Famous mathematicians in history

How these ten mathematicians were chosen

This list follows one thread: the ideas you meet in school maths and where they came from. Geometry and proof (Euclid), pi (Archimedes, Aryabhata), algebra (al-Khwarizmi), graphs with x and y axes (Descartes), calculus (Newton), and the first thinking about what a computer could do (Lovelace). It covers Greece, Egypt, India, Iraq, France and England, from the 6th century BCE to 1920.

Each entry gives dates, what the person really did, a detail most lists miss, and the text to look at. Two warnings: the further back you go, the more the stories are later legend, and a theorem’s name does not always tell you who found it.

Pythagoras (about 570 to 495 BCE): number as the key to nature

Pythagoras of Samos founded a community at Croton in southern Italy that linked numbers with music, the soul and the order of the cosmos. Aristotle reports that the later “Pythagoreans” thought the principles of mathematics were the principles of all things.

Most lists miss: there is no evidence that Pythagoras proved the theorem named after him. The relationship between the sides of a right triangle was known in Babylon over a thousand years earlier, as the clay tablet Plimpton 322 (about 1800 BCE) shows, and he wrote nothing that survives.

Euclid (active about 300 BCE): the Elements

Euclid worked in Alexandria in Egypt and wrote the Elements, thirteen books that build geometry and number theory step by step from definitions and postulates. Book IX, Proposition 20 proves that there are more prime numbers than any given list of them.

Most lists miss: we know almost nothing about his life. The famous line that there is “no royal road to geometry” comes from Proclus, writing about 750 years later. The Elements was one of the first mathematical books ever printed, in Venice in 1482, and was used as a school textbook into the 20th century.

Archimedes (about 287 to 212 BCE): pi, spheres and the lever

Archimedes of Syracuse showed that pi lies between 3 10/71 and 3 1/7 by fitting polygons of 96 sides inside and outside a circle (Measurement of a Circle). He proved that a sphere has two thirds of the volume of the cylinder that just contains it, and set out the law of the lever.

Most lists miss: he was proudest of the sphere and cylinder result and asked for it to be carved on his tomb. In 75 BCE the Roman Cicero, serving in Sicily, found the tomb overgrown with brambles and recognised it by that carving (Tusculan Disputations 5.64 to 66). See Pi Day and Archimedes.

Hypatia (about 355 to 415 CE): teacher and editor in Alexandria

Hypatia taught mathematics, astronomy and philosophy in Alexandria. Her father Theon records that she prepared the edition of book III of his commentary on Ptolemy’s Almagest, and the Suda says she wrote commentaries on Diophantus’s Arithmetica and Apollonius’s Conics.

Most lists miss: none of her own commentaries survives under her name, so her mathematics is known mostly through others. Some scholars think her editing shaped the text of Diophantus that later readers used. She was murdered in 415 during a political conflict in the city.

Aryabhata (476 to about 550 CE): pi to four decimal places

Aryabhata wrote the Aryabhatiya in 499 CE at Kusumapura (usually identified with Pataliputra, modern Patna), stating that he was 23 years old. In 121 short Sanskrit verses it covers arithmetic, algebra, trigonometry and astronomy, including the claim that the stars seem to move westward because the Earth rotates.

Most lists miss: he called his value of pi “approximate” himself, and gave the kuttaka (pulveriser) method for solving equations in whole numbers. India’s first satellite, launched in 1975, was named after him. See Indian scientists in history.

Al-Khwarizmi (about 780 to 850): the book that named algebra

Al-Khwarizmi worked in Baghdad under the caliph al-Ma’mun. His book on calculation by al-jabr (completion) and al-muqabala (balancing), written around 820, sorted equations into six types and solved quadratics by completing the square, for example “a square and ten roots equal thirty-nine”, which gives 3. Another of his books explained the Indian number system with a sign for zero.

Most lists miss: two everyday words come from him. “Algebra” comes from al-jabr in his title, and “algorithm” comes from Algoritmi, the Latin spelling of his name in translations of his book on Indian numerals. See Golden Age of Islam scholars.

René Descartes (1596 to 1650): coordinate geometry

René Descartes published La Géométrie in 1637 as an appendix to his Discourse on the Method. It showed how to turn geometric curves into algebraic equations and back, the basis of every graph with x and y axes you draw in school.

Most lists miss: La Géométrie is also where the habit of using x, y and z for unknowns and a, b and c for known quantities took hold. The grid we call “Cartesian” was developed further by later mathematicians; Descartes himself did not draw the two perpendicular axes in the form we use now.

Isaac Newton (1643 to 1727): calculus and the Principia

Isaac Newton worked out his method of “fluxions”, an early form of calculus, in 1665 and 1666, and in the Principia (1687) used mathematics to derive the laws of motion and universal gravitation.

Most lists miss: Gottfried Leibniz developed calculus independently and published first, in 1684. When the Royal Society investigated who came first, Newton, its president, secretly wrote the committee’s report himself (1712). Our dx/dy notation is Leibniz’s. See Isaac Newton 300 years.

Ada Lovelace (1815 to 1852): the Notes on the Analytical Engine

Ada Lovelace, trained in mathematics by tutors including Augustus De Morgan, wrote the 1843 Notes on Charles Babbage’s Analytical Engine. Note G sets out how the machine could compute Bernoulli numbers, step by step, in a table often called the first published program.

Most lists miss: her deepest idea was not about numbers. She saw that a machine manipulating symbols could work on anything that could be expressed in its notation, even music, while insisting that it could not originate anything by itself. See Ada Lovelace Day.

Srinivasa Ramanujan (1887 to 1920): the self-taught genius

Srinivasa Ramanujan, a clerk in the Madras Port Trust with no degree, wrote to G. H. Hardy in Cambridge on 16 January 1913 with pages of theorems. Hardy brought him to Cambridge, where they proved a formula for the number of partitions of a whole number. He was elected a Fellow of the Royal Society in 1918 and died in India in 1920, aged 32.

Most lists miss: not everything in that famous letter was right: Hardy showed his formula for counting primes was wrong. But much was new and correct, and in his last letter to Hardy (January 1920) he described “mock theta functions”, which mathematicians are still working on. India marks his birthday, 22 December, as National Mathematics Day: see National Mathematics Day.

Summary table: mathematicians and their contributions

Project ideas using famous mathematicians

• Redo the maths: compute Aryabhata’s value of pi from his verse, then Archimedes’ two bounds, and compare both with a calculator.
• Solve like al-Khwarizmi: solve x² + 10x = 39 by drawing his square and completing it, then explain each step in words.
• Myth check: find three popular claims (Pythagoras proved his theorem, Newton invented calculus alone, Ramanujan had no help) and test each against the sources here.
• Talk to a mathematician: practise questions by voice with Srinivasa Ramanujan or Isaac Newton on Yuga. The AI recreations are built from their writings and the record but are not the real people and can make mistakes, so check maths and dates against sources and cite those.

For more, read Newton vs Galileo and questions to ask Ramanujan.