A Tentative
Academic Lineage
Erasmus  
 
Erasmus in 1523 as depicted by Hans Holbein the Younger 
 
Desiderius Erasmus of Rotterdam (1466/69-1536), Theologiae Baccalaureus / Divinitatis Doctor, Collège de Montaigu / University of Turin, 1497 /1506. A Dutch Renaissance humanist and Catholic theologian, he has been called "the crowning glory of the Christian humanists." He was a prolific author, and he prepared important new Latin and Greek editions of the New Testament.
Thesis advisor
Jakob Milich (1501-1559), Liberalium Artium Magister / Med. Dr., Albert-Ludwigs-Universität Freiburg im Breisgau / Universität Wien, 1520 / 1524. His other thesis advisor was Ulrich Zasius (1461-1536).
Thesis advisor
Erasmus Reinhold (1511-1553), Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1535.
Thesis advisor
Johannes Hommel, Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1543. His other thesis advisor was Philipp Melanchthon, the theologian and educator who was Martin Luther's "right hand man."
Thesis advisor
Valentin Thau, Magister artium, Universität Leipzig, 1555. Besides Wittich, another student of Thau was Tycho Brahe, and Johannes Kepler was a student of Brahe.
Thesis advisor
Paul Wittich, Magister artium, Universität Leipzig / Martin-Luther-Universität Halle-Wittenberg, 1566.
Thesis advisor
Duncan Liddel, Magister artium / Medicinae Dr., Universität Viadrina Frankfurt an der Oder / Universität Breslau / Universität Helmstedt, 1582 / 1596. His thesis was titled Themata De Melancholia. His other advisor was John Craig, whose academic ancestry can be traced back to Andreas Vesalius (1514-1564), who wrote De humani corporis fabrica (On the Workings of the Human Body) and who is considered the founder of modern human anatomy.
Thesis advisor
Cornelius Martini, Magister artium, Universität Helmstedt, 1592. His thesis was titled Disputatio de philosophia eiusque instrumentis.
Thesis advisor
Georg Calixt, Magister artium / Theol. Dr., Universität Helmstedt, 1607.
 
 
Copernicus in the early 1500s;
portrait from Toruń (Thorn)
 
Nicolaus Copernicus (1473-1543), Juris utriusque Doctor, Uniwersytet Jagielloński / Università di Bologna / Università degli Studi di Ferrara / Università di Padova, 1499. His academic pedigree can be traced back to Heinrich von Langenstein, Magis-
ter artium / Theol. Dr., Université de Paris, 1363 /1375. Copernicus was the first person to produce a scientifically-based heliocentric model of the solar system. His book De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) is generally considered to mark the beginning of modern astronomy and even the beginning of the Scientific Revolution.
Teacher, mentor, collaborator –› only student
Georg Joachim von Lauchen Rheticus* (1514-1574), Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1535. He facilitated the publication of Copernicus' De revolutionibus and popularized its concepts.
Mentor, collaborator
Valentin Otto (d. 1603), Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1570.
Thesis advisor
Melchior Jöstel, Magister artium / Medicinae Dr., Martin-Luther-Universität Halle-Wittenberg, 1583 / 1600. His other advisor besides Otto was Andreas Schato, an academic descendant of Copernicus (by a longer path than Otto) and also of Erasmus.
Thesis advisor
Ambrosius Rhodius, Magister artium / Medicinae Dr., Martin-Luther-Universität Halle-Wittenberg, 1600 / 1610. His other advisor besides Jöstel was Ernestus Hettenbach, an academic descendant of Copernicus (by a longer path than Jöstel) and also of Erasmus.
Thesis advisor
Christoph Notnagel, Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1630.
                Thesis advisors
 
