> do you feel you already had good mathematical intuition earlier too and the PhD made it better? Or did the PhD by itself help you build such skills from scrat

> do you feel you already had good mathematical intuition earlier too and the PhD made it better? Or did the PhD by itself help you build such skills from scratch? I really think that the PhD experience was the major factor in me developing this, though I think I showed a certain promise earlier on. I think it's certainly true that, without the PhD, I wouldn't have known how to go about the process of learning and thinking in the way that I do now. > Do you feel it can be self taught to some extent? I think you'd have to be a much smarter and more dedicated person than I am to achieve the same results without the environment, and as I mentioned in a cousin comment, I think that environment might be tough to replicate. I am a big proponent of formal education for exactly this reason. Academia certainly has many flaws, and I'm a harsh critic of them, but I personally experienced what I consider to be the best side of it, and it's this side that formed the opinion that I'm expressing here. EDIT0: Repeating what I posted in a cousin comment: 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.