From Ahmes to Ramanujan: A Timeline of Mathematicians

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
3. 1500 BC
8. 1000 BC
12. 1
13. 4500 BC
14. 7
15. 4
16. 2
18. 3AD 1
19. 4
20. 1
21. 3
22. 2
23. 1500
24. 1
26. 3
27. 1
28. 1000
29. 2
30. 2
31. 2
32. 4
33. 211500
34. 24
35. 25
36. 27
37. 81900

Mathematicians in the list alive in each century, 1700 BC to AD 1999.

Lifelines

Turn on JavaScript to explore the lifelines; the table below lists every one.

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 everyone Pythagoras (2) Hippocrates (5) Plato (10) Hippias (3) Theaetetus (4) Archytas (4) Xenocrates (2) Theodorus (2) Aristotle (5) Menaechmus (2) Euclid (27) Archimedes (15) Nicomedes (3) Eratosthenes (10) Diocles (1) Hipparchus (3) Heron (4) Ptolemy (11) Nicomachus (3) Theon (3) Diophantus (5) Pappus (11) Iamblichus (2) Proclus (7) Brahmagupta (3) al-Khwarizmi (3) Thabit (5) Mahavira (1) Bhaskara (1) Fibonacci (6) al-Banna (1) Pacioli (6) da Vinci (1) Dürer (3) Stifel (2) Tartaglia (5) Cardano (4) Recorde (2) Ferrari (2) Viète (9) van Ceulen (3) Stevin (6) Napier (3) Cataldi (5) Briggs (3) Kepler (6) Oughtred (2) Bachet (3) Mersenne (9) Girard (4) Desargues (4) Descartes (10) Fermat (15) Brouncker (7) Pascal (9) Huygens (8) Newton (12) Leibniz (8) J. Bernoulli (4) Machin (5) N. Bernoulli (6) Goldbach (6) Stirling (5) Euler (17) Buffon (2) Lambert (5) Lagrange (12) Wilson (2) Laplace (8) Legendre (9) Ruffini (3) Argand (1) Gauss (8) Brianchon (1) Binet (6) Möbius (1) Babbage (2) Lamé (6) Steiner (3) De Morgan (2) Liouville (6) Shanks (2) Catalan (6) Hermite (5) Riemann (6) Venn (2) Lucas (2) Cantor (5) Lindemann (3) Hilbert (6) D. N. Lehmer (1) Hardy (4) Ramanujan (1)

• 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. Source

References

Wells, D. (1987) The Penguin dictionary of curious and interesting numbers. Reprinted with revisions. London: Penguin Books, pp. 9–11.