Johann Andreas Quenstedt, Magister artium / Theol. Dr., Universität Helmstedt / Martin-Luther-Universität Halle-Wittenberg, 1643 / 1644. His theses were titled Disputatio astronomico-Geographica de Insperato Solis Exortu, qui Hollandis contigit in Nova Zembla anno 1597 and De Transsvbstantiatione Contra Pontificios Exercitatio.
Thesis advisor
Michael Walther, Jr., Magister artium / Theol. Dr., Martin-Luther-Universität Halle-Wittenberg, 1661 / 1687. His theses were titled Manichaeismi recensio historica and Disputatio theologica inauguralis de Paulina Petri increpatione.
Thesis advisor
Johann Pasch, Magister artium, Martin-Luther-Universität Halle-Wittenberg, 1683. His thesis was titled Conjunctiones in genere dissertatione astronomico-theorica.
Thesis advisor
Johann Andreas Planer, Magister artium / Medicinae Dr., Martin-Luther-Universität Halle-Wittenberg / Eberhard-Karls-Universität Tübingen, 1686 / 1709. His theses were titled Gynaeceum Doctum, sive Dissertatio Historico-literaria and Disputatio medica inauguralis, sistens aegrum dysentericum.
Dissertation advisor
Christian August Hausen, Dr. phil., Martin-Luther-Universität Halle-Wittenberg, 1713. His thesis was titled De corpore scissuris figurisque non cruetando ductu.
Dissertation advisor
Abraham Gotthelf Kästner (1719-1800), Ph.D., Universität Leipzig, 1739. His thesis was titled Theoria radicum in aequationibus.                         
Dissertation advisor
Johann Friedrich Pfaff (1765-1825), Dr. phil., Georg-August-Universität Göttingen, 1786. His thesis was titled Commentatio de ortibus et occasibus siderum apud auctores classicos commemoratis.
Dissertation advisor
Gauss 
Gauss, by Christian Albrecht Jensen
Johann Carl Friedrich Gauss* (1777-1855), Ph.D., Universität Helmstedt, 1799. His thesis was titled Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors [i.e., polynomials] of the first or second degree). Gauss contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He came to Göttingen in 1807 and remained there the rest of his life. In 1831 Wilhelm Eduard Weber* arrived at Göttingen as physics professor, and Gauss soon began his important collaboration with Weber. In addition to their theoretical advances, they built a primitive telegraph device which could send messages over a distance of 5000 ft.
Gauss' grave 
Gauss' grave at Albanifriedhof in Göttingen, Germany
Dissertation advisor
Gustav Karsten* (1820-1900), director of the Physics Institute at Christian-Albrechts-Universität Kiel.
 
Dissertation advisor
 
Georg Friedrich Bernhard Riemann* (1826-1866), Ph.D., Georg-August-Universität Göttingen, 1851. His thesis was titled Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen complexen Größe (Foundations for a general theory of functions of one complex variable). He was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity. He began his studies at Göttingen, then went to Berlin to study under Steiner, Jacobi, Dirichlet and Eisenstein. Returning to Göttingen to work on his Ph.D., he was Wilhelm Weber's assistant for 18 months. In 1854 Gauss selected the topic for Riemann's now famous habilitation lecture, Über die Hypothesen, welche der Geometrie zu Grunde Liegen (On the hypotheses that lie at the foundations of geometry). On the way home from Riemann's lecture, Weber reported that Gauss was full of praise and excitement.
 
