SUPERVISOR ANCESTORS⁰

The line

Joseph Lagrange (no dissertation ) ¹
Jean Baptiste Fourier (18??) ²
Gustav Dirichlet (1827)³
Rudolf Lipschitz (1853)
Felix Klein (1868) ⁴
Carl Louis Lindeman (1873)
Arnold Sommerfeld (1891)
Ernst Guillemin (1926)⁵
Robert Fano (1947)
Charles Desoer (1953)⁶
Robert Newcomb (1960)
Brian Anderson (1966)⁷

Peter Moylan (1972)⁸

David Hill (1976)⁹

Notes

0 The original list for Anderson to Lagrange was provided by e-mail from Bob Williamson on 23-1-2007.

1 Wikipedia states that Lagrange’s “academic advisor” (in what sense is unclear if there was no dissertation) was Leonhard Euler, whose advisor was Johann Bernoulli; the line continues back as Jacob Bernoulli (his brother), Gottfried Leibniz (the co-inventor of calculus seems to have done two theses in philosophy and law) and Erhard Weigel (mathematician, astronomer and philosopher, 1625-1699) where the line seems to end. Euler was one of the most prolific mathematicians in history and the inventor of graph theory in his famous solution to the Königsberg bridges problem (1736). According to Barabási, this initiated the subject of networks; Lagrange and Euler could not be better ancestors for work in dynamic networks.

2 The date for a dissertation is not clear. From http://www-history.mcs.st-andrews.ac.uk/Biographies/Fourier.html: “Later in 1794 Fourier was nominated to study at the École Normale in Paris…. He was taught by Lagrange, who Fourier described as the first among European men of science, and also by Laplace, who Fourier rated less highly, ……. In 1797 he succeeded Lagrange in being appointed to the chair of analysis and mechanics. … he does not appear to have undertaken original research during this time……It was during his time in Grenoble that Fourier did his important mathematical work on the theory of heat. His work on the topic began around 1804 and by 1807 he had completed his important memoir On the Propagation of Heat in Solid Bodies. The memoir was read to the Paris Institute on 21 December 1807 and a committee consisting of Lagrange, Laplace, Monge and Lacroix was set up to report on the work. Now this memoir is very highly regarded but at the time it caused controversy. …..The first objection, made by Lagrange and Laplace in 1808, was to Fourier's expansions of functions as trigonometrical series, what we now call Fourier series. …Fourier was elected to the Académie des Sciences in 1817. … the Académie published his prize winning essay Théorie analytique de la chaleur in 1822.” (This is referred to as a book elsewhere.) It seems 1807 is the most likely year for a dissertation.

3 Wikipedia lists Simeon Poisson as a second advisor. Poisson’s advisor is unclear but may be taken as Lagrange: “This success at once procured for Poisson an entry into scientific circles. Joseph Louis Lagrange, whose lectures on the theory of functions he attended at the École Polytechnique, early recognized his talent, and became his friend (the Mathematics Genealogy Project lists Lagrange as his advisor, but this may be an approximation); while Pierre-Simon Laplace, in whose footsteps Poisson followed, regarded him almost as his son.”

4 Wikipedia states that he had a second supervisor, Julius Plücker, from whom the line continues back mostly in German mathematics through Christian Gerling (physics, astronomy), notably Carl Friedrich Gauss (arguably the founding father for signals and systems ideas used in EE) and then Johan F Pfaff and Abraham Kästner (1719-1800); there is no article about Kästner’s advisor, given as Christian Hausen.

5 Guillemin did his basic degrees in EE at Wisconsin and MIT and went to Munich on a Fellowship where he worked in Sommerfeld’s large and powerful theoretical physics group; six of his students got Nobel prizes. From Wikipedia: “Over his 32 years of teaching at Munich, Sommerfeld taught general and specialized courses, as well as holding seminars and colloquia. The general courses were on mechanics, mechanics of deformable bodies, electrodynamics, optics, thermodynamics and statistical mechanics, and partial differential equations in physics.” This is clearly where the turn towards engineering science came and the subject of electrical networks flourished with his students and their students. (My favourite circuits text is still Desoer and Kuh which I tutored – for Brian Anderson – and taught my first course from in Newcastle while still a PhD student.)

6 Lectures and discussions with Charlie Desoer were a memorable part of my postdoctoral studies at Berkeley; KYP Lemma history, criticism of fuzzy control etc in the corridor come to mind, not to mention his precise lectures, disputes in seminars, e.g. with Doyle. His and Vidyasagar’s stability book arrived during my thesis and, with Brian’s books on optimal control and networks, provided the extra basics (to the Lyapunov theory learned quite well previously) to build upon.

7 Brian Anderson set up the school in Newcastle almost straight from his PhD at Stanford; through the late 1960’s and 1970’s (until he left for ANU with John Moore in 1982) it remains in my mind the formative and best period of systems and control in Australia; his influence over the school, which produced a generation of professors operating at the highest international levels, was immense and led directly to today’s excellent systems type schools operating in Newcastle, ANU and Melbourne and also influenced other developments.

8 I had in mind that I would probably work with Brian for my thesis after meeting John Moore in Brisbane and had studied a lot of mathematics in preparation, but Brian was on study leave when I arrived. I started on problems of passivity and finite-gain (combined into dissipativity following Willems) of nonlinear systems with Peter, which followed naturally from his own thesis on nonlinear optimal control presented a couple of years earlier and fitted nicely with my own interests; Brian was looking at new things such as category theory, so to work with him would have involved some change of direction; I got quick results, the dissipativity problems were too interesting to leave and a lot was achieved working with Peter in what might be called co-opetition more than supervision, i.e. I had to be quick. He was very good at systems theory, but ultimately more interested in personal development and computers it seems. In a traditional sense, Brian was more of a supervisor and mentor to me in the early stages of my career.

9 So how many are there in my generation of descendants? Assuming x_ij next students at generation i+1 for student j gives the total of N_k at generation k descended from Lagrange; if x_ij = 5, then N₁₃ = 5¹³ = 1,220,703,125, more than a billion, i.e. 20% of the world’s population which is absurd; x_ij = 2 gives N₁₃ = 8,192 and x_ij=3 gives 1,594,323. The Mathematics Geneology Project (http://www.genealogy.math.ndsu.nodak.edu/index.html) mentions 38,286 accumulated descendants (out of their database of 103,293 records), but this would ignore a lot of people working away from mathematics departments as a quick check for Charlie and Brian confirms. One in systems and control from a quite separate line (10^th generation) is John Doyle via Sarason, Halmos, Doob, … Poisson, Lagrange.

Expanded (according to Wikipedia)

Erhard Weigel

Gottfried Leibniz

Jacob Bernoulli

Johann Bernoulli Christian Hausen

Leonhard Euler Abraham Kästner

Joseph Lagrange Johan F Pfaff
Jean Baptiste Fourier Joseph Lagrange Carl Friedrich Gauss
Gustav Dirichlet --- Simeon Poisson Christian Gerling
Rudolf Lipschitz --------- --------------------- Julius Plücker
Felix Klein

New names in italics.