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In Gian-Carlo Rota's Indiscrete Thoughts, there a list of mathematical gossip among which one reads: [...] What would have happened [...] if Grothendieck had known the theory of distributive latti …

The entry on Alexandre-Théophile Vandermonde at the MacTutor History of Mathematics archive ends with the description of the contents of Vandermonde's fourth and last mathematical paper, concluding w …

In the long process that resulted in the classification of finite simple groups, some of the exceptional groups were only shown to exist after people had computed (most of) their character tables and …

One of the nicest results I know of is (Auslander-Buchsbaum-)Serre's theorem asserting that a (commutative!) local ring is regular iff it has finite global dimensional. I'd like to ask a somewhat vag …

Two quick questions on notation, motivated by my being reading Cayley at the moment (I stumbled across a random volume of his Collected Works and now I am unable to do anything else but read it throug …

A possibly non-associative algebra is flexible if it satisfies the identity $$(xy)x=x(yx).$$ This is clearly a very weak form of associativity —and obviously an associative algebra is flexible— but it …

While the Kronecker-Weber theorem —that every finite abelian extension of $\mathbb Q$ is contained in a cyclotomic field— is always attributed to, well, Leopold Kronecker and Heinrich Martin Weber, mo …

In his answer to a recent MO question, Johannes Ebert sketches the proof of a very nice result (implying that homotopy spheres are parallelizable) which, as he says, involves the whole plethora of top …

In a recent answer to a recent question, BCnrd wrote [...] beyond the coherent case one cannot expect information about a fiber (e.g., vanishing, 6 generators, etc.) to "propogate" to information …

In an opinion piece which appeared in the AMS Notices of January 2010, John Wermer tells us that he once heard about a seminar given by Grothendieck which was described as "a telegram by Grothendieck …