- The Gelfand Principle
Whenever you state a new concept, definition, or theorem, (and better still, right before you do) give the SIMPLEST possible non-trivial example.
- The Buchberger Principle (my rephrase)
- When presenting your work (paper etc.), apply your method to a simple case, which can easily be followed, then state that the same method worked on the complicated case as well, and provide proof elsewhere that it did work indeed.
[...] but please, have mercy on the rain forest! You don't need 30 pages, and frankly all this EXPLICIT LANGUAGE of hairy computer output is almost pornographic.
Hence, both the Gelfand and the Buchberger principles are as useful when we teach our students (at all levels, K-grad_school), as when we try to teach our colleagues, in other words, write understandable research papers. But, last but not least, when we teach ourselves, in other words, do research.
Very true. Of course I start writing papers with best intentions, but in hindsight the outcome is not always optimal due to time constraints etc. I will try to adhere to those principles more (and I hope others will too).