At the start of David Wells’s book The Penguin Dictionary of Curious and Interesting Numbers, there is a list of 98 mathematicians in order of time, from Ahmes in ancient Egypt to Srinivasa Ramanujan in India (Wells, 1987, pp. 9–11). In this post, I turn that list into charts, so we can see when they lived, where they worked, and how they learned from each other. The charts are interactive: you can zoom into any part of history, and tap a name to see what that person gave to mathematics.
From Ahmes to Ramanujan: A Timeline of Mathematicians
From Ahmes to Ramanujan: A Timeline of Mathematicians
Contents
At the start of David Wells’s book The Penguin Dictionary of Curious and Interesting Numbers, there is a list of 98 mathematicians in order of time, from Ahmes in ancient Egypt to Srinivasa Ramanujan in India (Wells, 1987, pp. 9–11). In this post, I turn that list into charts, so we can see when they lived, where they worked, and how they learned from each other. The charts are interactive: you can zoom into any part of history, and tap a name to see what that person gave to mathematics.
1. 1
2. 1500 BC
3. 1000 BC
4. 1
5. 4500 BC
6. 7
7. 4
8. 2
9. 3AD 1
10. 4
11. 1
12. 3
13. 2
14. 1500
15. 1
16. 3
17. 1
18. 1000
19. 2
20. 2
21. 2
22. 4
23. 211500
24. 24
25. 25
26. 27
27. 81900
Mathematicians in the list alive in each century, 1700 BC to AD 1999.
Lifelines
- Egypt
- Greek world
- China
- India
- Islamic world
- Europe
Turn on JavaScript to explore the lifelines; the table below lists every one.
− + Whole timeline
Ancient Egypt Classical Greece Hellenistic & Roman India & the Islamic world Late Middle Ages Renaissance Scientific Revolution Enlightenment Nineteenth century Ahmes Pythagoras Hippocrates Plato Hippias Theaetetus Archytas Xenocrates Theodorus Aristotle Menaechmus Euclid Archimedes Nicomedes Eratosthenes Diocles Hipparchus Heron Ptolemy Nicomachus Theon Diophantus Pappus Iamblichus Proclus Zu Chongzhi Brahmagupta al-Khwarizmi Thabit Mahavira Bhaskara Fibonacci al-Banna Zhu Shijie Pacioli da Vinci Dürer Stifel Tartaglia Cardano Recorde Ferrari Viète van Ceulen Stevin Napier Cataldi Briggs Kepler Oughtred Bachet Mersenne Girard Desargues Descartes Fermat Brouncker Pascal Huygens Newton Leibniz J. Bernoulli Machin N. Bernoulli Goldbach Stirling Euler Buffon Lambert Lagrange Wilson Wessel Laplace Legendre Nieuwland Ruffini Argand Gauss Brianchon Binet Möbius Babbage Lamé Steiner De Morgan Liouville Shanks Catalan Hermite Riemann Venn Lucas Cantor Lindemann Hilbert D. N. Lehmer Hardy Ramanujan
Show the list as a table
| Mathematician | Dates | Region | Known for |
| -------------------------------------- | -------------------------- | ------------- | ---------------------------------------------------------- |
| Ahmes | c.1650 BC | Egypt | Copied the Rhind Mathematical Papyrus |
| Pythagoras | c.540 BC | Greek world | The Pythagorean theorem, named after him |
| Hippocrates of Chios | c.440 BC | Greek world | Squared the lunes; wrote the first Elements |
| Plato | c.430–c.349 BC | Greek world | Founded the Academy; the Platonic solids |
| Hippias of Elis | c.425 BC | Greek world | The quadratrix curve |
| Theaetetus | c.417–369 BC | Greek world | Classified irrationals; the five regular solids |
| Archytas | c.400 BC | Greek world | Doubled the cube with a 3D construction |
| Xenocrates | 396–314 BC | Greek world | First recorded attempt to count combinations |
| Theodorus of Cyrene | c.390 BC | Greek world | Proved √3 to √17 irrational |
| Aristotle | 384–322 BC | Greek world | Formal logic and the syllogism |
| Menaechmus | c.350 BC | Greek world | Discovered the conic sections |
| Euclid | c.300 BC | Greek world | The Elements |
| Archimedes | c.287–212 BC | Greek world | Area and volume of the sphere; bounds on π |
| Nicomedes | c.240 BC | Greek world | The conchoid, used to trisect angles |
| Eratosthenes | c.230 BC | Greek world | Sieve for primes; measured the Earth |
| Diocles | c.180 BC | Greek world | The cissoid; focus of the parabola |
| Hipparchus | c.180–c.125 BC | Greek world | Founded trigonometry with a table of chords |
| Heron of Alexandria | c.75 | Greek world | Heron's formula for a triangle's area |
| Ptolemy | c.85–c.165 | Greek world | The Almagest |
| Nicomachus of Gerasa | c.100 | Greek world | Introduction to Arithmetic |
| Theon of Smyrna | c.125 | Greek world | Side and diagonal numbers approaching √2 |
| Diophantus | 1st or 3rd century | Greek world | Arithmetica; early algebraic notation |
| Pappus | c.320 | Greek world | The Collection; Pappus's hexagon theorem |
| Iamblichus | c.325 | Greek world | Commentary on Nicomachus; Pythagorean number lore |
| Proclus | 410–485 | Greek world | Commentary on Book I of Euclid |
| Zu Chongzhi | 430–501 | China | π ≈ 355/113 |
| Brahmagupta | c.628 | India | Rules for zero and negative numbers |
| Al-Khwarizmi | c.825 | Islamic world | Algebra (al-jabr); 'algorithm' is his name |
| Thabit ibn Qurra | 836–901 | Islamic world | A rule for finding amicable numbers |
| Mahavira | c.850 | India | Ganita Sara Samgraha; formula for combinations |
