Saturday, 2 October 2010

Halmos, Full Stop

As long as I'm mentioning things on this date, I should add that this was the date in 2006 that Paul Halmos died.

Halmos always protested the common view that held mathematicians were "number crunchers" and proposed that mathematics was much closer to art.

His description of how to do (and learn) mathematics is still the best advice I could give my students.

" Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"

He was also the originator of IFF for If and Only If... and the use of the tombstone symbol to indicate the end of a proof.

"The symbol is definitely not my invention — it appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like ▯, and is used to indicate an end, usually the end of a proof. It is most frequently called the 'tombstone', but at least one generous author referred to it as the 'halmos' ".", Paul R. Halmos, I Want to Be a Mathematician: An Automathography, 1985, p. 403.
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