You said “Government funding for basic research in math or any other pure sciences are probably bloated, which explains why all these advance math department are seeing so many foreign-borns, when taking away these fundings would do more good and discourage such overt foreign slave-labor.”

I am from a third-world nation. I intend on pursuing a math phd from a good school in the US. I doubt i’m ’slave labor’. I want to go to the US because it has many good mathematicians. Your phrase sheds much light on the limitations of your thinking.
Moreover, I do math not because it has applications…its a bit like asking a musician why he makes patterned sound-waves which can’t be used for anything (perhaps heavy metal can scare away crows?).
Perhaps you’ve never felt joy doing math.
Strangely this is not much different from the joy ive seen felt by my physics peers..i remember being asked in my first year by a math student what possible use could there be of hilbert spaces…he shifted to physics…he loves QM and now he loves functional analysis too…but not ONLY because it has uses in QM or because its a beautiful fact that beautiful math explains deep things about nature. But because he now apprehends the beauty of the idea.
When i or any other serious student of math (even physics and some eco students) do math, applications is the last thing on out minds. Its not even a goal. And remember i come from a third world country — earning ‘big bucks’ is a big thing for us and we are aware of the fact that a banker gets more money than a mathematician. And yet many of us want to stick to the ‘irrational’ choice of taking up math as a career and perhaps come to the US where the pay for being just a phd student is better than what it is in my country (that helps, I wouldnt care to own a bentley, but its nice to be able to buy a small house and pay for your kids education).

- zf

I’m not religious. The question wasn’t rhetoric but a real one.
Sorry for the word ‘all’ which is a bit too strong - I actually meant ’some/most’.
Anyway, the comparative advantage and ‘do what you like’ arguments are good ones. Still its a matter of finding the correct balance. Whether society would be better off with more/less pure mathematicians than there are today I guess nobody could ever tell.

“Had Terry Tao worked on Engineering, I doubt that he would have contributed to Engineering as much as he has done in Mathematics. ”

Probably true. But there are opposite examples like Shannon.

is it feasible to patent certain mathematical results so that royalt fees can be collected for commercial applications that make use of the results? the fees can then go into the “International Monetary Fund For The Advancement Of Mathematics”.

kt

To address Oz’s question “had all these terry tao’s and their likes worked on applied problems in engineering and science, wouldn’t their work lead to more useful stuff?”, I’d like to add another argument, although it’s non-falsifiable. Had Terry Tao worked on Engineering, I doubt that he would have contributed to Engineering as much as he has done in Mathematics.

As Terry pointed out earlier, a person’s productivity/talent depends so much on his passion and hard work rather than raw intelligence.