History of Mathematics

The life of Bernhard Riemann

Timeline 1826Born on 17 September in Breselenz, in the Kingdom of Hanover, the son of a Lutheran pastor. 1846Enters the University of Göttingen to study theology, but soon moves to mathematics. 1847Goes to study in Berlin, with Dirichlet, Jacobi, Steiner and Eisenstein. 1851Doctorate in Göttingen, supervised by Gauss, with the thesis on complex functions. 1854On 10 June, gives his habilitation lecture on the foundations of geometry. 1857Publishes the theory of abelian functions and becomes an associate professor. 1859Succeeds Dirichlet in the chair at Göttingen and is elected to the Berlin Academy. Publishes the paper on prime numbers. 1862Marries Elise Koch. Falls ill with tuberculosis. 1866Dies on 20 July in Selasca, Italy, aged 39. The pastor’s son Georg Friedrich Bernhard Riemann was born on 17 September 1826 in Breselenz, a village in the Kingdom of Hanover, in northern Germany. His father, also named Friedrich Bernhard, was a Lutheran pastor who had fought in the wars against Napoleon. The family was poor, and Bernhard was the second of six children. It was his father who taught him until he was ten.

October 30, 2026 Read

The life of Pierre-Simon Laplace

Timeline 1749Born on 23 March in Beaumont-en-Auge, Normandy, the son of a cider merchant. 1765Enters the University of Caen to study theology. 1768Goes to Paris with a letter of recommendation to d’Alembert. 1770Becomes professor of mathematics at the Military School in Paris. 1773Is elected to the Academy of Sciences, at the third attempt. 1783Publishes with Lavoisier the memoir on heat and the ice calorimeter. 1785Examines the cadet Napoleon Bonaparte. Explains the great inequality of Jupiter and Saturn. 1788Marries Marie-Charlotte de Courty de Romanges. 1793Leaves Paris during the Terror. 1796Publishes the Exposition of the System of the World. 1799The first two volumes of Celestial Mechanics appear. He is Minister of the Interior for six weeks. 1806Becomes a count of the Empire. 1812Publishes the Analytic Theory of Probabilities. 1814Publishes the Philosophical Essay on Probabilities. 1817Receives the title of marquis from Louis XVIII. 1827Dies in Paris on 5 March. ◀ Previous Follow the journey Next ▶ 1749–1765 Beaumont-en-AugeHe is born on 23 March 1749, the son of a cider merchant. He studies at the town’s Benedictine school. 1765–1768 CaenHe enters the University of Caen to study theology. Two teachers, Gadbled and Le Canu, discover his talent for mathematics. 1769–1793 ParisHe arrives in Paris with a letter for d’Alembert, who finds him a post as professor at the École Militaire. In 1785 he examines the young Napoleon. 1793–1794 MelunDuring the Terror he leaves Paris with his family and takes refuge some 50 km from the capital. He returns after Robespierre’s fall. 1795–1814 ParisHe teaches at the École Normale, leads the Bureau des Longitudes, is Minister of the Interior for six weeks and then a senator and chancellor of the Senate, which meets at the Luxembourg. 1806–1827 ArcueilHe buys a country house next to that of the chemist Berthollet. The Society of Arcueil, a circle of young scientists, meets there. 1888 Saint-Julien-de-MaillocHe dies in Paris on 5 March 1827 and is buried at Père-Lachaise. In 1888 his remains are moved to the family mausoleum in Normandy. Enable JavaScript to see the map. The stages are listed below. From Normandy to Paris, with the refuge during the Terror and the country house at Arcueil, and back to Normandy for the grave. Map: © OpenStreetMap contributors

October 30, 2026 Read

The life of Archimedes

Timeline c. 287 BCBorn in Syracuse, the son of the astronomer Phidias. c. 270 BCHiero II becomes master of Syracuse; later he proclaims himself king. c. 250 BCAround this time, he writes to Conon of Samos and to Dositheus, in Alexandria, sending them his results. c. 240 BCWrites to Eratosthenes, in Alexandria, the letter we know as The Method. 215 BCHiero dies. Syracuse allies itself with Carthage against Rome. 214 BCThe Roman general Marcellus begins the siege of Syracuse. Archimedes’s machines defend the city. 212 BCSyracuse falls. Archimedes is killed by a Roman soldier. 75 BCCicero, a Roman magistrate in Sicily, finds his tomb again. A Greek city in Sicily Archimedes was born around 287 BC in Syracuse, on the east coast of Sicily. The date comes from a twelfth-century Byzantine author, John Tzetzes, who says he died at 75. Syracuse was then one of the largest cities in the Greek world, with two harbours and a fortified island, Ortygia, at the heart of the ancient city.

