From Eric Paulos's investigations:
"Seems like a silly thing but I was curious one day so I traced it back as far as I could. Updates to this as I learn more. Individuals are listed in the form (Name / Place of PhD / Date of PhD). I traced it by hand back to 1954 but through the genius of the Theory of Computation Ph.D. Genealogy Database and The TCS Genealogy I was able to go back to 1856. Very nice.
Things get really interesting because Franz Neumann was influenced by Euler and Kirchhoff was one of his students. Also, Carl Neumann was a friend of Ludwig Otto Hesse and studied Riemann surfaces."
Camerarius? / Tubingen / 1687

Christian August Hausen / Wittenberg Academy / 1713

Anraham
Gotthelf Kaestner / Göttingen University / 1739

Johann Friedrich Pfaff / Göttingen University / 1788
Dissertation tite: Programma inaugurale in quo peculiarem differentialia investigandi rationem ex theoria functionum deducit

Johann Carl Friedrich Gauss / Brunswick Collegium Carolinum / 1799

Georg Friedrich Bernhard Riemann / Göttingen University / 1849

Carl Gottfried Neumann / University of Königsberg, Prussia / 1856
(Note: Carl was the son of
Franz Neumann / Berlin / 1825)

William Edward Story / Leipzig / 1875

Solomon Lefschetz / Clark University, Worcester, MA / 1911

Albert Tucker / Princeton / 1932

Marvin Minsky
/ Princeton / 1954

Berthold Horn / MIT / 1970

Tomas LozanoPerez / MIT / 1980

Bruce Donald / MIT / 1987

Former Ph.D. Students
Current Students
PostDocs
I have not constructed a lineage for my postdocs but that would be
interesting to do.
Issues/Questions:
(1) Since I did not do a postdoc, would I be the root of that
tree?
(2) Are Ph.D. students of former postdocs considered `descendents'?
(3) If so, the relations postdoc1 and Ph.D1 do not commute, but in terms of closeness are
they to be treated differently?
(4) Which is more closely related, a postdoc4
or a Ph.D.4 descendent?
(5) More generally, which is more closely related, a postdocn Ph.Dm, or a
postdocm Ph.Dn, descendent?
AUTHOR: Horn, Berthold K. P.
TITLE: Shape from shading; a method
for obtaining the shape of a smooth opaque object from one view.
PUBLISHED: 1970
AUTHOR: LozanoPerez, Tomas.
TITLE: Spatial planning with polyhedral models
PUBLISHED: c1980.
5  Marvin Minsky  Degree  Ph.D. [2,3,6], Mathematics [8] 
Institution  Princeton University [2,3,6,8]  
Date  1954 [2,3,6]  
Title  Neural Nets and the Brain Model Problem (Theory of NeuralAnalog Reinforcement Systems and Its Application to the Brain Model Problem [6])  
Advisor  Albert Tucker [2,3,8]*  
6  Albert Tucker  Degree  Ph.D. [2,3], Mathematics 
Institution  Princeton University [2,3]  
Date  1932 [2,3]  
Title  An Abstract Approach to Manifolds  
Advisor  Solomon Lefschetz [2,3]  
7  Solomon Lefschetz  Degree  Ph.D. [2,3,6], Mathematics 
Institution  Clark University [2,3,6]  
Date  1911 [2,3,6]  
Title  On the Existence of Loci with Given Singularities [6]  
Advisor  William Edward Story [2,3,6]  
8  William Edward Story  Degree  Ph.D. [2,3,6] 
Institution  University of Leipzig [2,3,6]  
Date  1875 [2,3,6]  
Title  On the Algebraic Relations Existing Between the Polars of a Binary Quantic [6]  
Advisor  Carl Gottfried Neumann [2,3,6]  
9  Carl Gottfried Neumann  Degree  Ph.D. [2,3,6] 
Institution  University of Königsberg, Prussia [2,3,6]  
Date  1856 [2,3,6]  
Title  De problemate quodam mechanico, quod ad primam classem integralium ultraellipticorum revocatur [6]  
Advisor  Georg Friedrich Bernhard Riemann [3]  
10  Georg Friedrich Bernhard Riemann  Degree  Ph.D. [3,6] 
Institution  Göttingen University [3] (GeorgAugustUniversit?t Göttingen [6])  
Date  1849 [3] (1851 [6])  
Title  Grundlagen f?r eine allgemeine Theorie der Funktionen einer ver?nderlichen complexen Gr??e [6]  
Advisor  Johann Carl Friedrich Gauss [3,6]  
11  Johann Carl Friedrich Gauss  Degree  Ph.D. [3,4,6] 
Institution  University of Helmstedt [4,6] ([3] gives Brunswick Collegium Carolinum)  
Date  1799 [3,4,6]  
Title  Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse [4,6]  
Advisor  Johann Friedrich Pfaff [3,4,6]  
12  Johann Friedrich Pfaff  Degree  Ph.D. [6] 
Institution  Göttingen University [3]  
Date  1788 [3]  
Title  Programma inaugurale in quo peculiarem differentialia investigandi rationem ex theoria functionum deducit [3]  
Advisor  Abraham Gotthelf Kaestner [3,4,6]  
13  Abraham Gotthelf Kaestner  Degree  Doctorate [5] (Ph.D. [6]) ** 
Institution  Universität Leipzig [4,5,6]  
Date  1739 [4,5,6]  
Title  
Advisor  Christian August Hausen [4]  
14  Christian August Hausen  Degree  Doctorate [5] *** 
Institution  Wittenberg Academy [4,5]  
Date  1713 [4,5]  
Title  Animaduerfa quaedam in demonftrationem Exiftentiae Dei [4]  
Advisor  Rudolph Jakob Camerarius  
15  Rudolph Jakob Camerarius  Degree  
Institution  
Date  
Title  
Biography 
*[6] gives M. Minsky's Advisor as John Wilder Tukey (Ph.D. Mathematics, Princeton, 1939, "On Denumerability in Topology"). Correction: Tukey was also a student of Lefschetz. Tucker, in an interview [8], states that he was Minsky's advisor, and that Tukey also read his dissertation.
**[7] shows a degree of L.L.M. under Hausen in 1737, same university.
***[7] shows an M.S. at Wittenberg in 1712, advisor not known.
[2] The SIGACT Theory of Computation Genealogy
The MacTutor History of Mathematics archive
[5] Research by A. M. Jacobi
[6] The Mathematics Genealogy Project, at Minnesota State University
[8] The Princeton Mathematics Community in the 1930s: An OralHistory Project