Written: Sept. 24, 2017
In the Princeton Companion to Mathematics edited by Tim Gowers (with the help of June Barrow-Green Imre Leader), great mathematicians (Sir Michael Atiyah, Bela Bollobas, Dusa McDuff, Alain Connes, and Peter Sarnak) gave some good advice to young mathematicians, to which, nine years ago, I added twenty more pieces of advice. But what about middle-aged mathematicians? They need advice too! So hear the advice of an older mathematician, and perhaps you can learn from his experience, and try not to repeat the errors that he has made.
As you will become more established, sooner or later you will be asked to write recommendation letters for younger mathematicians. Writing such a letter is a big pain, first, since it takes time from your research, and second because it forces you to lie. If you tell the exact truth, then you would be lying. Such letters expect you to "lie" or at least exaggerate, and if you don't, the subject of the letter won't have a chance.
If you want to climb the academic ladder, there is no way that you can refuse such requests, since writing such letters is considered one of your professional duties (along with refereeing and sitting on committees), and unless you are Andrew Wiles, you would need to perform such chores. (In fact, even Andrew Wiles does write such letters, but he can get away with very short ones.)
I probably have written more than one hundred such letters on behalf of then young (and also not so young, those up for promotion for associate and full professor), and believe that I helped them a lot in getting the job they applied for or for getting the desired promotion and tenure. Imagine my disappointment, and feeling like a sucker, when these people became editors of math journals and rejected my papers, and my students' papers, not because they found errors or pointed out that the we were scooped, but because they dismissed the whole approach of experimental mathematics and computer-generated research, so dear to my heart.
So my advice to you, up-and-coming middle-aged mathematician, is a follows.
ONLY AGREE TO WRITE A LETTER OF RECOMMENDATION IF THE PERSON WILL GIVE YOU A SIGNED PROMISE (that you can post in your website, if needed) never to reject any of your or your students' submissions because "it is not important enough".
Of course, the subject of the recommendation letter does not have to agree, but then it would save you some work!