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I'm not sure what you mean by "real world problems". Most mathematicians do mathematics because they find it beautiful, rewarding, fun, and for various other re

I'm not sure what you mean by "real world problems". Most mathematicians do mathematics because they find it beautiful, rewarding, fun, and for various other reasons that have little to do with creating things in the physical world. Mathematics is extremely interconnected and some minor discovery in a certain field can later become extremely important in some seemingly unrelated field, similarly - real world applications often arise unexpectedly out of things which at first seem completely theoretical (famous example: public key cryptography), and we cannot foresee in advanced what will lead to what. Timothy Gowers - 1998 Fields medalist - gave a lecture in 2000 titled "The Importance of Mathematics". I advice everyone to watch/read it: Video: https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 PDF: https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf Edit: more philosophically, this question always seems puzzling to me, because we can always ask: whats so important about "real world applications" anyway? We can start from any activity and ask "why is it important?", and then ask the same about the answer, etc'. This chain of "why"s eventually comes to an end: we can still ask the question, but there is no meaningful answer other than the realization that the things which are important are the things people find important - whether it is to get faster from point A to point B, have a baby, go to a party, or to solve mathematical problems. Something isn't more important because it's in the "real world".

trevyn 13y ago
I think many "real world applications" tend to directly or indirectly support our biological goals of individual and/or species survival and reproduction. Of course, the same could be said of basic research, but it is further removed and so requires more forward thinking to appreciate.
- pavelrub 13y ago
  I don't see how this is true. If the question is "what are the real world applications of X in mathematics?", most people would be satisfied by any absurd answer as long as it's "in the real world", regardless of what biological goals, if any, it supports. It could be that a certain mathematical research allowed us to develop sturdier pencils, and suddenly everybody is satisfied that we are not wasting our money because now it has "real world applications". The human drive to discover and invent new things in math is fundamentally no different than the human drive for doing the same in the fields of technology, arts, etc'. But we perceive anything touchable as good, and anything imaginary as useless, because that's the kind of culture we live in: Making a slightly faster smartphone so that the activity of swiping a finger on a capacitive touch screen to play candy crush now takes 0.7 seconds instead of 0.8 doesn't need any justification, but thinking about math does.

trevyn 13y ago

I think many "real world applications" tend to directly or indirectly support our biological goals of individual and/or species survival and reproduction. Of course, the same could be said of basic research, but it is further removed and so requires more forward thinking to appreciate.

pavelrub 13y ago
I don't see how this is true. If the question is "what are the real world applications of X in mathematics?", most people would be satisfied by any absurd answer as long as it's "in the real world", regardless of what biological goals, if any, it supports. It could be that a certain mathematical research allowed us to develop sturdier pencils, and suddenly everybody is satisfied that we are not wasting our money because now it has "real world applications". The human drive to discover and invent new things in math is fundamentally no different than the human drive for doing the same in the fields of technology, arts, etc'. But we perceive anything touchable as good, and anything imaginary as useless, because that's the kind of culture we live in: Making a slightly faster smartphone so that the activity of swiping a finger on a capacitive touch screen to play candy crush now takes 0.7 seconds instead of 0.8 doesn't need any justification, but thinking about math does.