In the early 1970s mathematician Donald Knuth spent a sabbatical with his wife in Norway. The time was meant to be spent relaxing. Yet one night he woke up his partner in a state of agitation.

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is ...