I'm not sure what you mean by this...I mean, two of the best-paid graduate jobs out there are actuarial work and investment banking. Both of which like maths graduates!Originally Posted by CaptainBlack
(Of course, you mean more `technical' jobs, and I would have to agree, but I'm not sure that this would increase the number of maths students - few of them want to design torpedos!)
2 questions often asked, in general, are:
why study humanities (what practical use is this information)?
why study mathematics (what practical use is this information)?
i submit that the answer, to both questions, is the same: to learn how to think. to ability to think clearly, in both an analytic\logical sense, and a naturalistic\linguistic sense, is of indespensable use in ANY endeavor, be it designing torpedos, painting a landscape, writing a government funding request, hunting deer, or making forum posts. too often, people who see the reasonableness of one kind of learning, deride the other. i believe that the mathematician without something of the poet and philosopher in them, is not much of a mathematician, and the poet or philosopher who cannot think logically, is not exemplary in their field, either.
we (humanity as a whole) desperately need both skill sets: we need to be able to form and communicate ideas, and we need to know how to sensibly discern between various ideas for value. two things essential for survival (and we learn this intuitively at an early age) are the ability to imagine things, and the ability to determine things that constrain our imaginings. now, for many people, the expansionist practice of accumulating ideas (having a "bigger bag of tricks") is of obvious value (but why the humanities? does it not stand to reason that we should start our idea acquisition from those whose ideas were considered good enough to keep, over the centuries?).
but mathematics is essentially "reductionist", mathematics is the gentle art of "forgetting stuff that's not relevant". linear algebra is a case in point...what the various entries in our matrices and vectors stand for, is of no help in determining their relationships, and keeping the "link" just slows down the calculations (and doesn't help notation, either). the hope is, of course, that by exposing young 'uns to numbers, they will see that this one example shows the value of such reductive abstraction ('rithmetic is as good a 'larnin' as 'ritin is), but many people get confused by the lesson....and deduce that calculation IS mathematics (odd that no one ever makes a similar mix-up between spelling and reading). that's too bad, as many of the "prettier" examples are only available when you have a large enough mathematical vocabulary to speak of them (just as many great books, or works of art, require understanding how they are put together, to get the most out of them).
what i think is needed, is a more categorical approach to being educated. the case for specialization has been made well, but how much are we missing, because people in different fields don't understand each other (or even try)? a historian with a knowledge of structures, has one more tool to analyze events with; a mathematician with a knowledge of history, has one more structure to add to his tools. the two sides of our nature are not at war: they inform each other, and the person who has access to both will be more successful, no matter what their chosen field.
(Considering the other posts, this is also a partial response to Deveno's post above as well.)
I guess I take an opposing viewpoint on this issue. Your statement is basically analogous to asking "Why learn how to paint?", and then answering "Because you can develop your fine motor skills and eye-hand coordination." I don't think that anybody would evaluate the craft of painting in that way. So in this light, I see the situation as the other way around. The primary purpose in developing mathematics is solve either real-world or theoretical problems. (More simply, it is useful and / or interesting! Though, to be fair, this doesn't seem obvious looking at the state of mathematical literature now.) It seems to me that developing one's thinking and analysis skills is the secondary benefit.
the trouble with this sort of point of view (and it certainly has its supporters amongst, oh, physicists, let's say) is that knowledge is justified in terms of its applications. but that's putting the cart before the horse. we don't always know before-hand just which problems will turn out to be important. now, we've built up a lot of knowledge over the millenia, and in so doing have raised a lot of unanswered questions. and it's certainly fine for some people (even a lot of people) to work on "clean-up". but i ask you: in your relationship with any body of knowledge, do you want to be the master, or the slave?
to take your painting analogy a bit further: if one wishes to be a better sniper, learning how to paint seems an excellent way to practice fine motor skills and hand-to-eye coordination. the japanese believed a samurai should learn calligraphy, so as to be a better soldier. i think they were onto something.
personally, and i might very well be in a minority here, seeing mathematics as just the hand-maiden of science is somewhat of a demeaning view. it carries with it the implication that our lives should be "practical", that the only challenges worth taking seriously in life, are problems to be solved, and put to bed. certainly, the utility of a subject is one possible justification for its study, but...we are so much more than objects with objectives. we ought to be encouraged to wonder about things, perhaps not exclusively, but certainly as a part of "becoming" whatever it is we wind up being.
of course, this flies in the face of the way almost every subject is taught (and perhaps more tellingly, funded). which convinces me (although you are free to disagree) that the leaders of our society are idiots, and don't deserve the trust society gives them so freely. i read somewhere that most american children don't have any idea where iraq is, and that a third of them don't even know where louisiana is. geography isn't taught because "it's not practical". we are breeding generations of people with blinders on, and i feel a very real possibility is that society, as a whole, could just wind up at a dead-end, with no answer to the question: "where do we go from here?". such is the weakness of using the past as a way to measure the future.
the best way forward isn't always "straight-ahead". sometimes "going sideways" is better. to just mine deeper and deeper, is to get stuck in a rut, sometimes a wider view is better, even with the added inefficiency.
all things considered, i would rather be a person who doesn't know, but can discover, rather than the person who knows, but cannot discover.
One thing which would make my life considerably easier: have more universities allow students to take a gap year before starting a math course. Honestly, I wouldn't be going to a university if I was incapable of obtaining study material during this time period.
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