October 29, 2026 Read

The life of Maria Gaetana Agnesi

Timeline 1718Born in Milan on 16 May, the first of the 21 children of Pietro Agnesi, a wealthy silk merchant. 1727At nine, recites in Latin a speech defending women’s education. 1738Publishes the Propositiones philosophicae, 191 theses on philosophy and natural science that she defended at the gatherings in her father’s house. 1739Asks her father to let her enter a convent; he refuses. 1748Publishes the first volume of the Instituzioni analitiche, dedicated to Empress Maria Theresa. The second comes out in 1749. 1750Pope Benedict XIV appoints her to the chair of mathematics at the University of Bologna. She never goes to Bologna. 1752Her father dies. Agnesi leaves mathematics and begins caring for poor and sick women. 1771The Pio Albergo Trivulzio, a hospice for the elderly poor, is founded in Milan. Agnesi is asked to direct the women’s wing. 1799Dies on 9 January, at the hospice, and is buried in a common grave. The girl of the salons Maria Gaetana Agnesi was born in Milan on 16 May 1718. The city was then the capital of a duchy ruled by the Habsburgs of Vienna. Her father, Pietro Agnesi, had grown rich in the silk trade and wanted the family to rise in Milanese society. He married three times and had 21 children. Maria Gaetana was the eldest.

October 28, 2026 Read

The life of William Rowan Hamilton

Timeline 1805Born on the night of 3 to 4 August in Dublin, the son of a solicitor. 1808Goes to live in Trim with his uncle James, a clergyman and schoolmaster, who teaches him languages. 1818Takes on the American calculating prodigy Zerah Colburn; the defeat leads him to mathematics. 1823Enters Trinity College Dublin in first place. 1827While still a student, is appointed Royal Astronomer of Ireland. Visits Wordsworth in the Lake District. 1832Predicts conical refraction, observed soon afterwards by Humphrey Lloyd. 1833Marries Helen Bayly. Presents complex numbers as couples. 1834Publishes his general method in dynamics. 1835Is knighted and becomes Sir William. 1837Becomes President of the Royal Irish Academy. 1843On 16 October discovers quaternions and carves the formula on a bridge. 1853Publishes the Lectures on Quaternions. 1857Invents the Icosian game. 1865Is the first foreigner elected to the National Academy of Sciences of the United States. Dies on 2 September at Dunsink. ◀ Previous Follow the journey Next ▶ 1805–1808 DublinHe is born on the night of 3 to 4 August 1805, in Dominick Street, the son of a solicitor. At three he is sent to live with an uncle. 1808–1823 TrimHe grows up with his uncle James, a clergyman and schoolmaster, who teaches him languages. At thirteen he claims to know a dozen, from Latin to Persian. 1823–1827 Trinity CollegeHe studies in Dublin and wins the top prizes in classics and in science. While still a student he presents his theory of systems of rays. 1827 Rydal MountHe visits William Wordsworth in the Lake District. The two become lifelong friends, and the poet advises him to leave poetry for science. 1827–1865 Dunsink ObservatoryAt 21 he becomes Royal Astronomer of Ireland. There he writes his optics, his mechanics and his quaternions. He dies at the observatory on 2 September 1865. 1843 Broom BridgeOn 16 October, walking with his wife along the Royal Canal, he finds the rule for quaternions and carves it on a stone of the bridge. Enable JavaScript to see the map. The stages are listed below. From Dublin to Dunsink, with a detour to Wordsworth’s house in the Lake District. Map: © OpenStreetMap contributors

