Academic lineage
Kragen Javier Sitaker, 2016-10-30 (updated 2019-05-31) (13 minutes)
I spent some time tracing academic lineages, helped by the Mathematics
Genealogy Project. It traces 132,301 mathematicians, 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. One path from al-Bukhārī to Gauss
through 22 generations is as follows:
- Shams ad-Din al-Bukhari
- Gregory Chioniadis
- Manuel Bryennios (aka Μανουήλ Βρυέννιος, Constantinople)
- Theodore Metochites (aka Θεόδωρος Μετοχίτης, 1315, Constantinople)
- Gregory Palamas (aka Γρηγόριος Παλαμάς, born in Constantinople and
archbishop of Thessaloniki)
- Nilos Kabasilas (aka Νεῖλος Καβάσιλας, 1363)
- Demetrios Kydones (aka Δημήτριος Κυδώνης, Thessalonica, three-term
Mesazon of Byzantium)
- Georgios Plethon Gemistos (1380, Nómoi)
- Basilios Bessarion (1436)
- Johannes Argyropoulos (Padova, 1444)
- Johannes Kapnion Reuchlin (Basel, 1477)
- Philipp Melanchthon (Heidelberg, 1511)
- Johannes Caselius (Halle-Wittenberg, 1560; Leipzig, 1566)
- Georg Calixt (Helmstedt, 1607)
- Johann Andreas Quenstedt (Helmstedt, 1643, De Transsvbstantiatione
Contra Pontificios Exercitatio)
- Michael Walther, Jr (Halle-Wittenberg, 1661, Manichaeismi recensio
historica; Disputatio theologica inauguralis de Paulina Petri
increpatione)
- Johann Pasch (Halle-Wittenberg, 1683, Conjunctiones in genere
dissertatione astronomico-theorica)
- Johann Andreas Planer (Halle-Wittenberg, 1686, Gynaeceum Doctum,
sive Dissertatio Historico-literaria)
- Christian August Hausen (Halle-Wittenberg, 1713, De corpore
scissuris figurisque non cruetando ductu)
- Abraham Gotthelf Kästner (Leipzig, 1739, Theoria radicum in
aequationibus)
- Johann Friedrich Pfaff (Göttingen, 1786, Commentatio de ortibus et
occasibus siderum apud auctores classicos commemoratis)
- Carl Friedrich Gauß (Helmstedt, 1799, Demonstratio nova theorematis
omnem functionem algebraicam rationalem integram unius variabilis in
factores reales primi vel secundi gradus resolvi posse)
There’s also a path to Euler that diverges in the 14th century via
Erasmus from Kydones:
- Kydones
- Manuel Chrysoloras
- Guarino da Verona (1408)
- Vittorino da Feltre (Padova, 1416)
- Theodoros Gazes (Mantova and Constantinople, 1433)
- Rudolf Agricola (Ferrara, 1478)
- Alexander Hegius (1474)
- Desiderius Erasmus (Montaigu, 1497/1506; Turin, 1506)
- Wolfgang Fabricius Capito (Freiburg im Breisgau, 1515)
- Simon Sulzer (Strasbourg, 1531)
- Johann Jacob Grynaeus (Basel, 1559)
- Sebastian Beck (Basel, 1610, Illustre Axioma, Ivstvs Avtem Fide Sva
Vivet)
- Theodor Zwinger, Jr. (Basel, 1630, De Illustri Sententia Apostolica
Hebr. c. 13. V. 8)
- Peter Werenfels (Basel, 1649, Diatribe In Psalmum S. S. Psalterii
Primum. De Vnica Et Vera Hominis Felicitate)
- Jacob Bernoulli (Basel, 1676, Primi et Secundi Adami Collatio)
- Johann Bernoulli (Basel, 1690, Dissertatio de effervescentia et
fermentatione; Basel, 1694, Dissertatio Inauguralis
Physico-Anatomica de Motu Musculorum)
- Leonhard Euler (Basel, 1726, Dissertatio physica de sono)
Nearly all modern mathematicians can trace their lineage to both Gauss
and 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:
- Erasmus, as above for Euler;