| Bhaskara | 1114–c.1185 | India | Lilavati; the cyclic method for Pell's equation |
| Leonardo of Pisa (Fibonacci) | c.1170–after 1240 | Europe | Liber Abaci; brought Hindu–Arabic numerals to Europe |
| Ibn al-Banna | 1256–1321 | Islamic world | Found the amicable pair 17296 and 18416 |
| Zhu Shijie | early 14th century, c.1303 | China | Jade Mirror of the Four Unknowns |
| Luca Pacioli | c.1445–1517 | Europe | Summa; double-entry bookkeeping |
| Leonardo da Vinci | 1452–1519 | Europe | Drew the polyhedra for Divina proportione |
| Albrecht Dürer | 1471–1528 | Europe | The magic square in Melencolia I |
| Michael Stifel | 1486/7–1567 | Europe | Arithmetica integra; coined 'exponent' |
| Niccolò Tartaglia | c.1500–1557 | Europe | Solved the cubic equation |
| Gerolamo Cardano | 1501–1576 | Europe | Ars Magna, publishing the cubic and quartic |
| Robert Recorde | c.1510–1558 | Europe | Invented the equals sign |
| Lodovico Ferrari | 1522–1565 | Europe | Solved the quartic equation |
| François Viète | 1540–1603 | Europe | Letters for unknowns; an infinite product for π |
| Ludolph van Ceulen | 1540–1610 | Europe | π to 35 decimal places |
| Simon Stevin | 1548–1620 | Europe | Popularised decimal fractions |
| John Napier | 1550–1617 | Europe | Invented logarithms |
| Pietro Antonio Cataldi | 1552–1626 | Europe | Continued fractions; the sixth and seventh perfect numbers |
| Henry Briggs | 1561–1630 | Europe | Base-10 logarithms |
| Johannes Kepler | 1571–1630 | Europe | Laws of planetary motion |
| William Oughtred | c.1574–1660 | Europe | The slide rule and the × sign |
| Claude Gaspard Bachet de Méziriac | 1581–1638 | Europe | Latin edition of Diophantus |
| Marin Mersenne | 1588–1648 | Europe | Mersenne primes |
| Albert Girard | c.1590–c.1633 | Europe | First statement of the fundamental theorem of algebra |
| Girard Desargues | 1591–1661 | Europe | Projective geometry; Desargues's theorem |
| René Descartes | 1596–1650 | Europe | Analytic geometry |
| Pierre de Fermat | 1601–1665 | Europe | Number theory; Fermat's Last Theorem |
| William Brouncker | c.1620–1684 | Europe | A continued fraction for 4/π |
| Blaise Pascal | 1623–1662 | Europe | Probability theory; Pascal's triangle |
| Christiaan Huygens | 1628–1695 | Europe | Pendulum clock; first book on probability |
| Isaac Newton | 1642–1727 | Europe | Calculus; laws of motion and gravitation |
| Gottfried Wilhelm Leibniz | 1646–1716 | Europe | Calculus and its notation |
| Johann Bernoulli | 1667–1748 | Europe | The brachistochrone; L'Hôpital's rule |
| John Machin | 1680–1751 | Europe | Machin's formula for π |
| Nicolaus Bernoulli | 1687–1759 | Europe | The St Petersburg paradox |
| Christian Goldbach | 1690–1764 | Europe | Goldbach's conjecture |
| James Stirling | 1692–1770 | Europe | Stirling's approximation for n! |
| Leonhard Euler | 1707–1783 | Europe | Founded graph theory; e^iπ + 1 = 0 |
| Georges-Louis Leclerc, Comte de Buffon | 1707–1788 | Europe | Buffon's needle |
| Johann Heinrich Lambert | 1728–1777 | Europe | Proved π irrational |
| Joseph-Louis Lagrange | 1736–1813 | Europe | Lagrangian mechanics |
| John Wilson | 1741–1793 | Europe | Wilson's theorem on primes |
| Caspar Wessel | 1745–1818 | Europe | Complex numbers as points in the plane |
| Pierre-Simon Laplace | 1749–1827 | Europe | Celestial mechanics; the Laplace transform |
| Adrien-Marie Legendre | 1752–1833 | Europe | The method of least squares |
| Pieter Nieuwland | 1764–1794 | Europe | The largest cube through a hole in a unit cube |
| Paolo Ruffini | 1765–1822 | Europe | First proof the quintic has no general formula |
| Jean-Robert Argand | 1768–1822 | Europe | The Argand diagram |
| Carl Friedrich Gauss | 1777–1855 | Europe | Disquisitiones Arithmeticae; the 17-gon |
| Charles Julien Brianchon | c.1783–1864 | Europe | Brianchon's theorem |
| Jacques Philippe Marie Binet | 1786–1856 | Europe | Binet's formula for Fibonacci numbers |
| August Ferdinand Möbius | 1790–1868 | Europe | The Möbius strip |
| Charles Babbage | 1792–1871 | Europe | The Analytical Engine |
| Gabriel Lamé | 1795–1870 | Europe | Fermat's Last Theorem for n = 7 |
| Jakob Steiner | 1796–1863 | Europe | Synthetic projective geometry |
| Augustus De Morgan | 1806–1871 | Europe | De Morgan's laws |
| Joseph Liouville | 1809–1882 | Europe | The first proven transcendental numbers |
| William Shanks | 1812–1882 | Europe | π to 707 places (527 correct) |
| Eugène Charles Catalan | 1814–1894 | Europe | Catalan numbers |
| Charles Hermite | 1822–1901 | Europe | Proved e transcendental |
| Bernhard Riemann | 1826–1866 | Europe | The Riemann hypothesis |
| John Venn | 1834–1923 | Europe | Venn diagrams |
| Édouard Lucas | 1842–1891 | Europe | Proved 2^127 − 1 prime; the Tower of Hanoi |
| Georg Cantor | 1845–1918 | Europe | Set theory and sizes of infinity |
| Ferdinand von Lindemann | 1852–1939 | Europe | Proved π transcendental |
| David Hilbert | 1862–1943 | Europe | His 23 problems |
| Derrick Norman Lehmer | 1867–1938 | Europe | Tables of primes and factors to 10 million |
