Diego VolpattoLNCC / MCTI

Academic genealogy

An academic family tree follows advisors and their own advisors. In mine, I found Stephen Timoshenko (beam theory and solid mechanics; 4 links) and Ludwig Prandtl (boundary-layer theory; 5 links). Including historical connections and a disputed attribution involving August Föppl leads to Carl Friedrich Gauss (numerical quadrature and least squares; 10 links) and Leonhard Euler (Euler’s method for ODEs and equations for inviscid flow; 12 links).

These paths also include Peter G. L. Dirichlet (boundary-value problems for PDEs; 9 links), Joseph Fourier (the heat equation and Fourier series; 10 links) and Joseph-Louis Lagrange (calculus of variations; 11 links) — contributions that remain central to the study of PDEs and the development of numerical methods.

Each relationship counts as one step; my advisor is one step away from me. Distances apply to this selection: earlier study and mentorship links are not necessarily doctoral supervision. The detailed diagram also includes collateral branches, which are not direct ancestors.

A line of academic training

From earlier scholars to recent training. Arrows point from mentor to student.

12* Links to Volpatto

Leonhard Euler

Euler’s method for ODEs and equations for inviscid flow.

5 links
via Joseph-Louis Lagrange → Joseph Fourier → Peter G. L. Dirichlet → Rudolf Lipschitz

Historical relationship · Doctoral supervision

10* Links to Volpatto

Carl Friedrich Gauss

Numerical quadrature and the method of least squares.

3 links
via Christian Ludwig Gerling → Julius Plücker

Doctoral supervision
  1. 7

    Felix Klein

    Geometry and the Erlangen program.

    Disputed relationship

  2. 6

    August Föppl

    Applied mechanics and elasticity.

    Historical relationship

  3. 5

    Ludwig Prandtl

    Boundary-layer theory and fluid mechanics.

    Historical relationship

  4. 4

    Stephen Timoshenko

    Beam theory and solid mechanics.

    Doctoral supervision

  5. 3

    Erastus H. Lee

    Plasticity and viscoelasticity.

    Doctoral supervision

  6. 2

    Luiz Bevilacqua

    Continuum mechanics and variational methods.

    Doctoral supervision

  7. 1

    Abimael Fernando Duarte Loula

    Finite element methods.

    Doctoral supervision

  8. 0

    Diego Tavares Volpatto

    Starting point for the count

The Euler and Gauss branches converge at Klein. This is a selection: the other branches, including Bruns, appear in the full diagram.
  • Doctoral supervision
  • Historical relationship
  • Disputed relationship

* The distance depends on the disputed link through Föppl. The count considers only relationships in this graph.

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Full diagramAll branches and relationships

Scroll to explore the diagram. With the figure focused, the arrow keys also let you navigate.

Complete graph of academic relationships, from mentor to student. Names, relationship types and sources are available in the text list below.
Relationships and sourcesText version and documentation

Relationships shown

mentor → student

  • mentor: Abimael Fernando Duarte Loulastudent: Diego Tavares Volpatto

    Doctoral supervision[1]

  • mentor: Luiz Bevilacquastudent: Abimael Fernando Duarte Loula

    Doctoral supervision[2]

  • mentor: Erastus H. Leestudent: Luiz Bevilacqua

    Doctoral supervision[3][4]

  • mentor: Stephen Timoshenkostudent: Erastus H. Lee

    Doctoral supervision[5][6]

  • mentor: Ludwig Prandtlstudent: Stephen Timoshenko

    Historical relationship[7]

  • mentor: August Föpplstudent: Ludwig Prandtl

    Historical relationship[8][9]

  • mentor: Felix Kleinstudent: August Föppl

    Disputed relationship[10][11]

  • mentor: Heinrich Brunsstudent: August Föppl

    Disputed relationship[10][11]

  • mentor: Gustav Heinrich Wiedemannstudent: August Föppl

    Historical relationship[11]

