The Weierstrass Lineage
Magnus Gösta Mittag-Leffler (1846-1927) and his student Robert Hjalmar Mellin (1854-1933) - see Street - received post-doctoral mentoring from...
Karl Weierstrass (1815-1897), first paper: Über die Entwicklung der Modularfunctionen (1841, unpublished until decades later), at the Akademische Lehranstalt Münster, which later became the University of Münster. At the time Weierstrass attended, Münster did not offer Ph.D. degrees. Weierstrass' paper was part of his examination for a secondary teaching certificate. After 12 years as a secondary school teacher he published Zur Theorie der Abelschen Functionen (Crelle's Journal 47, 1854) and received an honorary doctorate from the University of Koningsberg before the end of that year. By 1856 he was in Berlin and into the German university system. An interesting short biography is here as PDF.
Weierstrass' first paper was written while he was a student of...
Christoph Gudermann (1798-1852), Dissertation: unknown, Georg-August-Universität Göttingen(?). There seems to be a significant error regarding Gudermann that has widely appeared in mathematical genealogies: Gudermann's dissertation is often listed as 1841 and the title typically given is the unpublished (at the time) paper that Weierstrass wrote for his teaching examination (see Weierstrass biography PDF). The 1841 date is suspcious from the outset as it would have meant Gudermann was 43 years old when earning his Ph.D. - unusually old for mathematicians of the time (or even today). Furthermore, by 1841 Gudermann had already been a decade teaching at Akademische Lehranstalt Münster (which later became the University of Münster). A publication list can be found here, with his earliest work listed as Allgemeiner Beweis des polynomischen Lehrsatzes ohne die Voraussetzung des binomischen (1825), which appears to have been published when Gudermann was teaching at the Kleve (Cleve) Gymnasium. Later works are available on Google Books: Grundriss der analytischen (1830) and Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833); in the latter he is represented as "Dr." on the title page. In an 1829 article he is referred to as Vom. Herrn Prof. Gudermann. With the series of journal articles in 1829, 1830, 1831 and the 1833 book, we can reasonably assume that he was awarded his doctorate prior to 1831. According to L. Ridgway Scott in a footnote on page 151 of Numerical Analysis (Princeton University Press) as well as many others (e.g. here), Gudermann was a student of Karl Friedrich Gauss at Göttingen University. However, I have not been able to find any primary sources or books confirming any relationship. The idea that he was Gauss' student may be wishful thinking. If he was indeed at Göttingen, he could have easily been a student of Bernhard Friedrich Thibaut, who was (apparently) a better lecturer and taught pure mathematics there (Gauss held the astronomy chair).
Following convention in the Mathematics Genealogy Project (without any other good evidence), Gudermann's dissertation supervised by…
Karl Friedrich Gauss (1777-1855) Dissertation: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (1799), Universität Helmstedt.
Gauss's dissertation supervised by…
Johann Friedrich Pfaff (1765-1825) Dissertation: Commentatio de ortibus et occasibus siderum apud auctores classicos commemoratis (1786), Georg-August-Universität Göttingen.
Pfaff's dissertation supervised by…
Abraham Gotthelf Kästner (1719-1800) Dissertation: Theoria radicum in aequationibus (1739), Universität Leipzig.
Kästner's dissertation was supervised by…
Christian August Hausen (1693-1743), Dissertation: De corpore scissuris figurisque non cruetando ductu (1713), Martin-Luther-Universität Halle-Wittenberg.
Hausen's dissertation was supervised by…
Johann Christoph Wichmannshausen (1663-1727), Dissertation: Disputationem Moralem De Divortiis Secundum Jus Naturae (1685), Universität Leipzig.
Wichmannshausen's was dissertation supervised by…
Otto Mencke (1644-1707), Dissertation: Ex Theologia naturali -- De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam (1665), Universität Leipzig.
Mencke's dissertation was supervised by…
Jakob Thomasius (1622-1684), Dissertation: title unknown (1643), Universität Leipzig.
Thomasius' dissertation was supervised by…
Friedrich Leibniz (1597-1652), Dissertation: Disputatio de Casibus perplexis in Jure (1622), Universität Leipzig. Supervisor unknown. Appears in history mainly as the father of Gottfried Wilhelm Leibniz. However, at neurotree - Friedrich's supervisor is listed as Johann Müller at Universität Leipzig with the evidence being a page from a book in German. I haven't been able to find confirmation that Müller was indeed his supervisor. Nor have I found further ancestors of Müller.
Further research in progress (last update June 1, 2012)