| G. H. Hardy | 1877–1947 | Europe | Analytic number theory with Littlewood |
| Srinivasa Ramanujan | 1887–1920 | India | Partitions and series for π |
Who knew whom
Show the links of
Pythagoras, c.540 BC: 2 links Pythagoras Hippocrates of Chios, c.440 BC: 5 links Hippocrates Plato, c.430–c.349 BC: 10 links Plato Hippias of Elis, c.425 BC: 3 links Hippias Theaetetus, c.417–369 BC: 4 links Theaetetus Archytas, c.400 BC: 4 links Archytas Xenocrates, 396–314 BC: 2 links Xenocrates Theodorus of Cyrene, c.390 BC: 2 links Theodorus Aristotle, 384–322 BC: 5 links Aristotle Menaechmus, c.350 BC: 2 links Menaechmus Euclid, c.300 BC: 27 links Euclid Archimedes, c.287–212 BC: 15 links Archimedes Nicomedes, c.240 BC: 3 links Nicomedes Eratosthenes, c.230 BC: 10 links Eratosthenes Diocles, c.180 BC: 1 links Diocles Hipparchus, c.180–c.125 BC: 3 links Hipparchus Heron of Alexandria, c.75: 4 links Heron Ptolemy, c.85–c.165: 11 links Ptolemy Nicomachus of Gerasa, c.100: 3 links Nicomachus Theon of Smyrna, c.125: 3 links Theon Diophantus, 1st or 3rd century: 5 links Diophantus Pappus, c.320: 11 links Pappus Iamblichus, c.325: 2 links Iamblichus Proclus, 410–485: 7 links Proclus Brahmagupta, c.628: 3 links Brahmagupta Al-Khwarizmi, c.825: 3 links al-Khwarizmi Thabit ibn Qurra, 836–901: 5 links Thabit Mahavira, c.850: 1 links Mahavira Bhaskara, 1114–c.1185: 1 links Bhaskara Leonardo of Pisa (Fibonacci), c.1170–after 1240: 6 links Fibonacci Ibn al-Banna, 1256–1321: 1 links al-Banna Luca Pacioli, c.1445–1517: 6 links Pacioli Leonardo da Vinci, 1452–1519: 1 links da Vinci Albrecht Dürer, 1471–1528: 3 links Dürer Michael Stifel, 1486/7–1567: 2 links Stifel Niccolò Tartaglia, c.1500–1557: 5 links Tartaglia Gerolamo Cardano, 1501–1576: 4 links Cardano Robert Recorde, c.1510–1558: 2 links Recorde Lodovico Ferrari, 1522–1565: 2 links Ferrari François Viète, 1540–1603: 9 links Viète Ludolph van Ceulen, 1540–1610: 3 links van Ceulen Simon Stevin, 1548–1620: 6 links Stevin John Napier, 1550–1617: 3 links Napier Pietro Antonio Cataldi, 1552–1626: 5 links Cataldi Henry Briggs, 1561–1630: 3 links Briggs Johannes Kepler, 1571–1630: 6 links Kepler William Oughtred, c.1574–1660: 2 links Oughtred Claude Gaspard Bachet de Méziriac, 1581–1638: 3 links Bachet Marin Mersenne, 1588–1648: 9 links Mersenne Albert Girard, c.1590–c.1633: 4 links Girard Girard Desargues, 1591–1661: 4 links Desargues René Descartes, 1596–1650: 10 links Descartes Pierre de Fermat, 1601–1665: 15 links Fermat William Brouncker, c.1620–1684: 7 links Brouncker Blaise Pascal, 1623–1662: 9 links Pascal Christiaan Huygens, 1628–1695: 8 links Huygens Isaac Newton, 1642–1727: 12 links Newton Gottfried Wilhelm Leibniz, 1646–1716: 8 links Leibniz Johann Bernoulli, 1667–1748: 4 links J. Bernoulli John Machin, 1680–1751: 5 links Machin Nicolaus Bernoulli, 1687–1759: 6 links N. Bernoulli Christian Goldbach, 1690–1764: 6 links Goldbach James Stirling, 1692–1770: 5 links Stirling Leonhard Euler, 1707–1783: 17 links Euler Georges-Louis Leclerc, Comte de Buffon, 1707–1788: 2 links Buffon Johann Heinrich Lambert, 1728–1777: 5 links Lambert Joseph-Louis Lagrange, 1736–1813: 12 links Lagrange John Wilson, 1741–1793: 2 links Wilson Pierre-Simon Laplace, 1749–1827: 8 links Laplace Adrien-Marie Legendre, 1752–1833: 9 links Legendre Paolo Ruffini, 1765–1822: 3 links Ruffini Jean-Robert Argand, 1768–1822: 1 links Argand Carl Friedrich Gauss, 1777–1855: 8 links Gauss Charles Julien Brianchon, c.1783–1864: 1 links Brianchon Jacques Philippe Marie Binet, 1786–1856: 6 links Binet August Ferdinand Möbius, 1790–1868: 1 links Möbius Charles Babbage, 1792–1871: 2 links Babbage Gabriel Lamé, 1795–1870: 6 links Lamé Jakob Steiner, 1796–1863: 3 links Steiner Augustus De Morgan, 1806–1871: 2 links De Morgan Joseph Liouville, 1809–1882: 6 links Liouville William Shanks, 1812–1882: 2 links Shanks Eugène Charles Catalan, 1814–1894: 6 links Catalan Charles Hermite, 1822–1901: 5 links Hermite Bernhard Riemann, 1826–1866: 6 links Riemann John Venn, 1834–1923: 2 links Venn Édouard Lucas, 1842–1891: 2 links Lucas Georg Cantor, 1845–1918: 5 links Cantor Ferdinand von Lindemann, 1852–1939: 3 links Lindemann David Hilbert, 1862–1943: 6 links Hilbert Derrick Norman Lehmer, 1867–1938: 1 links D. N. Lehmer G. H. Hardy, 1877–1947: 4 links Hardy Srinivasa Ramanujan, 1887–1920: 1 links Ramanujan
- taught
- met or wrote to
- rivals
- built on the work of
Show all 239 links as a list
1. Plato clashed with Hippias (c.390 BC): Plato's dialogues mock Hippias as vain and arrogant. Source
2. Plato met or wrote to Theaetetus (c.380 BC): Plato's friend; Theaetetus probably worked in the Academy; Plato named dialogues after him. Source
3. Plato taught Xenocrates (c.376 BC): Xenocrates studied at the Academy; went with Plato to Syracuse. Source
4. Plato taught Aristotle (367–347 BC): Aristotle studied at Plato's Academy for twenty years. Source
5. Plato met or wrote to Menaechmus (c.350 BC): Proclus calls Menaechmus an associate of Plato. Source
