What Did Archimedes Ask to Be Carved on His Tomb?

Archimedes asked that his tomb be marked with a sphere and a cylinder. Cicero later described visiting that tomb and finding it exactly as requested, surmounted by the sphere and the cylinder.

To understand why this image mattered to him, it helps to know who Archimedes was. He was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from Sicily. He is considered one of the leading scientists of classical antiquity and one of the greatest mathematicians of all time.

A Mathematician Ahead of His Time

Archimedes anticipated modern calculus by applying the concept of infinitesimals and the method of exhaustion. He derived rigorous proofs for the area of a circle, the surface area and volume of a sphere, and the area under a parabola. This is exactly why the sphere on his tomb was not a random decoration. His proof about the relationship between a sphere and a cylinder that encloses it was, by his own request, the image he wanted remembered.

Archimedes also devised an approximation of pi. He defined what is now called the Archimedean spiral. He also created a system using exponentiation for expressing very large numbers, a genuinely difficult problem before positional notation existed.

Physics, Engineering, and the Sky

Archimedes was one of the first people to apply mathematics to physical phenomena, working on statics and hydrostatics. He proved the law of the lever. He also enunciated the law of buoyancy now known as Archimedes' principle.

He is even said to have boasted to King Hiero II that he could move any large weight using leverage, a claim that reflects how confident he was in his own theory of the lever. According to Vitruvius, Archimedes solved a wreath problem for the king using water displacement to detect gold mixed with silver, a different and separate story from the lever boast, though both involve testing his ideas in front of Hiero.

Archimedes did not stop at engineering problems on the ground. He made measurements of the apparent diameter of the Sun. He also made estimates of the size of the universe. He is said to have built a planetarium device that demonstrated the movements of the known celestial bodies, an extraordinary mechanical feat for the era.

His practical inventions were just as significant. Archimedes designed a screw pump. He designed compound pulleys. He also designed defensive war machines to protect his home city of Syracuse, which was under threat for much of his later life.

Family, City, and Circle of Scholars

In the Sand-Reckoner, Archimedes gives his father's name as Phidias, who was himself an astronomer. Plutarch wrote that Archimedes was related to King Hiero II, the ruler of Syracuse, which helps explain why the king trusted him with problems like the wreath test. Even so, Archimedes was not isolated in Sicily. He maintained collegial relations with Alexandrian scholars through his written works, exchanging ideas across the Mediterranean world despite the distance and the slowness of travel and correspondence at the time.

Death During the Siege of Syracuse

Archimedes died during the siege of Syracuse, killed by a Roman soldier despite orders that he should not be harmed. This detail matters for the tomb story: the very tomb Cicero later found, marked with the sphere and cylinder, belonged to a man whose city had just fallen to the very army whose soldier killed him. That contrast between violent death and a quiet, geometric memorial is part of why the tomb has stayed a famous image for centuries.

How His Work Survived, and Nearly Didn't

Archimedes' mathematical writings were little known in antiquity, though Alexandrian mathematicians did quote him. The first comprehensive compilation of his works was made around 530 AD by Isidore of Miletus in Byzantine Constantinople, centuries after Archimedes had died. From there, his works were translated into Arabic in the 9th century. They were translated into Latin in the 12th century, which is roughly how his ideas eventually reached the scholars of medieval and early modern Europe.

Even after all that, parts of his method remained hidden until surprisingly recently. The Archimedes Palimpsest, discovered in 1906, provided new insights into his mathematical methods that had been overwritten and lost for centuries.

Language Notes: Words Built on Archimedes' Legacy

Several everyday English expressions trace back to the concepts Archimedes worked with, even when his name is not spoken. Understanding the story behind them makes them easier to remember.

• Archimedes' principle — the law of buoyancy he enunciated, now a standard term in physics classes everywhere.
• the law of the lever — the mechanical principle he proved, still used to describe any situation where a small force multiplies into a large effect.
• method of exhaustion — the ancient technique he applied that anticipated modern calculus, a phrase still used in the history of mathematics.
• Archimedean spiral — the curve he defined, a term now standard in geometry and design.

Each of these terms carries a small piece of the story above: a mathematician in Syracuse, working under threat of siege, who still found time to define a spiral, prove a law of levers, and ask that a sphere and a cylinder mark the place where he would be buried.