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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

30 votes
11 answers
5k views

What are your favorite concrete examples of limits or colimits that you would compute during...

(The title was initially "What are your favorite concrete examples that you would compute on the table during lunch to convince a working mathematician that the notions of limits and colimits are not …
39 votes
3 answers
4k views

In which situations can one see that topological spaces are ill-behaved from the homotopical...

In the eighties, Grothendieck devoted a great amount of time to work on the foundations of homotopical algebra. He wrote in "Esquisse d'un programme": "[D]epuis près d'un an, la plus grande partie d …
58 votes

The half-life of a theorem, or Arnold's principle at work

I am unsure it fits the OP's requirements but, in connection with Ryan Budney's most-upvoted answer regarding the rediscovery of trapezoidal method, let me recall that Grothendieck spent about three y …