6. Archytas built on Hippocrates (c.400 BC): Solved cube duplication using Hippocrates' two-mean-proportionals reduction. Source
7. Archytas met or wrote to Plato (c.388–361 BC): Close friends who wrote letters; Archytas saved Plato from Dionysius. Source
8. Xenocrates met or wrote to Aristotle (347 BC): Left Athens together for Assos after Plato's death. Source
9. Theodorus taught Plato (c.399 BC): Theodorus taught Plato mathematics; Plato visited him in Cyrene. Source
10. Theodorus taught Theaetetus (c.400 BC): Plato's dialogue Theaetetus shows Theodorus as his teacher. Source
11. Aristotle clashed with Hippocrates (c.350 BC): Aristotle called Hippocrates a good geometer but foolish in business. Source
12. Euclid built on Hippocrates (c.300 BC): Hippocrates' earlier Elements covered material in Euclid's Books I–II. Source
13. Euclid built on Theaetetus (c.300 BC): Books X and XIII of the Elements record Theaetetus's work. Source
14. Euclid built on Archytas (c.300 BC): Archytas' proof uses theorems later found in Elements Book VII. Source
15. Archimedes built on Euclid (c.250 BC): Cites Euclid's Elements in On the Sphere and Cylinder. Source
16. Archimedes met or wrote to Eratosthenes (c.240 BC): Wrote The Method as a letter to Eratosthenes; sent Cattle Problem. Source
17. Nicomedes built on Hippias (c.240 BC): Used Hippias' quadratrix to square the circle. Source
18. Nicomedes clashed with Eratosthenes (c.240 BC): Attacked Eratosthenes' mean-proportional method at length. Source
19. Eratosthenes built on Hippocrates (c.230 BC): Built a mean-proportionals device from Hippocrates' cube reduction. Source
20. Eratosthenes built on Plato (c.230 BC): Wrote Platonicus on the mathematics behind Plato's philosophy. Source
21. Eratosthenes clashed with Archytas (c.230 BC): His epigram dismisses "the difficult business of Archytas's cylinders". Source
22. Eratosthenes clashed with Menaechmus (c.230 BC): His epigram dismisses Menaechmus's cone-cutting solution. Source
23. Diocles built on Archimedes (c.180 BC): Solved Archimedes' problem of cutting a sphere in given ratio. Source
24. Hipparchus clashed with Eratosthenes (c.150 BC): Wrote three books "Against the Geography of Eratosthenes". Source
25. Heron built on Euclid (c.60): Wrote a Commentary on Euclid's Elements. Source
26. Heron built on Archimedes (c.60): Metrica quotes and builds on Archimedes' measurement results. Source
27. Ptolemy built on Aristotle (c.150): Almagest justifies Aristotle's Earth-centred system. Source
28. Ptolemy built on Euclid (c.150): Tried to prove Euclid's parallel postulate (Proclus reports). Source
29. Ptolemy built on Hipparchus (c.150): Almagest uses, and is our main source for, Hipparchus's work. Source
30. Theon built on Plato (c.125): Expositio written as mathematics needed to read Plato. Source
31. Theon built on Eratosthenes (c.125): Expositio draws heavily on Eratosthenes' Platonicus. Source
32. Theon taught Ptolemy (c.130): Ptolemy used "Theon the mathematician's" observations; probably his teacher. Source
33. Pappus built on Hippias (c.320): Collection Book IV describes Hippias' quadratrix and squaring the circle. Source
34. Pappus built on Theaetetus (c.320): Book X commentary describes Theaetetus's work on irrationals. Source
35. Pappus built on Euclid (c.320): Commentary on Elements Book X; Collection Book VII on Euclid. Source
36. Pappus built on Archimedes (c.320): Collection reports Archimedes' semiregular solids and spiral. Source
37. Pappus built on Nicomedes (c.320): Collection reports Nicomedes' conchoid and his angle trisection. Source
38. Pappus built on Eratosthenes (c.320): Lists Eratosthenes' On means among the great geometry books. Source
39. Pappus built on Heron (c.320): Collection Book VIII describes Heron's mechanics. Source
40. Pappus built on Ptolemy (c.320): Wrote a commentary on Ptolemy's Almagest. Source
41. Pappus clashed with Nicomachus (c.320): Pappus reportedly despised Nicomachus's arithmetic. Source
42. Iamblichus built on Pythagoras (c.300): Wrote a biography of Pythagoras (On the Pythagorean Life). Source
43. Iamblichus built on Nicomachus (c.300): Wrote a commentary on Nicomachus's Introduction to Arithmetic. Source
44. Proclus built on Hippocrates (c.450): Euclid commentary records Hippocrates' lunes and first Elements. Source
45. Proclus built on Plato (c.450): Head of Plato's Academy; wrote commentaries on Plato's dialogues. Source
46. Proclus built on Aristotle (c.450): Elements of Physics largely restates Aristotle's Physics. Source
47. Proclus built on Euclid (c.450): Wrote the Commentary on Euclid, Book I. Source
48. Proclus built on Hipparchus (c.450): Hypotyposis re-proves results first given by Hipparchus. Source
49. Proclus built on Ptolemy (c.450): Hypotyposis introduces Ptolemy's astronomy and re-proves its results. Source
50. Proclus built on Pappus (c.450): His Euclid commentary cites Pappus's commentary three times. Source
51. Brahmagupta built on al-Khwarizmi (c.825): Sindhind zij tables derived from Brahmasphutasiddhanta. Source
