Written: Oct. 4, 2026
Once upon a time there was analysis tout court, done by Newton, Leibnitz, and later Laplace, Legendre, Lagrange, Cauchy, Weierstrass, and many other smart people. This took place in the good old cosy Rn for n=1,2,3, and even general n, but a finite one. Then came the 20th century with, pardon my French, analysis on infinitely-dimensional "spaces", of Banach and Hilbert, that was "modern", and was sometimes called functional analysis. In order to distinguish the good-old-analysis from this new-fangled intrusive species, it was renamed classical analysis.
Once upon a time there was combinatorics tout court, done by Pascal, Euler, Sylvester, MacMahon, and many other smart people. Then came Erdos and the Hungarian Mafia, and before him, Kirkman with his schoolgirls, not to mention Birkhoff, Tutte, et. al, with their graphs, and once again, it was necessary to find an appropriate term. Dominique Foata had the brilliant idea to call good-old combinatorics, classical combinatorics. Unfortunately the name didn't stick and now it is more commonly called enumerative and algebraic combinatorics.
Call it what you will, Dominique made this important part of mathematics what it is today, with his two seminal transformations (the first sending descents to excedances (see here) , and the second the number of inversions to the major index (see here) ), and his gorgeous proof of the Mehler formula for Hermite polynomials, co-founding (along with Joe Gillis) combinatorial orthogonal polynomials (see here), to name just a few highlights. Then there were his two classics. One with his illustrious doctorat d'etat advisor, Marco Schutzenberger, of formal language and Chomsky-Schutzenberger fame (see here), and one with his good friend, Bourbakist Pierre Cartier (see here).
All these gems, and many other ones, are available in Dominique's website (all free downloads), and I really hope that it will stay intact for everafter.
Dominique also co-founded, with Volker Strehl and Adalbert Kerber, the still-going-strong Séminaire Lotharingien, see his nice article: The Lotharingian impact on Combinatorial Mathematics:myth or reality?
But Dominique was not only the patron saint of classical combinatorics, he was also a saint in the colloquial sense of the word, what jews call a mensch. When he was 25-year-old, in his postdoc at Ohio-State, way back in 1960, [see this fascinating memoir, edited and type-set (Dominique was a TeX-whiz, and a good friend of Don Knuth) when he was 91-years-old!], he was told that a young visiting student, a French young woman by the name of Anne, was seriously injured due to a fall from an unsecured balcony, and was at a local hospital. Out of French solidarity, he paid her a visit, and fell in love. When he returned to France, they got married, and raised a charming daughter, Stephanie. Anne never recovered completely, but thanks to Dominique's loving care she prospered, and became a notable literary scholar. Dominique and Anne travelled extensively, loved operas, and he was such a good husband. Of course he was also a great father, friend, and colleague.
Please refer to the 26-year-old FoataFest website, aptly named Classical Combinatorics, co-organized with, at-the-time, my PhD student Aaron Robertson (good job Aaron, sill having it intact), that contains a tribute by Herb Wilf, (see here), and more recently, Dominique's 90th birthday surprise party.
Let me conclude with the apt motto that GuoNiu Han, his most devoted élevé and disciple, and most prolific coauthor, chose in his moving obituary. A free translation of the second part is
"I don't want to brag, but I am so lucky to have a character that never lets me get bored."
And indeed, he was lucky to have such an exciting life, with never a dull moment.