Short answer: Archimedes (c. 287–212 BC) has no IQ score and no scholarly IQ estimate. He lived two millennia before intelligence testing, and Catharine Cox's 1926 study covered only people born 1450–1850. Numbers on list sites have no traceable method. The evidence lies in his surviving treatises: bounds on π, the sphere-and-cylinder theorem and a way of summing infinitely thin slices that anticipated integral calculus.
At a glance
| Estimated IQ | No scholarly estimate |
|---|---|
| Basis of estimate | None. No test, no record of his youth, and outside Cox's 1450–1850 range |
| Measured score | None on record |
| Born – died | c. 287 BC – 212 BC, Syracuse, Sicily |
| Field | Geometry, mechanics, hydrostatics, engineering |
| Signature achievement | A sphere has two-thirds the volume of its enclosing cylinder; 223/71 < π < 22/7 |
| Comparable minds | Isaac Newton, Carl Friedrich Gauss, Pythagoras |
Why no IQ number exists
Archimedes was killed at Syracuse in 212 BC, more than 2,100 years before the Binet–Simon scale. There is no score, and the historiometric route is closed as well. Catharine Cox's 1926 estimates depended on detailed records of a subject's childhood and youth; she dropped even William Shakespeare for lack of them. For Archimedes almost nothing survives about his early life beyond his own mention, in The Sand Reckoner, of his father Phidias, an astronomer. List sites that print a figure for him cite no rater and no method.
Any IQ attached to him is therefore invented. Our Archimedes profile covers what is known of his life, and how historical IQ estimates are built explains why the method cannot reach back this far.
The mathematics that survives
Archimedes' treatises are the hardest evidence of any ancient mind, because the proofs can still be checked line by line.
- Pi: inscribing and circumscribing polygons of 96 sides, he proved that π lies between 223/71 (about 3.1408) and 22/7 (about 3.1429).
- Sphere and cylinder: a sphere has two-thirds the volume of the cylinder that encloses it. He asked for the figure to mark his tomb, and Cicero found it there around 75 BC.
- Parabola: the area cut off by a straight line from a parabola is 4/3 that of the inscribed triangle, proved by the method of exhaustion.
- The Sand Reckoner: he built a system of orders and periods for huge numbers to show that the universe, sized on Aristarchus' Sun-centered model, would hold no more than 10⁶³ grains of sand.
Each result demanded new technique as well as skill in applying it. That is the signature of a mind setting problems nobody else could yet frame.
The Method: a working notebook recovered
The most revealing text nearly vanished. In the 13th century a 10th-century copy of Archimedes' works was scraped and overwritten with prayers. In 1906 the Danish philologist Johan Ludvig Heiberg examined the palimpsest in Constantinople and found The Method of Mechanical Theorems, lost for centuries. It shows Archimedes balancing figures on an imaginary lever, treating them as made of infinitely many lines to discover areas and volumes before proving them rigorously. The logic is that of integral calculus, about 1,900 years before Newton and Leibniz.
The manuscript sold at Christie's on 29 October 1998 for about $2 million to an anonymous buyer, who lent it to the Walters Art Museum for imaging and conservation from 1999 to 2008. Stanford's Reviel Netz argued that the Stomachion fragment it preserves is a counting problem; modern analysis finds 17,152 ways to arrange its 14 pieces into a square. If Netz is right, Archimedes was doing combinatorics too.
Eureka, the death scene and other legends
Much of what people know about Archimedes is late. The bath and the cry of "Eureka" come from Vitruvius, writing roughly two centuries after his death. "Do not disturb my circles" appears in no ancient source. The sources do agree on the ending: during the Roman capture of Syracuse in 212 BC a soldier killed him, although the Roman commander, Marcellus, had ordered that he be spared. The engineering tales, from the Claw of Archimedes to burning mirrors, range from plausible to doubtful.
For the stories themselves, read the Eureka story and his inventions and discoveries. None of them adds to the case for his intelligence as much as a single surviving proof.
Archimedes vs Newton, Gauss and Pythagoras
Archimedes is often ranked with Isaac Newton and Carl Friedrich Gauss as one of the three greatest mathematicians. Only one of the three has a scholarly IQ estimate: Newton, at Cox's corrected 190. Newton's IQ page explains how thin even that figure is, and Gauss's famous 250 has no source at all. Against Pythagoras, Archimedes is by far the better-documented mathematician: his proofs survive in his own words, while Pythagoras left nothing in writing.
Compare the records directly in Archimedes vs Newton and Archimedes vs Gauss, or see the full mathematicians' IQ ranking.
What a number would miss
An IQ test measures reasoning against contemporaries under a time limit. Archimedes worked without algebraic notation, without a symbol for zero and without calculus, and still reached results Europe took until the 17th century to extend. Measured against his tools, his achievement is arguably the steepest in the history of mathematics.
Even a genuine score for a man of the third century BC could not express that. An invented one, such as an IQ of 200, would express only the writer's admiration. Our assessment rests on the surviving treatises, the Archimedes Palimpsest research and standard histories; we report no figure because none can be defended.
Frequently asked questions
What was Archimedes' IQ?
Archimedes has no IQ score and no scholarly estimate. He died in 212 BC, and the main historical IQ study, Catharine Cox's 1926 work, covers only people born between 1450 and 1850 with documented childhoods. Figures on list sites cite no method. His surviving proofs are the only reliable evidence of his ability.
Was Archimedes a genius?
Yes. He bounded π between 223/71 and 22/7, proved that a sphere has two-thirds the volume of its enclosing cylinder, found the area of a parabolic segment and devised a way to name numbers as large as 10⁶³. His rediscovered Method shows reasoning close to integral calculus.
Who had a higher IQ, Archimedes or Newton?
Neither was tested. Newton has a retrospective estimate of 190 from Catharine Cox's 1926 study; Archimedes has none, because no record of his youth survives. The fair comparison is by work: both built methods for summing infinitely small parts, Archimedes roughly 1,900 years earlier.
Did Archimedes invent calculus?
Not as a formal system. But his method of exhaustion and the mechanical reasoning in The Method, recovered from a palimpsest in 1906, divide areas and volumes into infinitely many slices in a way that closely anticipates integral calculus. Newton and Leibniz turned such ideas into a general method in the 17th century.
Sources
- Archimedes — Wikipedia — Dates, π bounds, sphere and cylinder, parabola, tomb, death, legends
- Archimedes Palimpsest — Wikipedia — Heiberg (1906), The Method, 1998 sale, imaging, Stomachion
- The Sand Reckoner — Wikipedia — 10⁶³ grains, number system, Aristarchus' model
- Simonton, D. K. (2020). Galton, Terman, Cox: The Distinctive Volume II in Genetic Studies of Genius. Gifted Child Quarterly — Cox's criteria: births 1450–1850 and documented childhoods (Shakespeare excluded)
- Cox's IQ Estimates of 301 Eminent Geniuses — IQ Comparison Site — Newton's corrected Cox estimate of 190
Editorial standard: IQ figures for historical figures are retrospective estimates and are labeled as such; scores for living people appear only when the person disclosed them or a reputable outlet reported them. Corrections: contact the editors.