"Revered teacher," probable dissertation advisor
 
Johann Friedrich Wilhelm von Bezold (1837-1907), Ph.D., Georg-August-Universität Göttingen, 1860. His thesis, titled Zur Theorie des Condensators (On the theory of condensers), is available online at http://books.google.com/books?id=1VRCAAAAYAAJ. (Condensers are today called capacitors.) At the end of his introduction (p. 6), von Bezold says, "Mit Freuden ergreife ich zugleich die mir hier dargebotene Gelegenheit, meinen hochverehrten Lehrern, dem Herrn Professor Riemann, der zuerst meine Aufmerksamkeit auf die hier noch offenen Fragen lenkte, und dem Herrn Professor Weber, der mir aufs Bereitwilligste die Räume und Instrumente des physikalischen Instituts für die Experimentaluntersuchungen zur Disposition stellte, öffentlich meinen innigsten Dank auszusprechen." There are no other similar acknowledgements in this thesis. Note that Wilhelm Weber's academic genealogy also can be traced back to Abraham Gotthelf Kästner, who appears above.
Major examiner of habilitation thesis
Franz Uri Boas* (1858-1942) received a Ph.D. in physics in 1881 under Karsten at Kiel. (He had wanted to write a dissertation on Gauss' law of the normal distribution of errors, but he instead reluctantly accepted his supervisor's choice of a research project involving the optical properties of water.) Later, having decided to apply for habilitation, he met with resistance from Heinrich Kiepert, geography professor at Humboldt-Universität Berlin, but found support from the university's new meteorologist, Wilhelm von Bezold. In 1886 he defended his habilitation thesis, Baffin-Land, and was named privatdozent in geography. Soon afterwards he spent some time in British Columbia and then decided to move to the United States. He taught anthropology for a while at Clark University and then had several museum posts. During this time he organized the Jesup North Pacific Expedition, a five-year long field-study of the natives of the Pacific Northwest. He began teaching at Columbia University in 1896, and in 1905 he negotiated with Columbia to create an anthropology department, which he would direct. Boas's program at Columbia became the first Ph.D. program in anthropology in America. He became “emeritus in residence” at Columbia in 1936 and “emeritus” in 1938.
Teacher –› post-doctoral student
Dissertation advisor
 
Alfred Marston Tozzer (1877–
1954) received a Ph.D. in 1904 from Harvard University, and he studied at Columbia University in fall 1904 under Franz Boas and Adolph Bandelier. He was appointed assistant professor of anthropology at Harvard in the fall of 1905 and spent most of his professional career there.
 
Dissertation advisor
 
 
Alfred Louis Kroeber (1876–1960) received a Ph.D. in 1901 from Columbia University. Kroeber spent most of his career in California, primarily at the University of California, Berkeley.
 
Dissertation advisor
 
William Duncan Strong (1899-1962) received a Ph.D. in 1926 from the University of California, Berkeley. Strong held academic positions at the University of Nebraska and Columbia University.
 
Dissertation advisor
 
Gordon Randolph Willey* (1913-2002) received an M.A. in anthropology in 1936 from the University of Arizona under Byron Cummings (1860-1954), first head of the Archaeology Department there. He received a Ph.D. in 1942 from Columbia University. Willey worked as an anthropologist for the Smithsonian Institution in Washington and later taught at Harvard University.
 
Dissertation advisor
 
David Humiston Kelley (1924-2011) received a Ph.D. in 1957 from Harvard University. He was Alfred Tozzer's last graduate student. After Tozzer's death, Gordon Willey was his dissertation advisor. Kelley taught at Texas Technological College (now Texas Tech University) in Lubbock, at the University of Nebraska in Lincoln, and beginning in 1968 at the University of Calgary in Canada.


Notation: the label above the curving arrow gives the role of the person above the arrow in relation to the person below, e.g., "Teacher." Several roles may be itemized, separated by commas, e.g., "Teacher, significant intellectual influence," though a role would not be itemized if it is subsumed or implied by a role already given. Note that "Correspondent" implies mutual intellectual influence. If needed, the role of the person below the arrow in relation to the person above can also be specified, following a "–›", e.g., "Teacher –› only student."







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An asterisk following a name (above) is a link to a note (below) about that person. Conversely, the name at the beginning of a note (below) is a link to the person's information (above).


This draft chart (at www.donstonetech.com/Charts/AcademicGenealogy/KelleyAcademicGenealogy.htm) was prepared by Don Stone, don@donstonetech.com. (It was most recently updated on 11/4/2011.) I would be grateful for any corrections or additional information, particularly for descriptions of the nature of some of the relationships (often not literally "advisor"). I hope that this webpage can be a vehicle for a collaborative process of refining and documenting especially the European portion of this lineage. Note that I have not verified most of the information for the period before 1750.


