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I like the characterization of pure vs. applied math being primarily about motivation. I've often said the difference is more on the "why" that the "what".
by ska 8y ago
I like the characterization of pure vs. applied math being primarily about motivation. I've often said the difference is more on the "why" that the "what".
- qubex 8y agoI studied applied mathematics. Roughly summarised: pure mathematicians create new math through the process of conjecture and proof. Applied mathematicians use those theorems and methods to solve simplified models of reality in order to draw conclusions about expected behaviour and/or for the sake of optimisation.
- ska 8y agoThat'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 agoAnd 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 agoYou 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 agoWe call them "physicists" :)
- ska 8y agohah. 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 agoI 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
- hopler 8y ago"Why" does not exist in science. "Why" is metaphysics. Pure math is increasing abstraction, moving away from physical reality, from examples to patterns. Applied math is the reverse direction. No matter which direction is your personal preference, sometimes switching direction helps you reach your goal.
- Pamar 8y agoMaybe you would prefer "what for" vs. "what"?
- ska 8y agoYou misread my intent, I'm sure I could have been more clear. "Why" in this case is not the subject of study, but the motivation (to repeat the OPs phrasing). Wearing an "applied" hat or "pure" hat I might end up studying the same objects, but for different reasons. For what it's worth I find your characterization awkward; an attempt to map onto a simple spectrum that seems to miss something important. I'll have to think about why that is.
- bradford 8y agoA common joke among students when I was in my computer-science program: when asked a how-many or how-much question that involved basic arithmetic, one would reply: "Yeah, I can't do that. That's applied math".
- ska 8y agoThe math equivalent was "I'm a mathematician, not an arithmetician", or a variant. It's true though, lots of mathematicians are lousy at arithmetic.