Academic lineage

Kragen Javier Sitaker, 2016-10-30 (updated 2019-11-24) (15 minutes)

I spent some time tracing academic lineages, helped by the Mathematics Genealogy Project. It traces 132,301 mathematicians [2019-09-05 update: now 246,469], most of whom are still alive, back to a 13th-century astronomer named Shams ad-Din al-Bukhari or Shams al‐Dīn al‐Bukhārī, who enabled Gregory Chionades to obtain Greek translations of the astronomical handbooks in circulation in the Islamic world.

Mathematical lineages

From al-Bukhārī to Gauss

One path through 22 generations is as follows:

Euler’s lineage

There’s also a path to Euler that diverges in the 14th century via Erasmus from Kydones:

Nearly all modern mathematicians can trace their lineage to both Gauss and (weakly) Euler, and indeed a quarter of them can be traced back to Felix Klein, who can be traced back to both Euler (weakly) and Gauss.

Tarski descends from Kant and Huygens

For personal reasons, I’m particularly interested in Tarski’s lineage, which does trace back to al-Bukhārī, but not via Gauss or Euler; it is a very distinguished line that runs as follows:

This puts Tarski only 31 generations from al-Bukhārī via Kant.

Tarski and Leibniz from Pacioli and Bessarion via Copernicus

I’ve also found some other paths from Tarski back to al-Bukhārī, but most of the others aren’t nearly as spectacular. There’s an interesting side path, though:

This reduces Tarski to 26 generations from al-Bukhārī.

Sierpiński

Wacław Sierpiński is a particularly interesting node in the graph. He doesn’t descend from Gauss or, except via Lagrange, from Euler; but he has a significant number of descendants today (about as many as Euler, discounting Lagrange), and a very distinguished line of descent indeed, one which traces back to Gauss’s advisor Pfaff and to d’Alembert. The Pfaff line:

This includes Lobachevsky, who with Riemann revolutionized geometry; Chebyshev, the crippled Tatar who revolutionized probability and polynomial function approximation and who taught Lyapunov; Markov, who created our modern theory of discrete dynamic processes; and Voronoy, the sickly Ukrainian whose “Voronoi diagram” underlies an enormous number of modern geometrical algorithms, and who brought the world-shaking St. Petersburg tradition to Poland.

This gives a path from al-Bukhārī to Sierpiński over 30 generations.

But Voronoy was not Sierpiński’s only advisor, and Sierpiński’s other lineage is no less distinguished for originating sui generis in France and Italy without a known earlier academic line of descent:

We are some 34 generations from al-Bukhārī today

Consider a relatively arbitrary modern scholar, chosen not because she is world-famous but just because I’ve met her here at the University of Buenos Aires, Sandra Martínez, who descends from both Hilbert and Sierpiński, and is thus 34 generations from al-Bukhārī:

Rajchman is the link to Hilbert, and thence to Klein and thus Gauß and Euler:

This, plus the six generations above from Steinhaus, puts Martínez at 34 generations from al-Bukhārī.

The rather weak path from Euler to Klein:

Unfortunatly, Euler was less prolific at training students than he was at engendering children or writing papers; if we discount Lagrange, Euler has only 5835 descendants, mostly in the Netherlands, many alive today.

Scholarchs of Plato’s Academy

In ancient times, we can trace the sequence of scholarchs of Plato’s Academy for some 300 years, who presumably each were in some sense the academic advisor of their successor:

At this point, the Academy was destroyed by Sulla during his siege of Athens, and Antiochus of Ascalon began teaching Stoicism; Cicero studied under him in 79 and 78 BCE and diffused Greek philosophy to the Romans.

This gives us two pieces of the chain connecting us over 2400-odd years to Socrates: one about 280 or 290 years long at the beginning, and another about 800 years long at the end. There’s a 1320-year-long gap in the middle which runs through the Macedonian, Western Roman, Byzantine, and Muslim empires, which I don’t know much about.

Presumably Archimedes of Syracuse (circa 287–212 BCE: “δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω”, “Transire suum pectus mundoque potiri”) was aware of the Academy at Athens; I don’t know if he was taught by anyone from the Academy, but he may have studied at Alexandria with Eratosthenes, the third Chief Librarian, shortly after Euclid wrote there.

Going back further, Imhotep (“He who comes in peace”), who designed Djoser’s Step Pyramid 2000 years before (circa 2650–2600 BCE), presumably had teachers and students, but they are lost to history; the scribe Ahmes, who wrote the Rhind Papyrus around 1650 BCE, is similarly mysterious. Socrates might have been a follower of Pythagoras (circa 570–495 BCE) who was likely taught mathematics through a line related to that of Ahmes; he is reputed to have traveled to Egypt (and Babylonia, and Chaldea, and maybe India) seeking knowledge.