ABBREVIATIONS:
   MGP: the Mathematics Genealogy Project (http://www.genealogy.ams.org/)
      See also (https://academictree.org/math/tree.php?pid=168355)
   PFT Blog: the Philosophy Family Tree Blog (http://philtree.blogspot.com/)


GENERAL COMMENTS:
   A proper presentation of an academic genealogy should have many of the characteristics of a well-done family genealogy: sources should be specified for all information, inferences and hypotheses should be identified as such and explained, conflicting sources should be analyzed (with greater weight generally given to "primary" sources, e.g., university records, dissertation title pages), etc. In addition, for academic genealogies the nature of each relationship should be specified (and sourced), e.g., "Teacher", "Significant intellectual influence", "Dissertation advisor", etc. I have made a start in this direction with the notes below, focusing first on disputed or murky areas.

COMMENTS ON RELATIONSHIPS:
   The interesting aspect of an academic pedigree is that it involves the transmission of knowledge, methodology, and even outlook, through a sequence of sustained mentor/student relationships. The relation of dissertation advisor to advisee is a typical means for this intellectual transmission in recent times. (Of course, in some cases the former students may revise the conceptual framework in which they were trained prior to transmitting it to others, or they may even reject it completely). In earlier times, the mentor/student relationship might not involve thesis advising and might even occur outside an academic context (e.g., the case of Copernicus/Rheticus). Biographical information must be examined in order to see whether the relationship was sustained over a period of time and whether significant intellectual transmission took place.
   In the above chart I have used two shades for the curved arrows connecting mentors and their students.
For the period from 1800 to the present:
   • The more frequent darker arrows are used to connect a dissertation advisor to the dissertation's author (or for some United Kingdom
      universities even into the early 1900s, an M.A. advisor to his/her advisee).
   • The lighter arrows are used for relationships other than advisor to advisee.
For the period prior to 1800:
   • The darker arrows also are used to connect an advisor to a student receiving the degree master of arts, philosophy, or law,
      or another degree in law, theology, or medicine.
   • The lighter arrows are generally used for relationships other than thesis advisor to author, but darker ones may be used in such cases
      if it seems clear that significant intellectual transmission occurred even though not via thesis advising.
This approach can require some biographical investigation and interpretation and thus can be somewhat subjective, but it reflects my emphasis on intellectual transmission.
   Note that Josh Dever, who maintains the PFT, says (https://webspace.utexas.edu/deverj/personal/philtree/philtree.html#questions, accessed 12/2/2008): "What relationship is being tracked in the tree? As much as possible, I have assigned parentage according to the official dissertation advisor. This means, in particular, that parentage should not be read as 'greatest philosophical influence'. If philosopher X worked closely with Y and Z in graduate school, and Y in fact played the greatest role in the shaping of the dissertation, but Z was the official chair, then Z goes down as the parent of X." The advantage of this approach is that it is completely objective. Since I have no reluctance to supply multiple "parents" (unlike Dever), I would handle this situation by having appropriately labeled arrows from both Y and Z to X.


MEDIA COVERAGE OF THIS LINEAGE:
   "Math Masters Trace Their Intellectual Lineage," by Samuel Arbesman, Wired, June 2011 (http://www.wired.com/magazine/2011/05/st_mathancestry/). This article and chart are based on the MGP, so it is surprising that the line from Abraham Kästner to Johann Pfaff to Carl Friedrich Gauss was not included in the chart.


TERMINOLOGY:
   The habilitation is the extra post-doctoral qualification needed to lecture at a university in Germany and other countries. It requires the candidate to prepare a thesis (the Habilitationsschrift) based on independent rather than supervised research. An academic committee examines the candidate on this thesis; a lecture by the candidate may also be part of the process.


NOTES:

   Some biographical information is from Wikipedia (a convenient first source to check, though not always reliable or well-documented). Most of the earlier data on degrees, universities and dates comes from the MGP. I have generally inferred the relation of "Thesis advisor" for this earlier period, except when I had explicit information to the contrary (as with Copernicus and Rheticus, for example).

