Is mathematical interest just a matter of taste?
Much of Akshay Venkatesh’s thought-provoking essay on the potential impact of automation on mathematical research is concerned with the question of what makes a mathematical statement interesting, and how that might change. One possibility that is sometimes brought up is that computers will be good at proving statements, but they will lack any aesthetic sense, so humans will have to tell them what to prove. I shall try to argue that being good at proving statements and knowing what is worth proving go so closely hand in hand that a program that cannot distinguish between interesting and boring statements will be extremely limited in what it can prove. I shall also try to argue (as Venkatesh also argues in his essay) that the extent to which a statement is interesting is related to objective features of how it fits into the corpus of mathematical knowledge, so it is not a hopeless task to teach computers to decide for themselves what is interesting.