IMO Bill Thurston is saying people are people first and mathematicians second. People often feel the need to contribute to the world and mathematicians often wonder how they can do it through mathematics. And of course he says it's not easy to answer that. There's nothing wrong in trying to pursue mathematics to improve some aspect of the world. There are millions of way in which pursuing mathematics can improve the world.
My above comment has started its slow descent into negative karma, and there's probably nothing I can do about it -- what's the point of karma if not to spend it from time to time anyway.
I'm currently reading "How Not to Be Wrong" by mathematician Jordan Ellenberg; here's what he has to say about his calling:
"Pure mathematics can be a kind of convent, a quiet place safely cut off from the pernicious influences of the world's messiness and inconsistency. I grew up inside those walls. Other math kids I knew were tempted by applications to physics, or genomics, or the black art of hedge fund management, but I wanted no such rumspringa. As a graduate student, I dedicated myself to number theory, what Gauss called "the queen of mathematics," the purest of the pure subjects, the sealed garden at the center of the convent, where we contemplated the same questions about numbers and equations that troubled the Greeks and have gotten hardly less vexing in the twenty-five hundred years since.
"At first I worked on number theory with a classical flavor, proving facts about sums of fourth powers of whole numbers that I could, if pressed, explain to my family at Thanksgiving, even if I couldn't explain how I proved what I proved. But before long I got enticed into even more abstract realms, investigating problems where the basic actors— "residually modular Galois representations," "cohomology of moduli schemes," "dynamical systems on homogeneous spaces," things like that—were impossible to talk about outside the archipelago of seminar halls and faculty lounges that stretches from Oxford to Princeton to Kyoto to Paris to Madison, Wisconsin, where I'm a professor now. When I tell you this stuff is thrilling, and meaningful, and beautiful, and that I'll never get tired of thinking about it, you may just have to believe me, because it takes a long education just to get to the point where the objects of study rear into view."
Maths appeal rests in it being a "sealed garden at the center of the convent". One should do math because this sealed garden brings you peace, because you belong there.
And now Ellenberg is trying to educate and contribute to the world with his writing, because he has some semi-moral push to do something more than just appreciate that sealed garden.
I find cohomology of moduli schemes thrilling too, but it is really cool when you can use a little math to solve someone's real problem, or more often, use a little math to try to dismantle something bad (see mathbabe.org for some economic applications).
That's right: not with his math. The math he talks about in his book has been around for at least 200 years.
I don't and will never pretend that when you're a mathematician you're forbidden to help others -- that would be meaningless and ridiculous. I react to the "feel good" sentiment that the motivation to do maths should be found in a desire to better the world.
Math is an end in itself; if you want to help the world that should be on your own time.
> Math is an end in itself; if you want to help the world that should be on your own time.
the marks of an idealist who doesn't do math "for a living." I am a mathematician. I've been doing it for years. You argue for a purity that is naive and counterproductive.
Mathematicians have all sorts of motivations to do mathematics. Intrinsic beauty is certainly primary, but in order to continue in this job that doesn't pay all that well and requires sacrifices our families don't understand, we've needed to come to some terms with our roles in the world. We've needed to justify our apparent uselessness, because some of us in conscience can't be useless people and can't morally continue to do pure math if it is indeed contributing nothing of value to the world. Doing math (or writing music, or making art) for the sole purity of thought, the simple beauty of it, is allowed only to people with a certain sort of psychological and financial privilege. I was not raised with that privilege.
The intrinsic beauty of math and the fact that it's a contribution to the world are not in contradiction. Bach wrote beautiful music that has changed the way we hear and the way we think, changed the path of human civilization. He did it for a paycheck. He did it for the audiences who would hear it then. He did it for the beauty. People who write programming languages because they want more beauty in programming do it for themselves and others. If Bach's music wasn't shared, if Ruby just sat hidden on a hard drive, neither of them would have made a lick of difference in the world and I would argue they'd have no value. Mathematics exists without and beyond us. Our discoveries, and the way they're shared, are what make them valuable to human life.
I do math because I desire to better the world: not by ending child abuse, but by discovering and then sharing the beauty of new mathematics. That's why we write papers, you know -- not just for jobs and tenure. Sharing has its own benefits, as in encountering the ideas of others we are sparked into new inspiration.
Move beyond the political and charitable in thinking about how one might better the world. Many software developers are interested in bettering the world and are doing it through their work, even if it's not an app for water in Africa. Can you so readily dismiss all of them? or is it ok because software development is a dirty business that contrasts with that pure garden of mathematics?
It seems we completely agree, but you have a peculiar way of putting things. I'm not the one accusing you of writing papers "just for jobs and tenure"... you are! In the same post! ;-)
I think it's good that you're "sharing the beauty of new mathematics" with your peers -- that's what I've been talking about all along.
But I also think it's presumptuous to want to have a job that "betters the world"; most jobs don't make any difference in the state of the world; many worsen it; and of course a lot of people don't even have a job in the first place.
What's more, history shows that most or all of math will be useful, eventually; the way it's put in the OP, it sounds like math should turn into some kind of vocational school producing teachings that should be immediately applicable; don't be in such a hurry.
You don't know what the future will need anyway; you only know the needs of the present, which are a very bad predictor of the future. It can be argued that by thinking about the present less, one helps the world more.
I see parallels between the garden you are describing and the society of intellectuals presented in Hesse's The Glass Bead Game, a game of pure mathematical abstraction that may only be played by the trained elite of the day.
The result for the protagonist in that book raises serious questions about the purpose of the purely intellectual pursuits and their role in society and human fulfilment.
The existence of sociopaths demonstrates that his advice isn't universal. Nevertheless, it's widely applicable. And math is too often painted as a hyperindividualistic endeavor, like shopping is.
Some wish to spend all their days in a garden. They exist too; good for them. But math is not just for those who rate high on a hermit spectrum.
