Today I met with Pietro Perona. He gave me some general advice about how to choose a thesis topic and an advisor.

In his opinion, the currently hot topics are energy and climate change. To which I replied: what about curing cancer? He told me that if one finds a cure for some kind of cancer, at best he might help, say, a million people, but if one solves either of those two problems, he will help all of humanity, and perhaps save some hundred million people that one day will die due to wars and chaos caused by the shortage of energy and the climate change.

He then told me that a good reference for choosing a topic is to visualize a simplified two-axis diagram. One axis is the novelty of a topic, and the other is its importance. Ideally, one would want to work on a topic which is highly innovative applied to a very important problem. However, realistically, it is easier to make either some incremental contribution to a well-studied important topic (a new technique for improving by 0.5% the efficiency of battery chargers) or to come up with some crazy theory which doesn’t have applications yet.

My impression is that, here in the US, professors have lots of PhD students available, therefore they can diversify the risk and work on lots of high-risk/high-reward projects (just like venture capitalists).