* Gordon R. Willey: See Willey's biographical memoir in Proceedings of the American Philosophical Society 148 (no. 3, Sept. 2004): 406-410, http://www.amphilsoc.org/sites/default/files/480314.pdf.

* Franz Boas: A helpful source has been Douglas Cole's Franz Boas: The Early Years, 1858-1906 (1999). Pages 51-53 cover Boas' work on his physics Ph.D.; his work on his habilitation is discussed on pp. 88-93 (p. 91 mentions the appointment of von Bezold as Boas' major examiner). Boas' habilitation work is briefly discussed in Andrew Zimmerman's Anthropology and Antihumanism in Imperial Germany (2001), p. 45. Zimmerman does not make von Bezold as supportive of Boas as Cole does, but Cole, whose focus is Boas, may be more sensitive to the nuances of this particular case.

Note that having Boas as an academic descendant of Carl Friedrich Gauss puts him in the appropriate intellectual tradition, since Boas wanted his physics dissertation to be on Gauss' law of the normal distribution of errors.

* Gustav Karsten: Some information on Karsten is available from the German Wikipedia (http://de.wikipedia.org/wiki/Gustav_Karsten, accessed 7/7/2011).

* Bernhard Riemann: The biography of Riemann in Eric Weisstein's World of Science points out that he studied mathematics under Gauss and physics under Wilhelm Weber (http://scienceworld.wolfram.com/biography/Riemann.html). Riemann's MacTutor biography further specifies that he was Weber's assistant for 18 months (http://www-history.mcs.st-andrews.ac.uk/Biographies/Riemann.html).

* Wilhelm Eduard Weber: Here is some information on Wilhelm Weber's education from http://www-history.mcs.st-andrews.ac.uk/Biographies/Weber.html or http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Weber.html, accessed 7/7/2011: "Wilhelm Weber entered the University of Halle in 1822 where he was taught and strongly influenced by the physicist Johann S C Schweigger and the mathematician Johann Friedrich Pfaff. He wrote his doctoral dissertation under Schweigger's supervision on the theory of reed organ pipes and submitted it to Halle in 1826. After that he taught at Halle from 1827 after completing his habilitation thesis on reed organ pipes as coupled oscillators with acoustic coupling of tongue and air cavity." Note that Weber appears in the MGP: http://www.genealogy.ams.org/id.php?id=57721; the following sequence of advisors takes him back to Abraham Gotthelf Kästner, who appears above: Johann Schweigger, Karl von Langsdorf, Kästner.

Here is some information on Weber from Wikipedia (http://en.wikipedia.org/wiki/Wilhelm_Eduard_Weber, accessed 7/7/2011): "During 1831, on the recommendation of Carl Friedrich Gauss, he was hired by the university of Göttingen as professor of physics, at the age of twenty-seven. His lectures were interesting, instructive, and suggestive. Weber thought that, in order to thoroughly understand physics and apply it to daily life, mere lectures, though illustrated by experiments, were insufficient, and he encouraged his students to experiment themselves, free of charge, in the college laboratory."

* Carl Friedrich Gauss: Information on Gauss can be found at http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Gauss.html, which reports that Gauss studied directly under Abraham Kästner. Kästner's biography says that Kästner "was an excellent expositor of mathematics although it is reported that Gauss did not bother to go to his lectures as he found them too elementary. However he did influence Gauss, in particular with his interest in Euclid's parallel postulate."

* Georg Joachim von Lauchen Rheticus: From Wikipedia (http://en.wikipedia.org/wiki/Rheticus, accessed 12/2/2008): "He is perhaps best known for his trigonometric tables, and for being the only pupil of Nicolaus Copernicus..." And later, "In 1536 Rheticus was aided by Melanchthon in obtaining appointment to a teaching position in astronomy and mathematics at Wittenberg University. Two years later, Melanchthon arranged a two year leave for Rheticus in order to study with noted astronomers of the day.... In May 1539 he arrived in Frombork (Frauenburg) and spent two years there with Copernicus."