Inspired by Terry Tao's career advice page and by a recent interview on Math-Life balance, I collected here some thoughts on productivity in math. The recent interview was with Saul Glasman and in it he mentioned, more as a side note, that math research is hard because one often gets stuck while working on a problem. It's just very hard to focus for a long time on a single problem, seemingly without any progress. But the crucial insight here is, in my opinion, the fact that it only seems as if there is no progress.

According to Glasman, when it happens that you work too long on a problem and then take a break, you can't really get yourself to work on it again and start feeling bad because you think you must work on that one problem until there is a breakthrough. This leads to a downward spiral because you think that it is your job to work on or solve this problem and you can't even get yourself to do your job. But this is probably false and Terry Tao knew this for a long time.

Motivation

After I've started working with reward-modulated STDP in spiking neural networks, I got curious about the background of research on which it was based. This led me to the book by Richard Sutton and Andrew Barto called "Reinforcement Learning".  The book is from 1998 and it's freely readable on the internet! In the book's Introduction they cover the example of an agent learning to beat a given (imperfect) agent in the game of Tic Tac Toe. Two remarks have to be made: 1. The agent has to be imperfect because a perfect agent in Tic Tac Toe (if it's the one doing the first move) can never be beaten. 2. The agent does not learn to play Tic Tac Toe, this skill is assumed, but it learns a value map for its policy.

Opposite to the Telegraph headline Having a messy desk makes you 'more creative', a messy desk does probably not make you more creative, but creative people produce more mess. Or, in other words, making a mess is definitely a part of the creative process.