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From nstarr@amherst.edu Tue Feb 11 16:34:18 1997
Return-Path: <NSTARR@amherst.edu>
Date: Tue, 11 Feb 1997 16:33:09 -0500 (EST)
Subject: Response to rotesque commentary
To: nevai@math.ohio-state.edu

Dear Paul Nevai,

   I write regarding the rotesque advice in "Ten Lessons I Wish I Had Been

Taught" about which you commented in the latest issue of the AMS Notices.

Rota's message was, of course, more suitable for a mature audience.

Indeed, his record suggests that he is able to ignore his own advice, when

appropriate.  For instance, although he recommended not worrying about

one's mistakes, I recall a striking instance of the recognition and

subsequent remedy of his own error:  In the first offering of his course on

combinatorial mathematics, which I audited, he made a hash of a lecture.

The next lecture it became evident that he was going over the same

material, and at first there was resentment at having again to deal with

the same subject.  But he gave such a magnificent presentation that one

almost appreciated the cause for the repetition.  Without any explicit

acknowledgment of the antecedent, he made clear his understanding of what

had happened and his ability to give the type of exposition for which he is

so famous.

     In another direction, Rota's work in analysis (I am more familiar with

that than with his work in other fields) did not display the duplication of

results that his advice would suggest.  He published seminal work in

numerous areas, without inappropriate reduplication.  (One could argue that

in those early years, there was an even greater premium on quantity than is

the case for a mature mathematician.)  Prominent examples of these

publications include:

On Models for Linear Operators, Comm. Pure and App. Math., XIII (1960),
469-472;  On the Spectra of Singular Boundary Value Problems, J. Math.
Mech., 10 (1961), 83-90;  Une theorie unifiee des martingales et des
moyennes ergodiques, Comptes Rendus (Paris), 252 (1961), 2064-2066;  On the
eigenvalues of positive operators, Bull. Amer. Math. Soc., 67 (1961), 556-
558;  An "alternierende Verfahren" for general positive operators, Bull.
Amer. Math. Soc., 68 (1962), 92-102; etc.  (One of my favorites is his
paper on averaging operators, which appeared in Rendiconti del Seminario
Matematico dell'Universita di Padova in 1960.  Scarcely a widely found
resource.)

These were and remain to this day catalysts for many other mathematicians -

Rota didn't mine out his own fields.  He intended to pursue suggestive

avenues illuminated by brief notes such as those just cited, and even tried

to find time and collaborators for a book on positive operators. However, I

suspect his fertile imagination exposed too many exciting new areas to allow

time to harvest the old ones.

     Third, though my analogy is off the mark, I doubt that those many

souls who have been skewered by his epigrammatic book reviews will view

Rota as a glad-hander.

     I must add that the most valuable pedagogical lesson I learned

from Gian-Carlo was to let class out just a tad early.  Run overtime 

and the audience frets; finish with some time to spare and they feel 

as though a gift has been bestowed.  (I couple this with starting on

time, without regard for latecomers.)

     So there is my own view of some historical connections to the

correctives you have contributed to the Notices.


          Sincerely,

          Norton Starr
          Amherst College

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