52. al-Khwarizmi built on Ptolemy (c.830): Geography book based on Ptolemy's Geography, corrected its maps. Source
53. Thabit built on Pythagoras (c.870): Generalised Pythagoras's theorem to arbitrary triangles. Source
54. Thabit built on Euclid (c.870): Revised Hunayn's Elements translation; basis of later Arabic versions. Source
55. Thabit built on Archimedes (c.870): Translated Archimedes; commentary on Liber Assumptorum; heptagon construction. Source
56. Thabit built on Ptolemy (c.870): Revised Almagest translation, translated Geography, studied Planetary Hypotheses. Source
57. Thabit built on Nicomachus (c.870): Amicable-number rule extends Euclid/Nicomachus on perfect numbers. Source
58. Mahavira built on Brahmagupta (850): Ganita Sara Samgraha written as updating of Brahmagupta's book. Source
59. Bhaskara built on Brahmagupta (c.1150): Extended Brahmagupta's number work; corrected division by zero. Source
60. Fibonacci built on Euclid (c.1220): Commentary on Elements Book X; Practica geometriae based on Elements. Source
61. Fibonacci built on al-Khwarizmi (1202): Liber abaci borrows 22 problems from al-Khwarizmi's algebra. Source
62. al-Banna built on Euclid (c.1300): Wrote an introduction to Euclid's Elements. Source
63. Pacioli built on Euclid (1509): Published a Latin translation of Euclid's Elements. Source
64. Pacioli built on Fibonacci (1494): Summa borrowed freely from Fibonacci and acknowledged him. Source
65. Pacioli taught da Vinci (1496–1506): Taught Leonardo maths in Milan; Leonardo illustrated Divina proportione. Source
66. Dürer built on Archimedes (1525): Underweysung shows how to construct the spiral of Archimedes. Source
67. Dürer met or wrote to Pacioli (1506): Dürer went to Bologna to meet Pacioli about proportion. Source
68. Stifel built on Euclid (1544): Arithmetica integra Book II treats Euclid's theory of irrationals. Source
69. Stifel built on Cardano (1544): Solved cubics/quartics with Cardano's methods, reworked his notation. Source
70. Tartaglia built on Euclid (1543): First Italian translation and edition of Euclid's Elements. Source
71. Tartaglia built on Archimedes (1543): Published Latin edition of Archimedes' works. Source
72. Tartaglia clashed with Pacioli (c.1556): Criticised Pacioli's solution to the problem of points. Source
73. Cardano clashed with Tartaglia (1539–1548): Cardano published Tartaglia's cubic solution despite oath; bitter feud. Source
74. Cardano taught Ferrari (1536–1545): Took secretary Ferrari on and taught him mathematics. Source
75. Recorde built on Euclid (1551): Pathwaie to Knowledge, an abridged version of the Elements. Source
76. Recorde built on Ptolemy (1556): Castle of Knowledge introduces Ptolemy's astronomy. Source
77. Ferrari clashed with Tartaglia (1547–1548): Cartelli challenges, then public Milan contest won by Ferrari. Source
78. Viète built on Archimedes (1593): Found π using Archimedes' method on a 393,216-sided polygon. Source
79. Viète built on Ptolemy (c.1580s): Manuscripts on the geometry of Ptolemy's planetary theories. Source
80. Viète built on Diophantus (1593): Zetetica re-solved Diophantus's problems with his analytic art. Source
81. Viète built on Cardano (c.1590): Based his algebra on Cardano and other Italians. Source
82. van Ceulen built on Archimedes (1596–1610): Extended Archimedes' polygon method to compute π digits. Source
83. van Ceulen met or wrote to Stevin (1600): Close friends; Stevin set up Leiden engineering school. Source
84. Stevin built on Euclid (1583): Problemata geometrica based largely on Euclid and Archimedes. Source
85. Stevin built on Archimedes (1586): Hydrostatics treatise improved Archimedes' work. Source
86. Stevin built on Dürer (1583): Problemata geometrica problems show Dürer's influence. Source
87. Napier built on Stevin (1614–1619): Took up Stevin's decimal fraction notation. Source
88. Napier met or wrote to Briggs (1615–1616): Briggs visited Napier twice; agreed on base-10 logarithms. Source
89. Cataldi built on Euclid (c.1620): Cataldi published an edition of Euclid's Elements. Source
90. Cataldi built on Heron (1613): Square-root continued fractions made Heron's ideas precise. Source
91. Cataldi built on van Ceulen (c.1613): Used van Ceulen's π digits for rational approximations. Source
92. Briggs built on Euclid (1620): Published edition of first six books of Elements. Source
93. Kepler built on Euclid (1596–1619): Five regular solids of Elements XIII; logarithm proof from Book 5. Source
94. Kepler built on Archimedes (1615): Nova stereometria extended Archimedes' volume methods using indivisibles. Source
95. Kepler built on Ptolemy (1619): Harmonices Mundi deliberately parallels Ptolemy's Harmonica. Source
96. Kepler built on Napier (1616–1627): Proved Napier's logarithms valid and computed log tables for Rudolphine Tables. Source
97. Oughtred built on Viète (1631): Clavis symbolic algebra drew on Viète without saying so. Source
98. Oughtred met or wrote to Briggs (1618): Visited "honoured friend" Briggs at Gresham College. Source
99. Bachet built on Diophantus (1621): Latin translation/edition of Diophantus's Arithmetica. Source
