〈 Berger | Dillon 〉

2) Don't work on it unless you have very novel and powerful ideas. Many of the best mathematicians of all times have failed. Something more than existing techniques and tools is needed. You need a good new idea. Most of what you believe is a good new idea is not. (cont.)

3) Don't work on it without a clear goal. You must first decide if you believe the conjecture or not. There is no point in trying to prove the conjecture one day and trying to disprove it the next day. A clear goal is a source of strength that is needed. (cont.)

4) Don't expect that the problem consists in resolving a single hard difficulty. In this kind of hard problem many enemies are on your way, well hidden, and waiting for you. (cont.)

5) Don't work on it without studying previous attempts. We know by now of several failed attempts, and you should learn from them in order to not repeat history again. (cont.)

6) Don't go for it unless you have succeeded in other serious problems. "Serious problems" means problems that have been open and well known for years. If you think that the Riemann Hypothesis will be your first major strike, you probably deserve failure. (cont.)

7) Don't tell anyone out of a close circle that you are working on the problem, or you will be put into the freak category, and it will put unwanted pressure on you. (cont.)

8) *Do* tell your very best mathematical friends your work on the problem, and discuss it with them. You will need to check very carefully the progress you make. (cont.)

9) Don't get obsessed. Don't make it your main goal, unless you want to ruin you mathematical career. (cont.)