Saturday, June 18, 2005

An Eulerian Tour

Chris Barwick (aka optionsScalper) is a fan of Euler and tracked down my academic legacy back to Euler and Gauss through many other great mathematicians. Of course the same legacy applies to the many theoretical computer scientists who descend from Manuel Blum.
  • Lance Jeremy Fortnow was a student of Sipser
    Awarded: 1989. Dissertation: Complexity-Theoretic Aspects of Interactive Proof Systems
  • Michael Fredric Sipser was a student of Blum (1938-)
    Awarded: 1980. Dissertation: Nondeterminism and the Size of Two-Way Finite Automata
  • Manuel Blum was a student of Minsky (1927-)
    Awarded: 1964. Dissertation: A Machine-Independent Theory of the Complexity of Recursive Functions
  • Marvin Lee Minsky was a student of Tucker
    Awarded: 1954. Dissertation: Theory of Neural-Analog Reinforcement Systems and Its Application to the Brain Model Problem
  • Albert William Tucker was a student of Lefschetz (1884-1972)
    Awarded: 1932. Dissertation: An Abstract Approach to Manifolds
  • Solomon Lefschetz was a student of Story
    Awarded: 1911. Dissertation: On the Existence of Loci with Given Singularities
  • William Martin Story was a student of Carl Gottfried Neumann (1832-1925) and Klein (1849-1925)
    Awarded: 1875. Dissertation: On the Algebraic Relations Existing Between the Polars of a Binary Quantic
  • Felix Christian Klein was a student of Julius Plücker (1801-1868) and Lipschitz (1832-1903)
    Awarded: 1868. Dissertation: Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form
  • Rudolf Otto Sigismund Lipschitz was a student of Dirichlet (1805-1859) and Martin Ohm
    Awarded: 1853. Dissertation: Determinatio status magnetici viribus inducentibus commoti in ellipsoide
  • Gustav Dirichlet was a student of Poisson (1781-1840) and Joseph Fourier (1768-1830)
    Awarded: 1827. Dissertation: Partial Results on Fermat's Last Theorem, Exponent 5
  • Simeon Poisson was a student of Lagrange (1736-1813)
    Awarded: Unknown. Dissertation: Unknown.
  • Joseph Lagrange was a student of Leonhard Euler (1707-1783)
    Awarded: Unknown. Dissertation: Unknown.
Also some Gauss starting at Klein and progressing through Plücker.
  • Felix Christian Klein was a student of Plücker (1801-1868) and Rudolf Otto Sigismund Lipschitz (1832-1903)
    Awarded: 1868. Dissertation: Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form
  • Julius Plücker was a student of Christian Gerling
    Awarded: 1823. Dissertation: Generalem analyeseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundamenta sunt e serie Tayloria deducit
  • Christian Gerling was a student of Johann Carl Friedrich Gauß (Gauss) (1777-1855)
    Awarded: 1812. Dissertation: Methodi proiectionis orthographicae usum ad calculos parallacticos facilitandos explicavit simulque eclipsin solarem die
Notes from Barwick:
  1. My sources are various in print and online, but they originate from The Mathematics Genealogy Project.
  2. Little is known of William Edward Story and Albert William Tucker and their lives.
  3. Martin Ohm is the brother of Georg Simon Ohm, for whom Ohm's Law is named.
  4. I find it interesting that Klein was awarded his doctorate the year of Plücker's death. Klein was Plücker's assistant for nearly three years.
  5. It had been believed, but not shown that Carl Gottfried Neumann was advised by Georg Friedrich Bernhard Riemann. Neumann was, in fact, advised by Otto Hesse and F. Richelot. Hesse was also a friend of Neumann's father, Franz. Many modern mathematicians mistakenly trace their roots through Neumann to Riemann and Gauss. Riemann received his doctorate in 1851 at Göttingen. Riemann was subsequently awarded a post at Göttingen by Gauss in 1851 to allow Riemann to study for his Habilitation. Riemann delivered his lecture to earn the Habilitation under Gauss in 1854. Gauss died the following year (Dirichlet was given his chair). Carl Gottfried Neumann was awarded his doctorate in 1855 at Königsberg.


  1. Yeah, I tried that once. If you go back further, you can also get to Leibniz and the Bernoullis.

  2. I did some research on this a while back out of idle curiosity, and as far as I remember the doctorate as we know it today is a German creation from the early XIX century. Dirichlet, as a French mathematician, had in fact no PhD until he wished to be appointed at a German university.

    This leads me to believe that Poisson and Lagrange whose dissertation is listed as "unknown" are likely to have had no dissertation and no formal PhD student-supervisor relationship.

    Alex Lopez-Ortiz

  3. Why is no year of birth listed for Sipser and Fortnow? =)

  4. Lopez-Ortiz brings to bear a few good points and I'll address them shortly. I do believe that this ancestry is intact for a number of reasons. As I'm verbose, I'll likely publish in my blog and trackback here with a distillation.

    My interest is in the ontology (the computer science kind, not the philosophical kind) of mathematics from the 16th century to the present, so my readings emphasize this period.

    The models of ontological representation in directed graphs and other emergence are still in their infancy and not likely to be mature in the first iteration (generation) of the semantic web.

    One only hopes that we aspire in our lifetimes to that promise of the confluence of Information Theory, Graph Theory, Theory of Computation and other disciplines that provide for improved measures of corroborated facts in these matters.

    Regarding "anonymous" on Drs. Sipser and Fortnow birth dates, I can only assume that they were both born in the same historical period as Tucker and Story as evidenced by Sipser and Fortnow pictures in the public domain. As I'm aware of only one source of information in these two data points, I cannot in good faith publish this information and continue to project any current (baseless) journalistic integrity. (Attempted humor; I'm not bound by the rules and regulations of the "Humor in Talks").


  5. Who was it that gave the recursive definition of a mathematician? That is,

    "You're a mathematician if a mathematician says you're a mathematician. Hilbert was a mathematician."

  6. To get hold of the missing birth years, use :o)

  7. It's not an Eulerian Tour.
    It's a Eulerian Tour.

  8. Note to anonymous on "A Eulerian Tour".

    Euler was Swiss, consequently for his era and continuing through modern times, the "Eu" in Euler is represented by the "oi" phoneme. It is common to mistake "Eu" with the "yoo" phoneme (as in Europe). "Euler" rhymes with "oiler" (since I cannot represent the phoneme for schwa here).

    The use of the indefinite article, i.e. Dr. Fortnow's choice between "a" and "an", requires under English morphology and grammar, the instance of "an" when preceding a word that begins with this phoneme.

    I hope this clarifies things.