For anyone who wishes to go into Mathematics as a career, here are Ten lessons from Gian-Carlo Rota .
Here are the key points I found interesting (that will hopefully spur you to read the article):
1. Never run overtime when lecturing: think of every 50 minutes as a microcentury.
2. “We all fall prey to the illusion that a listener will find the time to read the copy of the slides we hand them after the lecture. This is wishful thinking.”
3. On publishing the same result several times: “It was clear that Riesz’s publications were few. What is more surprising is that the papers had been published several times. Riesz wold publish the first rough version of an idea in some obscure Hungarian journal. A few years later he would send a series of notes to the French Academy’s Comptes Rendus in which the same material was further elaborated. A few more years would pass, and he would publish the definitive paper, either in French or in English. Adam Koranyi, who took courses with Frederick Riesz, told me that Riesz would lecture on the same subject year after year while meditating on the definitive version to be written. No wonder the final version was perfect.. It may soon be indispensable to present the same result in several versions, each one accessible to a specific group; the price one might have to pay otherwise is to have our work rediscovered by someone who uses a different language and notation and who will rightly claim it as his own”
4. On phenomenology: “It so happens that the fundamental treatises of phenomenology are written in thick, heavy, philosophical German. Tradition demands that no examples ever be given of what one is talking about.” Of course he went on to exemplify the concepts in these volumes and to publish them, which was well received in the field.
5. On not sweating the mistakes in papers: “When the Germans were planning to publish Hilbert’s collected papers and to present him with a set on the occasion of one of his later birthdays, they realized that they could not publish the papers in their original versions because they were full of errors, some of them quite serious. Thereupon they hired a young unemployed mathematician, Olga Taussky-Todd to go over Hilbert’s papers and correct all the mistakes… At last, on Hilbert’s birthday a freshly printed set of Hilbert’s collected papers was presented to the Geheimrat. Hilbert leafed through them carefully and did not notice anything.” Although I feel like in this story it is far more likely that I will end up as Olga than as Hilbert.
6. On giving effusive acknowledgement: “I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else. One day I tried an experiment. After writing a rather long paper, I began to draft a thorough bibliography. On the spur of the moment I decided to cite a few papers which ahd nothing whatsoever to do with the content of my paper to see what might happen. Somewhat to my surprised, I received letters from two of the authors whose papers I believed were irrelevant to my article. Each of the authors warmly congratulated me for being the first to acknowledge their contribution to the field.
7. On not having your stuff read: “Nowadays reading a mathematics paper from top to bottom is a rare event.” Conclusion? Write longer introductions :P
8. On institutionalization: “You must realize that after reaching a certain age you are no longer viewed as a person. You become an institution, and you are treated the way institutions are treated. You are expected to behave like a piece of period furniture, an architectural landmark, or an incunabulum. It matters little whether you keep publishing or not. If your papers are no good, they will say “What did you expect? He is a fixture!”; and if an occasional paper of yours is found to be interesting, they will say, “What did you expect? He has been working at this all his life!” The only sensible response is to enjoy playing your newly found role as an institution.”