October 27, 2026 Read

The life of John von Neumann

Timeline 1903Born on 28 December in Budapest, the son of a banker. 1913His father receives a title of nobility; the son becomes “von Neumann”. 1921Finishes the Lutheran gymnasium in Budapest, where he studied alongside Eugene Wigner. 1923Publishes, at 19, his definition of ordinal numbers. 1926Diploma in chemical engineering in Zurich and doctorate in mathematics in Budapest. 1927Becomes the youngest Privatdozent at the University of Berlin. 1928Publishes the minimax theorem, the basis of game theory. 1930Moves to Princeton. In 1933 he is one of the first professors of the Institute for Advanced Study. 1932Publishes the Mathematical Foundations of Quantum Mechanics. 1943Begins working at Los Alamos, on the atomic bomb project. 1944Publishes, with Oskar Morgenstern, the Theory of Games and Economic Behavior. 1945Writes the EDVAC report, which describes the stored-program computer. 1946With Stanisław Ulam, develops the Monte Carlo method. 1952The IAS computer comes into operation. 1955Appointed to the Atomic Energy Commission. Discovers he has cancer. 1957Dies on 8 February, in Washington, aged 53. ◀ Previous Follow the journey Next ▶ 1903–1921 BudapestHe is born on 28 December, the son of a banker. He studies at the Lutheran gymnasium, where Eugene Wigner is a schoolmate. 1921–1923 BerlinHe studies chemistry, at his father’s insistence, while enrolled for a doctorate in mathematics in Budapest. 1923–1926 ZurichHe graduates in chemical engineering at the Polytechnic. He attends classes by George Pólya, who would say he was the only student he was ever afraid of. 1926–1927 GöttingenHe works with David Hilbert on the foundations of mathematics and of the new quantum mechanics. 1927–1930 BerlinThe university’s youngest Privatdozent. In 1928 he publishes the minimax theorem. 1930–1957 PrincetonProfessor at the university and, from 1933, at the Institute for Advanced Study, alongside Einstein and Gödel. There he builds the IAS computer. 1943–1955 Los AlamosConsultant to the atomic bomb project. With Ulam, he creates the Monte Carlo method. 1955–1957 WashingtonMember of the Atomic Energy Commission. He dies of cancer on 8 February 1957, at Walter Reed Hospital. Enable JavaScript to see the map. The stages are listed below. From Budapest to Washington, by way of Zurich, Göttingen, Berlin, Princeton and Los Alamos. Map: © OpenStreetMap contributors

October 26, 2026 Read

The life of Augustin-Louis Cauchy

Timeline 1789Born on 21 August in Paris, five weeks after the fall of the Bastille. 1794During the Terror, the family takes refuge in Arcueil, next door to Laplace. 1805Enters the École Polytechnique, second in the entrance examination. 1810Goes to Cherbourg as an engineer on Napoleon’s military harbour. 1813Returns to Paris in poor health and proves Fermat’s polygonal number theorem. 1816Appointed to the Academy of Sciences by royal decree, in place of Monge. 1821Publishes the Cours d’analyse of the École Polytechnique. 1825Presents the memoir on integrals between imaginary limits. 1830Refuses to swear allegiance to Louis-Philippe and goes into exile. 1833In Prague, becomes tutor to the Duke of Bordeaux, grandson of Charles X. 1838Returns to Paris. 1848The new republic abolishes the oath; the following year he takes up the chair at the Sorbonne. 1857Dies on 23 May at Sceaux, aged 67. A child of the Revolution Augustin-Louis Cauchy was born in Paris on 21 August 1789. The Bastille had fallen on 14 July, and his father, Louis-François Cauchy, was a senior official of the Paris police, an Ancien Régime post that became dangerous overnight. In 1794, during the Terror, the family fled to their country house in Arcueil, south of the city. There they knew hunger and poverty; Augustin was a frail child, and poor health stayed with him all his life.

