27 September 2007

What is the simplest problem you cannot solve?

I'm currently reading The Cauchy-Schwarz Master Class (link goes to MAA review, which pretty well explains the book's raison d'etre and contents) by J. Michael Steele. (How did I find this book? I'm taking Steele's course "Probability Inequalities and Machine Learning"; he alludes to this book every so often.)
It is full of interesting inequalities, and I may have something to say about them later, but I just wanted to share the following, where Steele is talking about George Polya and his book How to Solve It:

Some of the richest of Polya's suggestions may be repackaged as the modestly paradoxical question: "What is the simplest problem you cannot solve?".... Perhaps no other discipline can contribute more to one's effectiveness as a solver of mathematical problems.

I think this is worth remembering.

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