Advice
A bunch of unrelated research advice I got, most of them good
- Alexander Clark, about learning to say no: When you decline an invitation, put it in the calendar anyway: when the day comes and you realise you have nothing to do, you will feel good about yourself
- Hubert Comon, about reviewing: When you review a paper, read the intro and statement of the results, put the paper on the side and try to prove them by yourself. After 10mn, take the paper back, you will appreciate the results better
- Mikołaj Bojanczyk, about citations: When you cite a paper, always cite a concrete statement (a theorem), or a definition
- Bartek Klin, about proving stuffs (it comes from Grothendieck): proving a theorem is like cracking a nut: you can crack them dry with a hammer and a lot of effort, or dip them in water and wait for them to become soft and easy. Always go for soft and easy.
- Joël Ouaknine, about choosing research projects: Before deciding to spend ages on solving a question, imagine yourself giving a talk about it: if you do not feel like doing this, don’t bother solving it
- Thomas Colcombet, about definitions: Go back to your definitions and notations as many times as it takes to feel satisfied with them, they say a lot about your problem
- Moshe Vardi, about advising students (I think it was a story about someone else): The best supervision move I did was to move to another university in the middle of the PhD: the student decided to work on a very hard conjecture against my initial advice and solved it
- Jean-Eric Pin, about proofs: Every theorem that is less than 24 hours old is wrong (this is an old theorem)
- James Worrell (Ben), about research: Nothing is ever new in research
- Florian Horn, about talks: Your first 100 research talks will suck, give them as soon as possible