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√2 is Alogon

The Pythagoreans (500 B.C.) claimed that "Number was Divine!" Their numbers were the integers and rationals (or ratios of the integers).

When Hippasus, a Pythagorean philosopher, supposedly discovered √2, an irrational number, the irate Pythagoreans threw Hippasus overboard while out at sea.

To the Pythagoreans, √2 became the Greek word alogon. Its meaning:

  • "unutterable" or "not to be spoken"
  • "not a ratio," which today means "irrational"
But, some math historians use the stronger Greek word arreton, which means "incomprehensible" or "incommensurable with understanding."

The latter is a nice twist, as irrational numbers are not only incommensurable with the rationals...but also, for too many students, they are incomprehensible!

And what is wrong with this whole story? First, Hippasus lived about a century after the assumed time of Pythagoras. Second, Plato describes how Theodorus of Cyrene, with his special spiral, proved the irrationality of √2, √3, √5, etc. up to √17 prior to Hippasus' time.

Who cares, though the story is alogon, it is interesting!