Mathematics
Bayes' Theorem and Updating Beliefs with New Evidence
Quick fact
Spam filters use Bayes' theorem to classify emails: they start with a prior probability that any email is spam, then update it using the likelihood of certain words appearing in spam versus legitimate mail. This same equation underlies medical tests, A/B testing, and even the way your brain processes sensory information.
Why this is interesting
You hear a weather forecast that says rain for tomorrow, but you look outside and see clear skies. Should you change your belief? Bayes' theorem is the mathematical rule that tells you exactly how much to update your beliefs when new evidence appears.