>And another thing: Only geniuses (or cranks) head straight for the grandest and most fundamental problems. You should multiply the importance of the problem by

>And another thing: Only geniuses (or cranks) head straight for the grandest and most fundamental problems. You should multiply the importance of the problem by the probability that you’ll solve it and maximize that product. This echoes something Terry Tao said:[0] >There is a particularly dangerous occupational hazard in this subject: one can become focused, to the exclusion of other mathematical activity (and in extreme cases, on non-mathematical activity also), on a single really difficult problem in a field (or on some grand unifying theory) before one is really ready (both in terms of mathematical preparation, and also in terms of one’s career) to devote so much of one’s research time to such a project. The "don't be too bright" advice matches what something Terry's said as well:[1] >Does one have to be a genius to do mathematics? >The answer is an emphatic NO. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the “big picture”. And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does not need some sort of magic “genius gene” that spontaneously generates ex nihilo deep insights, unexpected solutions to problems, or other supernatural abilities. Nowhere do they say that you shouldn't care about, think about, or try to solve big important unsolved problems. The point is that there is a lot of work out there that isn't the grand fundamental problems, that it's still really important work, and that you probably aren't ready to tackle those problems yet. Give them a go, but don't spend years of your early career trying to solve the Riemann hypothesis, because that's the route to publishing your work on vixra. [0]: https://terrytao.wordpress.com/career-advice/dont-prematurely-obsess-on-a-single-big-problem-or-big-theory/ https://terrytao.wordpress.com/career-advice/dont-prematurel... [1]: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/does-one-have-t...