Gian-Carlo Rota

Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician, philosopher, author, and editor. He was elected in 1978 a Fellow of the American Association for the Advancement of Science and in 1982 a Member of the United States National Academy of Sciences. Quotes The spectacular results in the fluctuation theory of sums of independent random variables, obtained in the last 15 years by Erik Sparre Andersen Andersen de, Glen E. Baxter Baxter, Frederic Bohnenblust Bohnenblust de, Dominique Foata Foata, Johannes Kemperman Kemperman, Frank Spitzer Spitzer, Lajos Takács Takacs and others, have gradually led to the realization that the nature of the problem, as well as that of the methods of solution, is algebraic and combinatorial. After Baxter showed that the crux of the problem lay in simplifying a certain operator identity, several algebraic proofs (Frederick Valentine Atkinson, John Kingman Kingman, Wendel) followed. It is the present purpose to carry this algebraization to the limit: the result we present amounts to a solution of the Word problem (mathematics) word problem for Rota–Baxter algebra Baxter algebras. The solution is not presented as an algorithm, but by showing that every identity in a Baxter algebra is effectively equivalent to an identity of symmetric functions independent of the number of variables. Remarkably, the identities used so far in the combinatorics of fluctuation theory "translate" by the present method into classical symmetric function identities of easy verification. The present method is nevertheless also useful for guessing and proving new combinatorial identities: by way of example, it will be shown in the second part of this note how it leads to a generalization of the Bohnenblust-Spitzer formula for the action of arbitrary Permutation group groups of permutations. Baxter algebras and combinatorial identities. I Bulletin of the American Mathematical Society March 1969 75 325-329 https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-75/issue-2/Baxter-algebras-and-combinatorial-identities-I/bams/1183530290.pdf It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance with those of artistic beauty. For example, courses in “art appreciation” are fairly common; it is however unthinkable to find any “mathematical beauty appreciation” courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term “beauty” as it is currently used by mathematicians. May 1997 The Phenomenology of Mathematical Beauty Synthese 171–182 111 2 https://doi.org/10.1023/A:1004930722234 10.1023/A:1004930722234 It cannot be a complete coincidence that several outstanding logicians of the twentieth century found shelter in Lunatic asylum asylums at some time in their lives: Cantor, Ernst Zermelo Zermelo, Gödel, Peano, and Emil Leon Post Post are some. Alonzo Church was one of the saner among them, though in some ways his behavior must be classified as strange, even by mathematicians' standards.He looked like a cross between a Giant panda panda and a large owl. He spoke softly in complete paragraphs which seemed to have been read out of a book, evenly and slowly enunciated, as by a Speech-generating device talking machine. When interrupted, he would pause for an uncomfortably long period to recover the thread of the argument. He never made casual remarks: they did not belong in the baggage of Logic#Formal logic formal logic. Indiscrete Thoughts Modern Birkhäuser Classics, edited by Fabrizio Palombi Springer Science & Business Media 2008 9780817647803 https://books.google.com/books?id=nFvY20pHghAC&pg=PA4 4 (280 pages; 1st edition 1997) The more experimental scientists and engineers are, the more common sense they have, and so on until you get to the mathematicians, who are totally devoid of common sense. as quoted by Denise Brehm in: https://news.mit.edu/1998/rota-1028 MIT News, Massachusetts Institute of Technology Rota reflects on math and mathematicians October 28, 1998 External links Category:1932 births Category:1999 deaths Category:Massachusetts Institute of Technology faculty Category:Mathematicians from Italy Category:Mathematicians from the United States Category:Members of the United States National Academy of Sciences Category:Princeton University alumni Category:Yale University alumni