October 25, 2026 Read

The life of Alan Turing

Timeline 1912Born on 23 June in London. His parents live in India. 1926Starts at Sherborne boarding school. 1930Christopher Morcom, his best friend, dies. 1931Enters King’s College, Cambridge. 1935Elected a fellow of King’s, aged 22. 1936Writes “On computable numbers”. Goes to Princeton. 1938Doctorate at Princeton. Returns to Cambridge. 1939Starts work at Bletchley Park, on breaking the Enigma. 1940The first electromechanical bombe comes into operation. 1945Moves to the National Physical Laboratory, where he designs the ACE. 1948Moves to the University of Manchester. 1950Publishes the paper on the imitation game. 1952Publishes the theory of morphogenesis. Convicted for homosexuality. 1954Dies on 7 June, in Wilmslow, aged 41. ◀ Previous Follow the journey Next ▶ 1912 LondonHe is born on 23 June in Maida Vale. His parents live in India, and he is brought up by a foster family in the south of England. 1926–1931 SherborneAt boarding school he meets Christopher Morcom, the friend whose death in 1930 leads him to think about the relation between mind and matter. 1931–1936 CambridgeHe studies at King’s College, becomes a fellow at 22 and writes “On computable numbers”. 1936–1938 PrincetonHe does his doctorate with Alonzo Church, who had reached the same result by another route. 1939–1945 Bletchley ParkDuring the war he heads the section that breaks the German naval Enigma and designs the electromechanical bombe. 1945–1947 TeddingtonAt the National Physical Laboratory he designs the ACE, a stored-program computer. 1948–1954 ManchesterHe programs one of the first computers, proposes the imitation game and studies morphogenesis. He dies in Wilmslow, near the city, on 7 June 1954. Enable JavaScript to see the map. The stages are listed below. From London to Manchester, by way of Princeton and Bletchley Park. Map: © OpenStreetMap contributors

October 17, 2026 Read

The life of John Napier

Timeline 1550Born at Merchiston Castle, near Edinburgh. His father, Archibald, is 16. 1563His mother dies. At 13, John enters the University of St Andrews. c. 1564Leaves St Andrews without a degree and goes to study on the Continent. 1571Returns to Scotland. 1572Marries Elizabeth Stirling. Goes to live at Gartness, where he builds a castle. 1593Publishes A Plaine Discovery of the Whole Revelation of Saint John, his most famous book in his lifetime. 1594Signs a contract to search for treasure hidden at Fast Castle. 1596Describes his “secret inventions” of war in a manuscript. 1608On his father’s death he becomes laird of Merchiston. 1614Publishes the Description of the Wonderful Canon of Logarithms. 1615Receives at Merchiston a visit from Henry Briggs, professor in London. 1617Publishes the Rabdologia, with his calculating rods. Dies on 4 April. 1619His son Robert publishes the Construction of the Wonderful Canon of Logarithms. The boy from Merchiston John Napier was born in 1550 in Merchiston Tower, a small stone castle a little over three kilometres from Edinburgh. His father, Sir Archibald Napier, was only 16. The family belonged to the Scottish nobility, and the name was spelled in many ways: Napier, Napeir, Nepair, and in Latin Neperus, from which comes the French form Neper.

October 16, 2026 Read

The life of Évariste Galois

Timeline 1811Born on 25 October in Bourg-la-Reine, near Paris. 1823Enters the Louis-le-Grand college in Paris. 1827Discovers mathematics and abandons everything else. 1828Fails the École Polytechnique entrance examination for the first time. 1829Publishes his first paper. Sends work to the Academy. His father commits suicide. Second failure at the Polytechnique. Enters the École Normale. 1830The paper entered for the Grand Prize is lost when Fourier dies. July Revolution. 1831Expelled from the École Normale. Poisson rejects his memoir. Arrested twice. 1832Dies on 31 May, aged 20, after being wounded in a duel. 1846Joseph Liouville publishes his works. ◀ Previous Follow the journey Next ▶ 1811–1823 Bourg-la-ReineHe is born in the town where his father will be mayor. His mother teaches him at home until he is 12. 1823–1829 Louis-le-GrandAt school he discovers mathematics at 15, “the frenzy of mathematics dominates him”. Having failed the Polytechnique twice, he enters the École Normale in 1829 and is expelled in 1831. 1831 Pont NeufOn 14 July he is arrested on the bridge, wearing the uniform of the disbanded artillery and armed. 1831–1832 Sainte-Pélagie prisonHe spends eight months in prison. In July 1831 he receives Poisson’s rejection. 1832 Cochin hospitalWounded in the duel of 30 May, he is taken to the hospital, where he dies on the morning of 31 May, aged 20. Enable JavaScript to see the map. The stages are listed below. Galois’s Paris, from school to prison and hospital, within a few kilometres. Map: © OpenStreetMap contributors

