Next on our advice-sharing project, Ashish Goel shares advice he got and advice he gives.
I was really excited about a new approach to decision making (https://arxiv.org/abs/1710.00771) and asked Don Knuth how I would go about convincing others that this is a good model. He gave me the following tip, which is useful for all modeling problems, and which I am paraphrasing since I don’t remember his exact words: Try to break your model in every conceivable way as if you were an adversary, and if you can’t, then whether or not anyone else is convinced, at least you will know that it is a good model.
I give the following two tips to new students who want to work with me:
(a) You have to start working on a problem that I give you, or that you are excited about and give to me. I don’t want to start a new collaboration by negotiating on a compromise problem that neither of us is passionate about or will take ownership of.
(b) Bad theory research happens for one main reason — we work on problems which superficially seem applied but we are not sufficiently committed to the application, just to our favorite technique. We should either do methodological research in our favorite area (eg. communication complexity), or become methodology-agnostic, and solve
the applied problem using the best tools for that problem. For example, “Using Semi-definite programming for VLSI layout” is not a good problem statement. Either develop the theory of semi-definite programming, or work on VLSI layout using the best algorithmic tools available. This tool may end up being semi-definite programming after
the fact, which is a great outcome, just not a good goal.