100. Mersenne built on Euclid (1644): Edited works of Euclid. Source
101. Mersenne built on Archimedes (1644): Edited works of Archimedes. Source
102. Mersenne met or wrote to Desargues (1630s): Desargues part of Mersenne's Paris circle. Source
103. Mersenne met or wrote to Descartes (1623–1648): Lifelong contact; Descartes' link to scientific world. Source
104. Mersenne met or wrote to Fermat (1636–1648): Mersenne wrote to Fermat; regular correspondent. Source
105. Mersenne met or wrote to Pascal (1637–1648): Pascal attended Mersenne's meetings from age 14. Source
106. Mersenne met or wrote to Huygens (c.1646–1648): Corresponded and encouraged young Huygens; never met in person. Source
107. Girard built on Diophantus (1625): Translated Arithmetica Books 5–6 into French. Source
108. Girard built on Fibonacci (1634): First to state the Fibonacci recurrence f(n+2)=f(n+1)+f(n). Source
109. Girard built on Viète (1629): Generalised Viète's root–coefficient formulas to all roots. Source
110. Girard built on Stevin (1625–1634): Edited and annotated Stevin's Arithmétique and collected works. Source
111. Desargues met or wrote to Pascal (1639–1640): Pascal admired Desargues; mystic hexagon in Desargues' projective style. Source
112. Descartes built on Pappus (1637): La Géométrie built around solving Pappus' locus problem. Source
113. Descartes built on Viète (1637): La Géométrie built on Viète's algebra, though Descartes denied reading it. Source
114. Descartes met or wrote to Desargues (c.1626): Descartes met Desargues in Paris; later asked him to referee. Source
115. Descartes clashed with Fermat (1637–1638): Bitter dispute over tangents, maxima and Dioptrique. Source
116. Descartes met or wrote to Pascal (1647): Descartes visited Pascal; argued about the vacuum. Source
117. Descartes met or wrote to Huygens (1630s–1640s): Visited Huygens home and took interest in young Christiaan. Source
118. Fermat built on Archimedes (1630s): Generalised Archimedes' On Spirals to compute areas. Source
119. Fermat built on Diophantus (c.1637): Number-theory claims annotated on Diophantus's Arithmetica problems. Source
120. Fermat built on Viète (1630s): Extended Viète's analysis and kept Viète's notation. Source
121. Fermat built on Cataldi (c.1640): Factored 2^23−1 and 2^37−1, refuting Cataldi's conjecture. Source
122. Fermat built on Bachet (c.1637): Last Theorem note written in margin of Bachet's Diophantus. Source
123. Fermat met or wrote to Brouncker (1657–1658): Brouncker solved Fermat's challenge nx²+1=y² in letters. Source
124. Fermat met or wrote to Pascal (1654): Letters founding probability theory. Source
125. Fermat met or wrote to Huygens (1656): Correspondence starting on probability, then number theory. Source
126. Brouncker built on Mersenne (1653): Notes proposed a variant of Mersenne's equal-temperament scale. Source
127. Brouncker built on Descartes (1653): Translated Descartes' Musicae Compendium with own notes. Source
128. Pascal built on Pacioli (1654): Solved the problem of points first posed in Pacioli's Summa. Source
129. Huygens built on Archimedes (1654): Preferred Archimedes' methods; Mersenne called him "new Archimedes". Source
130. Huygens met or wrote to Desargues (1655): Met Desargues at Paris scientific societies. Source
131. Huygens met or wrote to Pascal (1655–1660): Met in Paris; Huygens' cycloid work answered Pascal's challenge. Source
132. Huygens clashed with Newton (1672–1673): Huygens criticised Newton's particle theory of light and colour. Source
133. Huygens taught Leibniz (1672–1676): Leibniz studied mathematics and physics under Huygens in Paris. Source
134. Newton built on Viète (1664): Studied Viète's algebra in van Schooten's 1646 edition. Source
135. Newton built on Kepler (1666–1687): Derived inverse-square law from Kepler's third law. Source
136. Newton built on Descartes (1664–1687): Studied La Géométrie; Principia refuted Cartesian vortex theory. Source
137. Newton met or wrote to Brouncker (1669–1672): Collins showed Royal Society president Brouncker Newton's results. Source
138. Newton clashed with Leibniz (1699–1716): Calculus priority dispute. Source
139. Newton met or wrote to Stirling (1717–1727): Friends; Newton helped him and proposed him for FRS. Source
140. Leibniz clashed with Descartes (1686): Leibniz attacked Descartes' mechanics (conservation of motion). Source
141. Leibniz built on Pascal (1675–1676): Made notes from Pascal's lost conics manuscript; studied Pascal's works. Source
142. Leibniz met or wrote to J. Bernoulli (1693–1716): Extensive correspondence, e.g. logarithms of negative numbers. Source
143. J. Bernoulli clashed with Newton (1713): Bernoulli strongly backed Leibniz in calculus dispute. Source
144. J. Bernoulli met or wrote to N. Bernoulli (1713): Uncle and nephew; Nicolaus brought him the Commercium epistolicum. Source
145. J. Bernoulli taught Euler (1720s): Gave young Euler private Saturday tuition in Basel. Source
146. Machin built on Kepler (1738): Published "The solution of Kepler's problem". Source