October 16, 2026 Read

The life of Niels Henrik Abel

Timeline 1802Born on 5 August near Stavanger, on the west coast of Norway. 1804The family moves to Gjerstad, where his father is the pastor. 1815Enters the Cathedral School of Christiania, today’s Oslo. 1818Bernt Holmboe becomes his mathematics teacher. 1820His father dies. Abel begins to support part of the family. 1821Enters the university. Believes he has solved the quintic and finds the mistake. 1824Publishes, at his own expense, the proof that there is no formula for the fifth degree. 1825Travels to Berlin, where he meets August Leopold Crelle. 1826In Paris, hands the Academy his great memoir on integrals. Cauchy loses it. 1827Returns to Norway, jobless and in debt. Publishes elliptic functions. 1829Dies of tuberculosis at Froland on 6 April, aged 26. 1830Receives, posthumously, the Grand Prize of the Paris Academy, with Jacobi. ◀ Previous Follow the journey Next ▶ 1802 near StavangerHe is born on the west coast of Norway, the second of seven children of a pastor. 1804–1815 GjerstadHe grows up in his father’s parish in the south of the country. 1815–1825 ChristianiaAt the Cathedral School his teacher Holmboe discovers his talent. In 1824 he publishes the six-page pamphlet on the quintic. 1825–1826 BerlinHe meets August Leopold Crelle, who publishes seven of his papers in the first volume of his journal. 1826 ParisHe hands the Academy his great memoir on integrals. Nobody pays attention to him, and Cauchy loses the manuscript. 1827–1828 ChristianiaHe returns jobless and in debt. He publishes elliptic functions and races Jacobi. 1828–1829 FrolandHe travels by sleigh at Christmas to see his fiancée, falls ill and dies of tuberculosis on 6 April. Two days later the appointment from Berlin arrives. Enable JavaScript to see the map. The stages are listed below. Abel’s great journey, from Norway to Berlin and Paris, and the return to die at Froland. Map: © OpenStreetMap contributors

October 16, 2026 Read

The life of John Nash

Timeline 1928Born on 13 June in Bluefield, West Virginia, in the United States. 1945Enters the Carnegie Institute of Technology, in Pittsburgh, to study chemical engineering. Switches to mathematics. 1948Arrives at Princeton. Invents the game his colleagues call “Nash”, known today as Hex. 1950Defends the thesis “Non-cooperative games”, with the Nash equilibrium. Publishes “The bargaining problem”. 1951Becomes an instructor at MIT. 1956Publishes the isometric embedding theorem. 1957Marries Alicia Lardé, a physics student at MIT. 1958Publishes the result on the regularity of parabolic equations. 1959First psychiatric hospitalisation. Three decades of illness begin. 1994Receives the Nobel Prize in Economics, with John Harsanyi and Reinhard Selten. 2001Remarries Alicia. The film A Beautiful Mind is released. 2015Receives the Abel Prize, with Louis Nirenberg. Dies in a car crash on 23 May, together with Alicia. ◀ Previous Follow the journey Next ▶ 1928–1945 BluefieldHe grows up in a railway and coal town. He reads Men of Mathematics and proves Fermat’s little theorem by himself. 1945–1948 PittsburghAt the Carnegie Institute of Technology he swaps chemical engineering for mathematics and has the bargaining idea. 1948–1951 PrincetonHe invents Hex and defends his 28-page thesis with the Nash equilibrium. 1951–1959 MITA professor at MIT. He proves the embedding theorem and the result on parabolic equations. In 1959 his illness begins. 1970–2015 PrincetonHe wanders the corridors as “the phantom of Fine Hall” and recovers at the end of the 1980s. 1994 StockholmHe receives the Nobel Prize in Economics, with John Harsanyi and Reinhard Selten. 2015 OsloHe receives the Abel Prize, with Louis Nirenberg. On the way home, on 23 May, he and Alicia die in a taxi crash in New Jersey. Enable JavaScript to see the map. The stages are listed below. John Nash’s places, from Bluefield to Princeton, and the journeys to receive the Nobel and the Abel. Map: © OpenStreetMap contributors

October 14, 2026 Read