- Jakob Milich (Freiburg im Breisgau, 1520, later Wien, 1524)
- Erasmus Reinhold (Halle-Wittenberg, 1535)
- Valentine Naibod (Halle-Wittenberg and Erfurt)
- Rudolph (Snel van Royen) Snellius (Heidelberg and Köln, 1572)
- Willebrord (Snel van Royen) Snellius (Leiden, 1607)
- Jacobus Golius (Leiden, 1621), advisor of Descartes
- Frans van Schooten, Jr. (Leiden, 1635), also student of Mersenne
- Christiaan Huygens (Leiden, 1647)
- Gottfried Wilhelm Leibniz (Leipzig, 1666, Disputatio arithmetica de
complexionibus), from whom most living mathematicians descend via
his other student Nicolas Malebranche
- Christian M. von Wolff (Leipzig, 1703, Philosophia practica
universalis, methodo mathematica conscripta)
- Martin Knutzen (Königsberg, 1732)
- Immanuel Kant (Königsberg, 1770, Meditationum quarundam de igne
succincta delineatio; Principiorum primorum cognitionis metaphysicae
nova dilucidatio)
- Karl Reinhold (Jena, 1787, Briefe über die Kantische Philosophie)
- Friedrich Adolf Trendelenburg (Berlin, 1826, Platonis de ideis et
numeris doctrina ex Aristotele illustrata)
- Franz Clemens Brentano (Tübingen, 1862, Von der mannigfachen
Bedeutung des Seienden nach Aristoteles)
- Kazimierz Twardowski (Wien, 1891/1892, Idee und Perzeption (“Idea
and Perception”)—An Epistemological Investigation of Descartes) who
also advised Banach
- Stanislaw Lesniewski (Lwów, 1912, A Contribution To Analysis Of
Existential Propositions)
- Alfred Tarski (Warsaw, 1924, O wyrazie pierwotnym logistyki)
This puts Tarski only about 32 generations from al-Bukhārī.
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:
- Bessarion, as in Gauß’s genealogy;
- Johannes Müller Regiomontanus (Leipzig and Wien, 1457)
- Domenico Maria Novara da Ferrara (Firenze, 1483) who also studied
under Pacioli
- Nicolaus (Mikołaj Kopernik) Copernicus (Padova and Ferrara, 1499)
- Georg Joachim von Leuchen Rheticus (Halle-Wittenberg, 1535)
- Moritz Valentin Steinmetz (Leipzig, 1567, De Peste Capita
Disputationis Ordinariae)
- Christoph Meurer (Leipzig, 1582, De Iride seu Arcu coelesti)
- Philipp Müller (Leipzig, 1604)
- Erhard Weigel (Leipzig, 1650, De ascensionibus et descensionibus
astronomicis dissertatio)
- Leibniz.
We are some 34 generations from al-Bukhārī today
Consider a modern scholar I’ve met here at the University of Buenos
Aires, Sandra Martínez, who descends from both Hilbert and
Sierpiński, and is thus 34 generations from al-Bukhārī:
- Sierpiński, with 5329 descendants (Jagiellonian)
- Stefan Mazurkiewicz (Lwów, same as Lesniewski above)
- Aleksander Michał Rajchman (Warsaw, 1921) (also a student of Hugo Dyonizy Steinhaus; see below)
- Antoni Zygmund (Warsaw, 1923; also directly a student of Mazurkiewicz)
- Eugene Barry Fabes (Chicago, 1965)
- Julio Esteban Bouillet, with 19 descendants (U Minn, 1972)
- Noemí Irene Wolanski (UBA, 1983)
- Sandra Rita Martínez (UBA, 2007)
Rajchman is the link to Hilbert, and thence to Klein and thus Gauß and
Euler:
- Gauß
- Christian Ludwig Gerling (Göttingen, 1812)
- Julius Plücker (Marburg, 1823)
- Klein (Bonn, 1868)
- Carl Louis Ferdinand Lindemann (Erlangen–Nürnberg 1873)
- Hilbert, with 2606 descendants (Königsberg, 1885)
- Hugo Dyonizy Steinhaus (Göttingen, 1911)
