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How Bayes's Theorem can be used to decide if mail is spam or not.

Very cool. Now that we see that mail filter software "adapts" to the user, we can address the problem in class of what would happen if a doctor who deals with prostate issues uses a filter and words such as viagra prop up when the email is not actually spam.

Although I did not enter the debate, I remember the Marilyn vos Savant vs. the mathematicians episode. I was in high school at the time. Marilyn's solution is sound, and her tactics are indeed wise: to people who disagreed with her explanation, she suggested they simply experiment and see what they find. So both the Bayesian and frequency models of probability are brought into play here. Persi Diaconis, the carnival card shark turned Harvard mathematics professor who I mentioned in class, is also quoted in this article. The Marilyn vs. the Mathematicians rematch did not turn out so well for her. When Wiles and Taylor finally proved Fermat's Last Theorem, she pronounced it phony because she didn't understand it. The mathematical consensus remains that the proof is good.