The Buddhist lineage of dharma transmission

There’s another similar academic lineage tradition: the transmission of the Buddha Dharma from one teacher to the next, which connects us personally with Siddhartha Gautama through an unbroken line of Buddhist monks. For example, Stephanie can traced Shunryu Suzuki’s dharma transmission lineage back to Bodhidharma, who brought Buddhism form India to China, as follows:

  1. Bodaidaruma (Bodhidharma, d. 532)
  2. Taiso Eka (Dazu Huike / Ta-tsu Hui-k’o, 487-593)
  3. Kanchi Sosan (Jianzhi Sengcan / Chien-chih Seng-ts’an, d. 606)
  4. Daii Doshin (Dayi Daoxin / Ta-i Tao-hsin, 580-651)
  5. Daiman Konin (Daman Hongren / Ta-man Hung-jen, 601-74)
  6. Daikan Eno (Dajian Huineng / Ta-chien Hui-neng, 638-713)
  7. Seigen Gyoshi (Qingyuan Xingsi / Ch’ing-yuan Hsing-ssu, 660-740)
  8. Sekito Kisen (Shitou Xiquian / Shih-t’ou Hsi-ch’ien, 700-90)
  9. Yakusan Igen (Yaoshan Weiyan / Yao-shan Wei-yen, 751-834)
  10. Ungan Donjo (Yunyan Tansheng / Yun-yen T’an-sheng, 780-841)
  11. Tozan Ryokai (Dongshan Liangjie / Tung-shan Liang-chieh, 807-69)
  12. Ungo Doyo (Yunju Daoying / Yun-chu Tao-ying, d. 902)
  13. Doan Dohi (Tongan Daopi / T’ung-an Tao-p’i, ???)
  14. Doan Kanshi (Tongan Guanzhi / T’ung-an Kuan-chih, ???)
  15. Ryozan Enkan (Liangshan Yuanguan / Liang-shan Yuan-kuan, ???)
  16. Taiyo Kyogen (Dayang Qingxuan / Ta-yang Ching-hsuan, d. 1027)
  17. Toshi Gisei (Touzi Yiqing / T’ou-tzu I’ch’ing, 1032-83)
  18. Fuyo Dokai (Furong Daokai / Fu-jung Tao-k’ai, 1043-1118)
  19. Tanka Shijun (Danxia Zichun / Tan-hsia Tzu-ch’un, d. 1119)
  20. Choro Seiryo (Zhenxie Qingliao / Chen-hsieh Ch’ing-liao, 1089-1151)
  21. Tendo Sokaku (Tiantong Zongjue / T’ien-t’ung Tsung-chueh, ???)
  22. Setcho Chikan (Xuedou Zhijian / Hsueh-tou Chih-chien, 1105-92)
  23. Tendo Nyojo (Tiantong Rujing / T’ien-t’ung Ju-ching, 1163-1228)
  24. Eihei Dogen (1200-1253)
  25. Koun Ejo (1198-1280)
  26. Tettsu Gikai (1219-1309)
  27. Keizan Jokin (1264-1325)
  28. Gasan Joseki (1276-1366)
  29. Taigen Soshin (d. 1371)
  30. Baizan Monpon (d. 1417)
  31. Shingan Doku
  32. Senso Esai (d. 1475)
  33. Iyoku Choyu
  34. Mugai Keigon
  35. Nenshitsu Yokaku
  36. Sesso Hoseki
  37. Taiei Zesho
  38. Nampo Gentaku
  39. Zoden Yoko
  40. Ten’yu Soen
  41. Ken’an Junsa
  42. Chokoku Koen
  43. Senshu Donko
  44. Fuden Gentotsu
  45. Daishun Kan’yu
  46. Tenrin Kanshu
  47. Sessan Tetsuzen
  48. Fuzan Shunki
  49. Jissan Mokuin
  50. Sengan Bonryo
  51. Daiki Kyokan
  52. Eno Gikan
  53. Shoun Hozui
  54. Shizan Tokuchu
  55. Nanso Shinshu
  56. Kankai Tokuan
  57. Kosen Baido
  58. Gyakushitsu Sojun (187?– 1891)
  59. Butsumon Sogaku (1858-1933)
  60. Gyokujun So-on (1877-1934)
  61. Shogaku Shunryu (Suzuki, 1904-1971)

Miscellaneous lineages

A third such academic lineage is the lineage of the rabbis.

Another is that descending from the Great Peacemaker of the Haudenosaunee, around 1200 CE, through Hiawatha, guardians of the Great Law of Peace, which was encoded on wampum belts and may have inspired the Western revival of democracy.

Topics