Sunday, April 19, 2009

Tricky Combinatorics

Some 14 years ago Professor Yum-Tong Siu taught a graduate Complex Analysis course at Harvard. In one of the lectures he wrote a theorem on the board, turned to the class, and asked, "how can we proof this?" The deafening silence and the blank stares on the students' faces seemed to have embarrassed Prof. Siu a bit. "Using the pigeonhole principle", he said shyly after a while, "After all there are only finitely many tricks in Mathematics".

Zzzzz...

[The pigeonhole principle states that when more than n pigeons are placed into n pigeonholes, at least one pigeonhole hosts two or more pigeons.]

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