I have the greatest admiration for Gian-Carlo Rota's mathematics, energy, talent, wit, personality, charisma, enthusiasm, and the list could (and perhaps should) be continued. However, the purpose of this letter is to point out that by publishing his ``Ten Lessons I Wish I Had Been Taught'' in the January 1997 issue of the AMS Notices (cf. p. 22-25) without any appropriate footnote indicating that some of the ``lessons'' are meant to be just read and enjoyed and must not be taken seriously without parental supervision, you (and, indirectly, Gian-Carlo Rota) may have caused irreparable damage to a large segment of our young (and not so young) mathematicians who are naive beyond belief and who will accept any advice no matter how absurd and nonsensical it is from such an international authority and supernova as Gian-Carlo Rota.
More specifically, Gian-Carlo Rota advises to ``Publish the Same Result Several Times'' and then uses the example of F. Riesz to illustrate his point. Poor F. Riesz and poor advice. First, F. Riesz was a perfectionist beyond help (just like yours truly). Second, his mother tongue was Hungarian, whereas his working languages were Hungarian, German, and to some extent English; and he lived in an era when the international language of mathematics was transforming towards (broken) English. Especially the latter played a major role in why some of his results appeared more than once in print. Gian-Carlo Rota writes, ``Riesz's example is well worth following today.'' If he means that it's worth following (F. or M.) Riesz's taste, talent, and depth, then I couldn't agree more. Let me put it this way: if you are a mathematician of (F. or M.) Riesz's caliber, please do whatever you want. Otherwise, please do not contribute indiscriminately to the information junkyard, and please publish only ``final'' definitive forms of your results, and spare us from being bombarded by $\epsilon$-improvements and generalizations.
By the way, Gian-Carlo Rota writes, ``I bought a copy of Frederick Riesz's Collected Papers as soon as the big, thick, heavy, oversize volume was published.'' I wonder if he realizes that he was grossly cheated, because it's really two big, thick, heavy, oversize volumes.
Then Gian-Carlo Rota advises ``Do Not Worry about Your Mistakes'' and brings up Hilbert and himself to make his point. Well, who the heck should worry about them if not the one who is responsible for them? This is nightmarish advice for readers and editors alike. In addition, it adds to the instability of our mathematical structure: just imagine theorem after theorem proved using erroneous results (sound familiar?). My advice is: forget it, and please do keep worrying about all your past, present, and future mistakes.
Then Gian-Carlo Rota tells the reader to ``Give Lavish Acknowledgments''. Funny but phony, and it may ruin one's credibility. My advice is: give fair acknowledgments, no more and no less. Never say ``I would like to thank Professor X ... .'' If ``you would like'', then please do so and say ``I thank ... '' (if I recall correctly, this comes from Paul Halmos). Don't use the word ``Professor''; it's superfluous.
Acknowledgment. I would like to sincerely thank Professor Gian-Carlo Rota for the remaining ``Seven Lessons I Wish I Had Been Taught''. I wish I had the words to describe how much his advice means to me. I also would like to thank the readers of my letter for their wisdom and infinite patience. If I may, I would also like to ask the readers to send me a complete set of their reprints so that I could lavishly refer to their invaluable mathematical contributions for years to come, whether or not they contradict my own results.
Paul Nevai
http://www.math.usouthal.edu/brick/ymn/V4/vol4.25.html).
P.P.S. Gian-Carlo Rota's recently published Indiscrete Thoughts (Birkhäuser, 1997) contains several chapters in the same spirit as the subject of this letter. Although I have not had a chance to read the entire book yet and therefore am in no position to praise or criticize it, I am sure that once I finish reading the book, I will heartily recommend it to all mathematicians, dead or alive.