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One of the graves of the kings of Elam at Tschoga Zanbil in Iran. If you haven’t invented any new mathematics, and are thinking of rounding up a gang of forced labourers to build a fancy tomb to give you immortal fame, keep in mind that the Assyrians may come around and dig up your bones! Photo by author, May 2016.

Stephen Hawking died on the 14th of March. I don’t have much to say about that, because there are worse lives than discovering a property of black holes, writing a best-selling book, taking a ride on the Vomit Comet, and guest starring on half a dozen nerdy TV shows before dying in your own bed at the age of 76. As Achilles said to Lycaon (Iliad 21.150) “ah, friend, you too must die. Why moan about it so?” This week I thought of an ancient aspect of his story which many people do not seem to have noticed.

At a workshop to celebrate his 60th birthday, Hawking heard that Ludwig Boltzmann the 19th century physicist had his eponymous formula for entropy engraved on his tombstone, and suggested that he would like the equation which describes Hawking radiation engraved on his own tomb (Dennis Overbye, New York Times, 22 January 2002 https://www.nytimes.com/2002/01/22/science/hawking-s-breakthrough-is-still-an-enigma.html But this story goes a lot further back than königlich- und kaiserlich Vienna.

There is a story that Archimedes was buried under a tomb marked with a cylinder and a sphere and an inscription describing their relative proportions which he had discovered. For Plutarch, this is proof that even though Archimedes was a practical engineer, his true love was pure mathematics:

And although he made many excellent discoveries, he is said to have asked his kinsmen and friends to place over the grave where he should be buried a cylinder enclosing a sphere, with an inscription giving the proportion by which the containing solid exceeds the contained

Plutarch, Marcellus, 17.7 http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Marcellus*.html#17.7

Now, a Neo-Platonist aristocrat like Plutarch had reasons for insisting that Archimedes was not a grubby tradesman, but he did not invent this story. In his Tusculan Dispositions, Cicero claimed to have found this tomb overgrown with brush outside the Akragas Gate of Syracuse, so we have an independent source within 150 years of Archimedes’ death. And because he and Plutarch retold it, the story about Archimedes’ tomb has never been forgotten. I know people before Archimedes who boasted of military victories or public offices on their tombs, but I can’t think of any who boasted of scientific or technical discoveries.

The New York Times reporter implied that Hawking got the idea from Boltzman, so I don’t know whether he knew the story directly. But I am sure that Ludwig Boltzmann knew his Plutarch. You didn’t get a Doktorat at Vienna in 1866 without a heavy dose of Greek and Latin. Even today, historians of ancient mathematics and natural philosophy are often mathematicians and physicists who study history as a hobby. The ancients had to describe the relationship between a sphere and a cylinder with the same height and diameter with words, but today we have algebraic notation and formulas, which is good if the local masons charge by the line. It hasn’t been announced whether his executors will indeed have such a stone made, but I hope they continue this ancient tradition.

You can learn more about Archimedes at Dr. Chris Rorres’ site https://www.math.nyu.edu/~crorres/Archimedes/contents.html