  • mentor: Julius Plückerstudent: Felix Klein

    Doctoral supervision[12]

  • mentor: Rudolf Lipschitzstudent: Felix Klein

    Doctoral supervision[12]

  • mentor: Christian Ludwig Gerlingstudent: Julius Plücker

    Doctoral supervision[13]

  • mentor: Carl Friedrich Gaussstudent: Christian Ludwig Gerling

    Doctoral supervision[14]

  • mentor: Carl Friedrich Gaussstudent: Bernhard Riemann

    Doctoral supervision[15]

  • mentor: Peter Gustav Lejeune Dirichletstudent: Rudolf Lipschitz

    Doctoral supervision[16]

  • mentor: Joseph Fourierstudent: Peter Gustav Lejeune Dirichlet

    Historical relationship[17]

  • mentor: Joseph-Louis Lagrangestudent: Joseph Fourier

    Historical relationship[18]

  • mentor: Leonhard Eulerstudent: Joseph-Louis Lagrange

    Historical relationship[19]

  • mentor: Karl Weierstrassstudent: Heinrich Bruns

    Doctoral supervision[20]

  • mentor: Ernst Eduard Kummerstudent: Heinrich Bruns

    Doctoral supervision[20]

  • mentor: Heinrich Brunsstudent: Felix Hausdorff

    Doctoral supervision[20]

  • mentor: Karl Weierstrassstudent: Georg Cantor

    Doctoral supervision[21]

  • mentor: Karl Weierstrassstudent: Hermann Amandus Schwarz

    Doctoral supervision[22]

  • mentor: Ernst Eduard Kummerstudent: Hermann Amandus Schwarz

    Doctoral supervision[22]

  • mentor: Hermann Amandus Schwarzstudent: Lipót Fejér

    Doctoral supervision[22]

  • mentor: Lipót Fejérstudent: John von Neumann

    Doctoral supervision[23]

  • mentor: Lipót Fejérstudent: Paul Erdős

    Doctoral supervision[23]

  • mentor: Felix Kleinstudent: Ferdinand von Lindemann

    Doctoral supervision[12]

  • mentor: Ferdinand von Lindemannstudent: David Hilbert

    Doctoral supervision[24]

  • mentor: Ferdinand von Lindemannstudent: Hermann Minkowski

    Doctoral supervision[24]

  • mentor: Ferdinand von Lindemannstudent: Arnold Sommerfeld

    Doctoral supervision[24]

  • mentor: Arnold Sommerfeldstudent: Werner Heisenberg

    Doctoral supervision[25]

  • mentor: Arnold Sommerfeldstudent: Wolfgang Pauli

    Doctoral supervision[25]

  • mentor: Arnold Sommerfeldstudent: Karl Ferdinand Herzfeld

    Historical relationship[26]

  • mentor: Karl Ferdinand Herzfeldstudent: John Archibald Wheeler

    Doctoral supervision[26]

  • mentor: John Archibald Wheelerstudent: Richard Feynman

    Doctoral supervision[27]

Sources consulted

  1. LNCC · Relatório de gestão de 2023

    Record of Volpatto’s doctorate and Loula’s supervision.

  2. UFRJ · Tese de Abimael Loula (1979)

    The acknowledgments identify Luiz Bevilacqua as advisor.

  3. Luiz Bevilacqua · Registro curricular

    Curriculum reproduction recording Erastus H. Lee as advisor; this is not the original Stanford dissertation record.

  4. Plataforma Acácia · Erastus H. Lee

    Supplementary source for the Brazilian academic lineage.

  5. Stanford · History of Aeronautics and Astronautics

    Identifies Lee among Timoshenko’s doctoral students.

  6. National Academy of Engineering · Erastus H. Lee

    Biographical memorial on Lee’s education and work.

  7. Stanford · Timoshenko’s formative years

    Timoshenko’s stay with Prandtl in Göttingen; study, not doctoral supervision.

