One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers.

The high number from the Middle East is only coincidence, he said. It is no particular choice on our part, ... We accept visa trainees from those countries. We'd accept them from other countries, too, but we don't get their applications.

A god whose creation is so imperfect that he must be continually adjusting it to make it work properly seems to me a god of relatively low order, hardly worthy of any worship.

Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all.

As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.

When reputable scientists correct flaws in an experiment that produced fantastic results, then fail to get those results when they repeat the test with flaws corrected, they withdraw their original claims. They do not defend them by arguing irrelevantly that the failed replication was successful in some other way, or by making intemperate attacks on whomever dares to criticize their competence.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.