Still Waters

Gauss’ scientific diary was a great boon to mathematical historians, but his notes could be frustratingly cryptic. On July 10, 1796, he made this entry:

ΕΥΡΗΚΑ! num = Δ + Δ + Δ

He had discovered that every positive integer is the sum of at most three triangular numbers.

Among the 146 entries, two remain completely opaque. On Oct. 11, 1796, Gauss had written:

Vicimus GEGAN.

And on April 8, 1799:

gauss diary entry

No one knows what either of these means — if they had mathematical significance, it was lost with Gauss.

So it goes. Dirichlet was famously uncommunicative, not even informing his family that his wife had given birth. His father-in-law later complained that he “should at least have been able to write 2 + 1 = 3.”

Education Reconsidered

Reflect, Socrates; you may have to deny your words.

I have reflected, I said; and I shall never deny my words.

Well, said he, and so you say that you wish Cleinias to become wise?


And he is not wise as yet?

At least his modesty will not allow him to say that he is.

You wish him, he said, to become wise, and not to be ignorant?

That we do.

You wish him to be what he is not, and no longer to be what he is?

I was thrown into consternation at this.

Taking advantage of my consternation he added: You wish him no longer to be what he is, which can only mean that you wish him to perish. Pretty lovers and friends they must be who want their favourite not to be, or to perish!

— Plato, Euthydemus

Two Milestones

The date 11/19/1999 contained only odd digits. Less than three months later, 2/2/2000 contained only even.

That’s a rare coincidence. It had been 1111 years since the last all-even date … and it’ll be 1111 more before the next all-odd one.


In 1907, Massachusetts physician Duncan MacDougall conceived a singular experiment. When he observed that a patient at his Haverhill hospital was nearing death, he installed him in a specially constructed bed in his office and measured his weight both before and after death. With six such weighings he determined that humans lose between 0.5 and 1.5 ounces at death.

“Is the soul substance?” he wrote. “It would seem to me to be so. … Here we have experimental demonstration that a substance capable of being weighed does leave the human body at death.”

Similar experiments with 15 dogs showed no change in mass, proving, he decided, that dogs have no souls. MacDougall’s findings were written up briefly in the New York Times and occasioned a flurry of correspondence in American Medicine, but after that they were largely forgotten. But who knows? Perhaps he was right.