I’ve come across a few mathematicians or scientists who have been so proud of their scholarly achievements that they’ve asked for them to be put on their headstone when they die (or have had their achievements placed on their headstones by someone else). Please let me know if you know of others. [Update: thanks to folks on Twitter I learned of a few more. I've added them to the list.]
Archimedes’s mathematical accomplishments are numerous. But he requested that his tombstone display a sphere inscribed in a cylinder with the ratio 3:2. He was proud of his discovery that the ratio of the volume of the cylinder to the sphere and the ratio of the surface area of the cylinder (including the top and bottom) to the sphere are both 3:2. (He not only discovered the volume and surface area formulas for the sphere, but also showed that the same constant, pi, appeared in these formulas and the formulas for the circle.)
The Greeks knew how to inscribe in a circle, using only a straightedge and compass, an equilateral triangle (3-gon), a square (4-gon), a regular pentagon (5-gon), a regular pentadecagon (15-gon), and any -gon, -gon, -gon, and -gon. That’s it. Then, 2000 years later, the 18 year old Gauss showed that it was possible to do the same with a 17-gon (and later certain other regular polygons). He was so proud of this discovery that he decided to pursue a career in mathematics. He also asked that a 17-gon be inscribed on his tombstone. His wish was not honored, but
it was later inscribed on a memorial in his honor in his home town of Brunswick. (If anyone knows where I can find a photo of it, please link to it in the comments.) [Update:] a 17-pointed star was inscribed on a memorial erected in his honor in his home town of Brunswick. In the photo below you can (barely) see the star under Gauss’s right foot. Here is a closeup.
Ludolph Van Ceulen—the first 35 digits of π
Ludolph Van Ceulen spent most of his life computing the first 35 digits of pi. He used Archimedes’ technique and polygons of sides! His tombstone contained his upper and lower bounds for pi. The original tombstone disappeared some time around 1800; a replica is shown below.
Bernoulli was so enamored with the logarithmic spiral that he wanted it engraved on his headstone. However, the engraver accidentally carved an Archimedean spiral.
The tombstone of physicist Ludwig Boltzmann contains his entropy formula .
Paul Dirac—the Dirac equation
This burial plaque can be found in Westminster Abbey, not far from Isaac Newton’s resting place. It contains Dirac’s relativistic electron equation, .
Ferdinand von Lindemann—circle, square, pi
In 1882 Lindemann proved that pi is a transcendental number. This put to rest the 2000+ year old question of whether it is possible to “square the circle“—i.e., construct, using only a compass and straightedge, a square having the same area as a given circle. (He proved that it was impossible.) His grave has a circle superimposed on a square, surrounding the symbol pi.
[Update: Here's a memorial for Lindemann that also has the circle/square/pi in it. It is in the city of his birth, Hanover. Thanks to Pat Ballew for the image!]
Henry Perigal was an amateur mathematician who discovered the “dissection proof” of the Pythagorean theorem. The proof can now by found carved into his headstone.