A two-part lecture course on Topology, by Professor N. The first part is in the spring semester, the second part in the following autumn semester; between them is the long summer break.
First week of the autumn semester, first lecture. Professor N comes into the room. He walks to the blackboard and picks up the chalk. He turns to the class and starts:
"Hence, ... "
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[Anectdote told by Paul Halmos in his autobiography. I quote from memory, so the details will vary.]
Indeed. And another re-arrangement of the axioms.
Paul Halmos in his autobiography reports on one of his colleagues who taught a course in measure theory (I quote from memory). He set out the axioms in lecture 1. Come lecture 2, and he explains that actually, the right axioms should be such and such. And so the semester progresses, each week a new, better axiom system, with no time left for any derivations.
I love that story, on so many levels.
#PaulHalmos #axiomatics #teaching #procrastination #TakeYourTime #yesthestudentswillhavelearntmoreinthislecturethaninanyother
the roamer