Mathematical musings: Graduate students and advisors

• If you want to make an impact in some area by doing math theory, should you choose an area with a lot of existing theory and no data, or an area with a lot of existing data and no theory?

  Commentary. This is purely rhetorical question, because we all know that mathematicians invariably choose the former. And wonder why the rest of the world finds us strange.

• One of a thesis advisor's main jobs is to discover the student's natural inclinations, and oppose them.

  Commentary. By which I mean that a student who likes problem-solving needs to be encouraged to read, and a student who likes reading needs to be encouraged to work on a problem. This is part of the training in "intellectual discipline" discussed above.

• Luke Skywalker had only one Dark Side to tempt him, but you will have three: hedge funds, the NSA, and Microsoft/Google/Facebook.

  Commentary. What I tell my grad students. Just kidding, Fort Meade. The computer franchise of Evil Empire, passed from IBM to Microsoft around 1990, then to Google around 2012, and now to Facebook; where next?