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The important tool: a PhD in applied mathematics that taught me how to think originally and creatively about problems, to abstract and codify them with mathemat
by achompas 10y ago
The important tool: a PhD in applied mathematics that taught me how to think originally and creatively about problems, to abstract and codify them with mathematics, and to approach them numerically and computationally.
What is a first approximation to this experience, particularly the creative thinking portion? As someone with a MS but without a PhD, I suspect you get to flex this ability during the research phase of your studies.
- laingc 10y agoI'm note really sure what a good first approximation would be, but maybe I can break down the elements of it a bit, and we can see whether there is some other experience that mimics it. * Spending several years, uninterrupted and undistracted, thinking deeply about a mathematical topic. * Being advised and supported, but not led or coddled, by an experienced researcher. * Being surrounded by clever people, who do research full-time. * Working in an environment where not knowing the answer. immediately, or even quickly, is not just accepted by expected. * Being "left in the dark", with the understanding that the process of being in that position and finding your way out is the very thing that you are trying to learn. * Having rigorous expectations for the "final result" (to the extent that one can be found). I can't think of a great approximation to that, but perhaps someone else can chime in. EDIT0: Formatting EDIT1: Also worth noting that by far the smartest person I know - a deep thinker, also nominally a data scientist, but foremost a truly original and creative mathematical thinker - didn't complete his PhD and left with a Masters. Intellectually, this guy makes me look like a geriatric Corgi on opium, and he didn't need a PhD to make him that way.