  8. TUM · August Föppl

    Working and mentoring relationship between Föppl and Prandtl.

  9. MacTutor · Ludwig Prandtl

    Distinguishes Föppl’s support from the thesis examination and describes the lack of formal supervision.

  10. Mathematics Genealogy Project · August Föppl

    Attributes supervision to Bruns and Klein. Retained as a disputed attribution rather than historical certainty.

  11. Deutsche Biographie · August Föppl

    Describes study with Wiedemann and a doctorate based on previous work; does not confirm the joint supervision listed by MGP.

  12. Mathematics Genealogy Project · Felix Klein

    Plücker and Lipschitz as advisors; Lindemann as a student.

  13. Mathematics Genealogy Project · Julius Plücker

    The Gerling–Plücker relationship.

  14. Mathematics Genealogy Project · Christian Ludwig Gerling

    The Gauss–Gerling relationship.

  15. Mathematics Genealogy Project · Bernhard Riemann

    Gauss’s supervision; Riemann appears as a collateral branch in this selection.

  16. Mathematics Genealogy Project · Rudolf Lipschitz

    The Dirichlet–Lipschitz relationship.

  17. Mathematics Genealogy Project · Dirichlet

    Lists Fourier and an honorary doctorate; the link is treated here as historical.

  18. Mathematics Genealogy Project · Joseph Fourier

    The link to Lagrange is interpreted as historical training, not a modern doctorate.

  19. TU Wien · Notes on academic genealogy

    Caveats about historical genealogy; Euler–Lagrange denotes correspondence and intellectual influence, not formal supervision.

  20. Mathematics Genealogy Project · Heinrich Bruns

    Weierstrass and Kummer as advisors; Hausdorff as a student.

  21. Mathematics Genealogy Project · Karl Weierstrass

    Supervision of Cantor and Schwarz.

  22. Mathematics Genealogy Project · Hermann Amandus Schwarz

    Weierstrass and Kummer as advisors; Fejér as a student.

  23. Mathematics Genealogy Project · Lipót Fejér

    Supervision of von Neumann and Erdős.

  24. Mathematics Genealogy Project · Ferdinand von Lindemann

    Links to Hilbert, Minkowski and Sommerfeld; these are collateral branches in this selection.

  25. Mathematics Genealogy Project · Arnold Sommerfeld

    Supervision of Heisenberg and Pauli. The relationship with Herzfeld is qualified separately by the biographical memoir.

  26. National Academy of Sciences · Karl Ferdinand Herzfeld

    Herzfeld earned his doctorate with Hasenöhrl, not Sommerfeld; he studied with Sommerfeld later and supervised Wheeler.

  27. MacTutor · Richard Feynman

    Wheeler’s supervision; Feynman is a collateral connection, not an ancestor of Volpatto.

  28. NIST DLMF · Gauss quadrature

    Reference for the Gauss highlight on numerical quadrature.

  29. MacTutor · Gaussian elimination and least squares

    Historical context on Gauss’s work on least squares; this does not imply sole authorship of the method.

  30. Jiří Lebl · Notes on Diffy Qs

    Section 1.7: numerical integration of ODEs using Euler’s method.

  31. Euler Archive · Principes généraux du mouvement des fluides

    Euler’s original paper on the equations of fluid motion.

  32. MacTutor · Lejeune Dirichlet

    Work on harmonic functions, boundary-value problems and potential theory.

  33. MacTutor · Joseph Fourier

    The heat diffusion equation and its solution using trigonometric series.

  34. MacTutor · Joseph-Louis Lagrange

    Contributions to calculus of variations and analytical mechanics.

And what difference does it make?

What does any of this mean for me, or for someone working with me? To me, nothing — but researching and building this tree was certainly fun. My thanks to the Mathematics Genealogy Project, Plataforma Acácia, MacTutor, the LNCC, UFRJ and Stanford archives, and the other sources listed above for preserving these stories.