice little piece entitled Pure Math, Pure Joy about the beauty and applicability of pure math as carried out at the Mathematical Sciences Research Institute. There is an accompanying slideshow of pictures of mathematicians in action; I particularly loved the picture titled Waging Mental Battle with a Proof."
I think that Mathematicians largely arent the philanthropists that scientists are.
However, seeing as how every science consists largely of mathematical models, the ends justify the means, so to speak.
In other words, while a mathematician isnt looking for a way to make a longer lasting lightbulb, his or her ideas eventually work their way into science and engineering applications, even if it takes decades to happen.
"Open the pod by doors, Hal" > "I'm afraid I can't do that, Dave" sudo "Open the pod bay doors, Hal" > alright
Mathematicians do it for the beauty. Society funds them because what is beautiful to a mathematician often turns out to be useful in many other ways. The NSF is paying me to do math research this summer, and honestly I don't care if what I'm doing has any relevance to anything -- I'm just doing it because what I'm studying is really cool and beautiful. But it may turn out that something I find is useful for something else that I never even thought of. This is what happened in large part with number theory -- many of the underlying results were discovered i nthe 1800's and early 1900's, and only later turned out to be useful in cryptography. You can't predict what will be useful and what won't.
If mathematicans aren't really interested in helping understand the world, why should society fund them?
These are two separate things. Many people are attracted to the natural sciences, and even engineering disciplines, not because of a desire to improve the world, but because they find pleasure and abstract beauty in those fields. Yet undeniably work in those areas can lead to benefits for "society", and therefore people doing research in those areas are funded, even if their personal reasons for doing the work have nothing to do with those benefits. Likewise with mathematics, many ideas thought of as purely abstract and disconnected from practical application have turned out, later on, to be useful tools in understanding various real-world phenomena.
It is totally unscientific and ultimately counter-productive to close off areas of inquiry because at the time they are undertaken no one can know exactly what the consequences will be. And ultimately the motivations of the people involved are irrelevant; we know based on history that there could turn out to be uses for it in the future, even if neither "we" (the society making the decision to support the research), nor those doing the research, can see any at this time, and this potentiality alone should justify providing support.
"(Man) tries to live his own life as if he were telling a story. But you have to choose: live or tell." --Sartre
I sure hope this isn't really true. If mathematicans aren't really interested in helping understand the world, why should society fund them? I certainly know that a major motivation for my career in science is that understanding the world through science will help people, cure diseases, etc.
Guess what? It gets worse.. it's not only the mathematicians, but just about anyone and everyone involved in fundamental research.
I know I am.. I do theoretical chemistry.. and although I'd love to see something useful come out of what I do, I cannot see any immediate uses for my work.
The point is: It's the foundation research, the fundamentals, that lead to the big, *big* innovations. Although it might not seem useful at the time, it may (or may not) turn out to be very very important in the future. However, by it's nature, we can't know which research is going to pay off in practical terms.
Einsteins work on stimulated emission probably didn't look very useful back in 1910 either, but it lead to the devlopment of the laser, which noone could've predicted at that time.
That's why we need to fund this stuff.
OK, not in it's entirety, and not it is a serious problem, but it would be nice if the editors could make sure that each Sunday, we don't see so many postings from a single news source. Maybe some sort of summary each Sunday on interesting stories in the NYT Sunday Edition.
Pure Math, Pure Joy
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I'd never studied linear algebra until recently when I had to learn just enough to work through the inverse kinematics of a robot arm. Actually, I never really got along with Mathematics very well anyway. But looking at how matrices can solve all kinds of problems just by drawing zig-zags through rows and columns of numbers made me wonder whether the problems they model or the problems themselves came first. As I was learning the little bit of this math that I did, it started to seem to me that the Math has an independent existence, and a somewhat mysterious set of relationships of correlations and causalities connected to but not dependant on physical nature.
For the most part, we're in it because we want to know. Maybe you think that's a selfish reason, and maybe it is, but when we discover something we immediately share it with the world. The enduring gifts of mathematics are that it extends the boundaries of what is possible with current technology, while presenting us with direction for the future.
In Soviet America the banks rob you!
Very large prime numbers are the basis of the RSA asymmetric encryption algorithms which you trust your credit card numbers and other private information to.
Anyway, I'm almost thinking you're trolling because the rest of your post demonstrates some sort of keen-ness for over-simplification. Maybe you're just not out of secondary school yet, but for your information, trig, calculus and the rest are useful for a lot more stuff than what you mention. All the different areas of maths often intermingle in any physical subject.
For the interesting tidbit of information, there has yet to be a mathematical discovery which has not found practical applications. Even group theory, which at first was thought to have nothing to do with physics or any engineering sciences, was found to be very applicable to some extremely interesting problems of fundamental physics (describing the symmetries of fundamental particles).
Daniel
Carpe Diem
How arbitrary is that?
How is e) (prime) less valid than the solution?
How about g) (The only number greater than 29)?
How about a) because its the "bad luck" number in Chinese culture (Too bad you missed out on that one, "white devil")?
How about j) (Because today is Sunday and I feel like its the correct answer)?
The surprise isn't how often we make bad choices; the surprise is how seldom they defeat us.
What is the next in the sequence of:
1,2,4,...
My answer was . The sequence is the largest number of separate enclosed areas it is possible to make by adding a single straight line to a circle. (i.e. 1 for no lines, 2 for one line, 4 for two lines)
I hate this kind of question, because it is possible to design a sequence such that any number comes next, so any test which includes the possibility of incorrect answers is just plain wrong. Of course you should have to justify your answer, but since the IQ tests are multiple choice...
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