147. Machin met or wrote to Newton (1712): Sat on Royal Society priority committee for Newton. Source
148. Machin clashed with Leibniz (1712): Committee member who ruled against Leibniz. Source
149. N. Bernoulli clashed with Newton (1712–1716): Backed Leibniz; exposed Newton's errors with higher derivatives. Source
150. N. Bernoulli met or wrote to Leibniz (1712–1716): Correspondence; included sum of reciprocal squares. Source
151. N. Bernoulli met or wrote to Euler (1742–1743): Letters criticising Euler's use of divergent series. Source
152. Goldbach met or wrote to Leibniz (1711–1713): Met in Leipzig, then exchanged letters. Source
153. Goldbach met or wrote to N. Bernoulli (1712): Met in Oxford; Bernoulli introduced him to infinite series. Source
154. Goldbach met or wrote to Euler (1729–1764): Famous correspondence; Goldbach conjecture in 1742 letter. Source
155. Stirling built on Brouncker (1730): Accelerated convergence of series Brouncker had studied. Source
156. Stirling met or wrote to Machin (1738): Machin wrote to Stirling on figure of the Earth. Source
157. Stirling met or wrote to N. Bernoulli (1717–1722): Friends at Venice/Padua; Stirling offered to be go-between with Newton. Source
158. Euler built on Euclid (1747): Proved converse of Euclid's perfect-number rule (Euclid–Euler theorem). Source
159. Euler built on Cataldi (1732–1738): Found next perfect number; disproved Cataldi's 2^29−1 claim. Source
160. Euler built on Fermat (1732–1760s): Disproved Fermat-number conjecture; proved little theorem, phi function. Source
161. Euler built on Brouncker (1730s–1760s): Built on Brouncker's Pell-equation solution but credited it to Pell. Source
162. Euler met or wrote to Stirling (1736–1738): Letters on series, harmonic series and Euler's constant. Source
163. Euler met or wrote to Lambert (1760–1766): Euler recommended Lambert; Berlin Academy colleagues. Source
164. Buffon built on Newton (1740): Translated Newton's Method of Fluxions into French. Source
165. Lambert built on Euclid (1766): Theory of parallel lines examined Euclid's fifth postulate. Source
166. Lambert met or wrote to Lagrange (1766–1777): Close friends at Berlin Academy. Source
167. Lagrange built on Diophantus (1770): Proved four-square theorem that Diophantus appears to have assumed. Source
168. Lagrange built on Bachet (1770): Proved four-square theorem, also called Bachet's conjecture. Source
169. Lagrange built on Fermat (1770): Proved four-square case of Fermat's polygonal number theorem. Source
170. Lagrange built on Brouncker (1766–1769): Proved the Brouncker–Wallis algorithm for Pell's equation always terminates. Source
171. Lagrange met or wrote to Euler (1754–1783): Sent tautochrone/variations results to Euler; long correspondence. Source
172. Lagrange built on Wilson (1771): Gave first proof of Wilson's theorem. Source
173. Laplace built on Newton (1799–1825): Mécanique céleste extended Newtonian gravitational theory. Source
174. Laplace built on Buffon (1812): Théorie analytique treats Buffon's needle problem. Source
175. Laplace met or wrote to Lagrange (1782–1813): Corresponded; colleagues at Académie and Bureau des Longitudes. Source
176. Laplace clashed with Legendre (1780s): Controversy over attraction of ellipsoids. Source
177. Legendre built on Euclid (1794): Éléments de géométrie reworked Euclid's Elements. Source
178. Legendre built on Fermat (1823–1825): Proof of Fermat's Last Theorem for n=5. Source
179. Legendre built on Euler (1785–1798): Quadratic reciprocity from Euler; named "Eulerian integrals". Source
180. Legendre built on Lambert (1794): Supplied result completing Lambert's irrationality of π proof. Source
181. Legendre built on Lagrange (1788): Proof-read and edited Lagrange's Mécanique analytique. Source
182. Ruffini built on Lagrange (1799): Quintic insolubility proof built on Lagrange's Réflexions; sent him book. Source
183. Ruffini clashed with Laplace (early 1800s): Wrote a work arguing against Laplace's philosophical ideas. Source
184. Ruffini met or wrote to Legendre (c.1800): Legendre on Institute committee examining Ruffini's proof. Source
185. Argand met or wrote to Legendre (1806): Argand showed Legendre his complex-plane essay. Source
186. Gauss built on Euclid (1796): Heptadecagon construction extended Euclid's ruler-and-compass constructions. Source
187. Gauss built on Fermat (1796): Proved triangular case of Fermat polygonal number theorem. Source
188. Gauss built on Euler (1796–1801): First proof of quadratic reciprocity, conjectured by Euler. Source
189. Gauss met or wrote to Lagrange (1804): Lagrange wrote praising Gauss's Disquisitiones Arithmeticae. Source
190. Gauss built on Wilson (1801): Generalized Wilson's theorem in Disquisitiones. Source
191. Gauss clashed with Legendre (1801–1820): Priority disputes: least squares, quadratic reciprocity, prime distribution. Source
192. Gauss taught Möbius (1813): Möbius studied astronomy under Gauss at Göttingen. Source
