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Hi, I'm sure I'm not the only Ph.D. mathematician on MO in serious need of career advice. I'm sure there will be other readers in similar situations, who will find any good advice very helpful. Can ...

I have recently started a PhD. and am researching an area that two now eminent mathematicians devoted considerable time to in the 1980s. However, there appears to have been fairly moderate focus on ...

I am a graduate student thinking about some stuff. 1) If I have an idea for a result but it is not yet complete, is it advisable to mention it to others (especially more experienced people)? Is it ...

First, my apology for this soft question. My excuse was that I really think this may be of interest to the community. I would understand if it gets closed (I have advocated closing some soft questions ...