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, email@example.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.
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/)
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.
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.
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."