He is well known for providing a simple proof of the Quillen–Suslin theorem, a result in commutative algebra, first conjectured by Jean-Pierre Serre in 1955, and then proved by Daniel Quillen and Andrei Suslin in 1976.
Leonid Vaseršteĭn later gave a simpler and much shorter proof of the theorem which can be found in Serge Lang's Algebra.
Liouville's theorem | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Andrei Suslin | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem | Wedderburn's little theorem | Vietoris–Begle mapping theorem |
"By Now" is the title of a song written by Dean Dillon, Don Pfrimmer and Charles Quillen, and recorded by American country music artist Steve Wariner.
In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable.
In 1934 Hollywood screen writer Lamar Trotti and producer George Marshall visited Quillen to use him as a prototype for a Will Rogers film, Life Begins at Forty, in which Rogers played a small-town newspaper editor.
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Quillen wrote for such major periodicals such as the Baltimore Sun, the Saturday Evening Post, and The American Magazine, and he "took the greatest pride" in one-liners picked up by Literary Digest.
Using the superconnection formalism of Quillen, they obtained a refinement of the Riemann–Roch formula, which links together the Thom classes in K-theory and cohomology, as an equality on the level of differential forms.