> Pure Number Theory is motivated by applications in cryptography,
> Pure Calculus is motivated by applications in ballistics and weather forecasting,
> Pure Combinatorics is motivated by analysis of computer networks and data processing,
> Pure Statistics is motivated by life assurance, insurance and gambling,
> Pure Linear Algebra is motivated by optimization problems and Google's Page Rank algorithm.
Math is really sweet, math allows you to make so much, just look around you. I see it as the most powerful, low level, oldest (probably) API in the world. And it's mostly free and open source ! Math gives you tools and tells you in what context they work and don't work. Then it's up to you using it to make or understand something cool. Actually, math purposely tries to abstract itself as much as possible from reality in order to give you a robust framework to work with.
I think this quote of David Hilbert's response upon hearing that one of his students had dropped out to study poetry made me understand why pure math and applied math were two distinct fields:
"Good, he did not have enough imagination to become a mathematician" [1]
Like honestly, who cares about whether or not all simply connected closed 3-manifold are homeomorphic to a 3-sphere. But the understanding it brings us about the behavior of manifolds in particular contexts is very real. Whether it's useful or not isn't a pure mathematician's problem though :D (but the truth is that it probably is, just that somebody else will make use of that)
> Pure Calculus is motivated by applications in ballistics and weather forecasting,
> Pure Combinatorics is motivated by analysis of computer networks and data processing,
> Pure Statistics is motivated by life assurance, insurance and gambling,
> Pure Linear Algebra is motivated by optimization problems and Google's Page Rank algorithm.
Math is really sweet, math allows you to make so much, just look around you. I see it as the most powerful, low level, oldest (probably) API in the world. And it's mostly free and open source ! Math gives you tools and tells you in what context they work and don't work. Then it's up to you using it to make or understand something cool. Actually, math purposely tries to abstract itself as much as possible from reality in order to give you a robust framework to work with.
I think this quote of David Hilbert's response upon hearing that one of his students had dropped out to study poetry made me understand why pure math and applied math were two distinct fields: "Good, he did not have enough imagination to become a mathematician" [1]
Like honestly, who cares about whether or not all simply connected closed 3-manifold are homeomorphic to a 3-sphere. But the understanding it brings us about the behavior of manifolds in particular contexts is very real. Whether it's useful or not isn't a pure mathematician's problem though :D (but the truth is that it probably is, just that somebody else will make use of that)
[1] http://www.amazon.com/The-Universal-Book-Mathematics-Abracad... pp. 151 (according to wikipedia, I haven't read the book)