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I studied applied mathematics. Roughly summarised: pure mathematicians create new math through the process of conjecture and proof. Applied mathematicians use t

• ska 8y ago
  That's not quite right, in my opinion. In a past life I was an (applied) research mathematician, but started off fairly pure. Wearing both hats you can find yourself creating new mathematics, but there is a difference in why you are doing it, and what you consider progress to mean.
  • salty_biscuits 8y ago
    And how worried you are about rigorous proofs. You can happily hand wave your way to some approximation in Applied Maths land (because you need the result, not that you are trying to prove that it is true). Then you can spend the next bit of time relaxing various assumptions about your approximation and see where it takes you. A lot of new tools come from thinking deeply about roadblocks to applied problems, that sort of thing tends to be the maths I am personally most engaged by.
    • ska 8y ago
      You still need rigorous proofs at the end, if you are trying anything new. I think I would look at it more as you might try an ugly/practical approximation, or add a term, or whatever just to see if it will improve things. And maybe it gets you "close enough" for the application. But if you have a deep think about where you are stuck and come up with a new tool, then you have to be careful.
      • salty_biscuits 8y ago
        We call them "physicists" :)
        • ska 8y ago
          hah. it's true ... there is a weird fuzzy line between theoretical physics and applied maths. Sometimes you're on the same page, sometime you really are not.
• opportune 8y ago
  I would say in my applied math degree we didn't really solve most problems (maybe an easy problem on a test) but we did work more directly with actual numbers in our proofs, and we usually proved theorems focused on solving computational problems. But mostly, no, we were not solving problems computaitonally