The rather weak path from Euler to Klein:
- Euler
- Lagrange (no degree from Euler, and Euler didn’t teach him in
person, but in their correspondence they invented the variational
calculus, and then Euler got him his position directing mathematics
at the Prussian Academy of Sciences and at Frederick’s court; he
actually studied at Turin)
- Fourier
- Dirichlet (Bonn, 1827)
- Rudolf Otto Sigismund Lipschitz, the Lipschitz continuity guy;
61,331 descendants (Berlin, 1853)
- Klein (Lipschitz’s only known student)
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:
- Socrates, in some sense, who died in 399 BCE
- Plato (from circa 387 BCE until his death in 348 or 347 BCE)
- Speusippus (347–339 BCE)
- Xenocrates (339–314 BCE)
- Polemo (314–269 BCE)
- Crates (circa 269–266 BCE)
- Arciselaus (circa 266–241 BCE)
- Lacydes of Cyrene (241–215 BCE)
- Evander and Telecles, jointly (215–circa 165 BCE)
- Hegesinus (circa 160 BCE)
- Carneades (circa 155 BCE)
- Clitomachus (129–circa 110 BCE)
- Philo of Larissa (circa 110–84 BCE)
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:
- Bodaidaruma (Bodhidharma, d. 532)
- Taiso Eka (Dazu Huike / Ta-tsu Hui-k’o, 487-593)
- Kanchi Sosan (Jianzhi Sengcan / Chien-chih Seng-ts’an, d. 606)
- Daii Doshin (Dayi Daoxin / Ta-i Tao-hsin, 580-651)
- Daiman Konin (Daman Hongren / Ta-man Hung-jen, 601-74)
- Daikan Eno (Dajian Huineng / Ta-chien Hui-neng, 638-713)
- Seigen Gyoshi (Qingyuan Xingsi / Ch’ing-yuan Hsing-ssu, 660-740)
- Sekito Kisen (Shitou Xiquian / Shih-t’ou Hsi-ch’ien, 700-90)
- Yakusan Igen (Yaoshan Weiyan / Yao-shan Wei-yen, 751-834)
- Ungan Donjo (Yunyan Tansheng / Yun-yen T’an-sheng, 780-841)
- Tozan Ryokai (Dongshan Liangjie / Tung-shan Liang-chieh, 807-69)
- Ungo Doyo (Yunju Daoying / Yun-chu Tao-ying, d. 902)
- Doan Dohi (Tongan Daopi / T’ung-an Tao-p’i, ???)
- Doan Kanshi (Tongan Guanzhi / T’ung-an Kuan-chih, ???)
- Ryozan Enkan (Liangshan Yuanguan / Liang-shan Yuan-kuan, ???)
- Taiyo Kyogen (Dayang Qingxuan / Ta-yang Ching-hsuan, d. 1027)
- Toshi Gisei (Touzi Yiqing / T’ou-tzu I’ch’ing, 1032-83)
- Fuyo Dokai (Furong Daokai / Fu-jung Tao-k’ai, 1043-1118)
- Tanka Shijun (Danxia Zichun / Tan-hsia Tzu-ch’un, d. 1119)
- Choro Seiryo (Zhenxie Qingliao / Chen-hsieh Ch’ing-liao, 1089-1151)
- Tendo Sokaku (Tiantong Zongjue / T’ien-t’ung Tsung-chueh, ???)
- Setcho Chikan (Xuedou Zhijian / Hsueh-tou Chih-chien, 1105-92)
- Tendo Nyojo (Tiantong Rujing / T’ien-t’ung Ju-ching, 1163-1228)
- Eihei Dogen (1200-1253)
- Koun Ejo (1198-1280)
- Tettsu Gikai (1219-1309)
- Keizan Jokin (1264-1325)
- Gasan Joseki (1276-1366)
- Taigen Soshin (d. 1371)
- Baizan Monpon (d. 1417)
- Shingan Doku
- Senso Esai (d. 1475)
- Iyoku Choyu
- Mugai Keigon
- Nenshitsu Yokaku
- Sesso Hoseki
- Taiei Zesho
- Nampo Gentaku
- Zoden Yoko
- Ten’yu Soen
- Ken’an Junsa
- Chokoku Koen
- Senshu Donko
- Fuden Gentotsu
- Daishun Kan’yu
- Tenrin Kanshu
- Sessan Tetsuzen
- Fuzan Shunki
- Jissan Mokuin
- Sengan Bonryo
- Daiki Kyokan
- Eno Gikan
- Shoun Hozui
- Shizan Tokuchu
- Nanso Shinshu
- Kankai Tokuan
- Kosen Baido
- Gyakushitsu Sojun (187?– 1891)
- Butsumon Sogaku (1858-1933)
- Gyokujun So-on (1877-1934)
- 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.