193. Gauss taught Riemann (1846–1854): Lectured him, supervised 1851 thesis, chose Habilitation lecture. Source
194. Brianchon built on Pascal (1806): Rediscovered Pascal's hexagon and proved its dual. Source
195. Binet built on Fibonacci (1843): Binet's closed formula for the Fibonacci numbers. Source
196. Binet built on Euler (1839): Memoir on Euler's integrals (beta/gamma functions). Source
197. Binet built on Lagrange (1816): Edited new edition of Lagrange's Mécanique analytique. Source
198. Babbage met or wrote to Laplace (1819): Laplace recommended Babbage for Edinburgh chair. Source
199. Babbage met or wrote to De Morgan (1830s–1860s): Corresponded; De Morgan tutored Babbage's collaborator Lovelace. Source
200. Lamé built on Euclid (1844): Bounded the number of steps in the Euclidean algorithm. Source
201. Lamé built on Fermat (1839): Proved Fermat's Last Theorem for n=7. Source
202. Lamé built on Laplace (1830s): Solved Laplace's equation in ellipsoidal coordinates. Source
203. Lamé built on Binet (1838): Followed up Binet's polygon-dissection problem. Source
204. Lamé taught Catalan (1833–1835): Catalan attended Lamé's courses at École Polytechnique. Source
205. Steiner built on Euclid (1833): Poncelet–Steiner theorem: Euclidean constructions with one circle. Source
206. Steiner built on Pascal (1828): Pascal lines meet three at a time at Steiner points. Source
207. Steiner taught Riemann (1847–1849): Riemann studied under Steiner at Berlin. Source
208. Liouville built on Goldbach (1840s): Inspired by reading Goldbach–Daniel Bernoulli correspondence. Source
209. Liouville met or wrote to Binet (1838): Liouville encouraged Binet's polygon-dissection paper for his Journal. Source
210. Liouville clashed with Lamé (1847): Liouville refuted Lamé's claimed Fermat proof (unique factorization). Source
211. Liouville taught Catalan (1833–1841): Taught at Polytechnique; Liouville advised and supported his career. Source
212. Liouville taught Hermite (1840s): Hermite attended Liouville's lectures; Liouville his academic advisor. Source
213. Shanks built on Machin (1853–1873): Computed π using Machin's arctangent formula. Source
214. Shanks built on Euler (1860s): Calculated Euler's constant γ to many places. Source
215. Catalan built on Euler (1838): Catalan numbers extend Euler's 1751 polygon-triangulation count. Source
216. Catalan built on Laplace (1888): Paper on Laplace's application of Bayes' theorem. Source
217. Catalan built on Binet (1838): Extended Binet's polygon-triangulation work (Catalan numbers). Source
218. Catalan taught Hermite (1841–1842): Tutored Hermite for Polytechnique entrance exam. Source
219. Hermite clashed with Cantor (1880s–1890s): Hermite disliked and opposed Cantor's set-theoretic world. Source
220. Hermite met or wrote to Hilbert (1886): Hilbert visited Hermite's home twice in Paris. Source
221. Riemann built on Euler (1859): Extended Euler's zeta function to complex variable. Source
222. Venn built on Euler (1880): Venn diagrams refine Euler's 1768 logic circles. Source
223. Venn built on De Morgan (1860s–1881): Studied and developed De Morgan's logic treatises. Source
224. Lucas built on Fibonacci (1870s): Studied Fibonacci sequence; Lucas numbers/sequences. Source
225. Lucas built on Mersenne (1876): Proved Mersenne number 2^127−1 prime. Source
226. Cantor built on Goldbach (1894): Verified Goldbach's conjecture up to 1000. Source
227. Cantor built on Liouville (1874): Gave new proof of Liouville's transcendental-number existence. Source
228. Cantor built on Riemann (1869–1872): Solved trigonometric-series uniqueness problem Riemann had attacked. Source
229. Cantor met or wrote to Hilbert (1896–1900s): Wrote Hilbert about paradoxes; Hilbert defended his set theory. Source
230. Lindemann built on Lambert (1882): Settled question Lambert's 1761 irrationality proof left open. Source
231. Lindemann met or wrote to Hermite (c.1877–1882): Visited Hermite in Paris to discuss transcendence methods. Source
232. Lindemann taught Hilbert (1883–1885): Doctoral advisor of Hilbert at Königsberg. Source
233. Hilbert built on Euclid (1899): Grundlagen der Geometrie axiomatized Euclidean geometry. Source
234. Hilbert built on Riemann (1901): Rigorously repaired Dirichlet principle underlying Riemann's proofs. Source
235. D. N. Lehmer built on Eratosthenes (1909): Factor tables continue work started by Eratosthenes' sieve. Source
236. Hardy built on Goldbach (1923–1924): Hardy–Littlewood results and conjectures on Goldbach's conjecture. Source
237. Hardy built on Riemann (1914): Proved infinitely many zeta zeros on critical line. Source
238. Hardy built on Hilbert (1920s): Hardy–Littlewood refined Hilbert's solution of Waring's problem. Source
239. Hardy met or wrote to Ramanujan (1913–1919): Letters from 1913; collaborated at Trinity College, Cambridge. SourceReferences
Wells, D. (1987) The Penguin dictionary of curious and interesting numbers. Reprinted with revisions. London: Penguin Books, pp. 9–11.
mathematics
Mathematics History of Mathematics
This post is licensed under CC BY 4.0 by the author.
Share
