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Wednesday, August 18, 2010


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Not directly related to the topic of potential vs actual infinite sets, but I do agree with your (Vallicelli's) view on the actual teaching of mathematics. Much to my chagrin, my own calculus teacher tried to teach our class about much of the history and controversy of calculus. If a person finished all three quarters of calculus, grades aside, he gave each one a book called the Tour of Calculus by David Berlinski. I read it 5 years later and realized I should have read it when I finished calculus.

It's surprising how many mathematics majors don't require any reading in either philosophy of mathematics nor mathematical pedagogy. For those interested one of the best readers is Benacerraf's Philosophy of Mathematics: Selected Readings. It has all the major 20th century papers on mathematical foundationalism. It's very easy to read (i.e. doesn't require a heavy philosophical background) and in my opinion is a must read for any mathematician (or person working heavily with mathematics like physicists).

I agree. Benacerraf and Putnam, eds. is required reading. An oldie but a goodie.

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