{
  "root": "volpatto",
  "updated": "2026-09-27",
  "scope": {
    "pt": "Recorte de orientação, estudo e mentoria, incluindo ramos colaterais. Distâncias mínimas apenas neste grafo, não em toda a rede acadêmica.",
    "en": "A selection of supervision, study and mentorship links, including collateral branches. Shortest distances within this graph only, not the entire academic network."
  },
  "people": [
    {
      "id": "volpatto",
      "name": "Diego Tavares Volpatto",
      "shortName": "Diego Volpatto",
      "contribution": "Numerical methods and computational thermodynamics.",
      "distance": 0,
      "ancestor": false
    },
    {
      "id": "loula",
      "name": "Abimael Fernando Duarte Loula",
      "shortName": "Abimael Loula",
      "contribution": "Finite element methods.",
      "distance": 1,
      "ancestor": true
    },
    {
      "id": "bevilacqua",
      "name": "Luiz Bevilacqua",
      "contribution": "Continuum mechanics and variational methods.",
      "distance": 2,
      "ancestor": true
    },
    {
      "id": "lee",
      "name": "Erastus H. Lee",
      "contribution": "Plasticity and viscoelasticity.",
      "distance": 3,
      "ancestor": true
    },
    {
      "id": "timoshenko",
      "name": "Stephen Timoshenko",
      "contribution": "Beam theory and solid mechanics.",
      "distance": 4,
      "ancestor": true
    },
    {
      "id": "prandtl",
      "name": "Ludwig Prandtl",
      "contribution": "Boundary-layer theory and fluid mechanics.",
      "distance": 5,
      "ancestor": true
    },
    {
      "id": "foppl",
      "name": "August Föppl",
      "contribution": "Applied mechanics and elasticity.",
      "distance": 6,
      "ancestor": true
    },
    {
      "id": "klein",
      "name": "Felix Klein",
      "contribution": "Geometry and the Erlangen program.",
      "distance": 7,
      "ancestor": true
    },
    {
      "id": "bruns",
      "name": "Heinrich Bruns",
      "contribution": "Mathematical astronomy and geodesy.",
      "distance": 7,
      "ancestor": true
    },
    {
      "id": "wiedemann",
      "name": "Gustav Heinrich Wiedemann",
      "contribution": "Experimental physics and thermal and electrical conduction.",
      "distance": 7,
      "ancestor": true
    },
    {
      "id": "plucker",
      "name": "Julius Plücker",
      "contribution": "Analytic geometry and line geometry.",
      "distance": 8,
      "ancestor": true
    },
    {
      "id": "gerling",
      "name": "Christian Ludwig Gerling",
      "contribution": "Astronomy and geodesy.",
      "distance": 9,
      "ancestor": true
    },
    {
      "id": "gauss",
      "name": "Carl Friedrich Gauss",
      "contribution": "Numerical quadrature and the method of least squares.",
      "distance": 10,
      "ancestor": true
    },
    {
      "id": "riemann",
      "name": "Bernhard Riemann",
      "contribution": "Riemannian geometry and analysis.",
      "distance": 11,
      "ancestor": false
    },
    {
      "id": "lipschitz",
      "name": "Rudolf Lipschitz",
      "contribution": "Analysis and differential equations.",
      "distance": 8,
      "ancestor": true
    },
    {
      "id": "dirichlet",
      "name": "Peter Gustav Lejeune Dirichlet",
      "shortName": "Peter G. L. Dirichlet",
      "contribution": "Boundary-value problems and potential theory.",
      "distance": 9,
      "ancestor": true
    },
    {
      "id": "fourier",
      "name": "Joseph Fourier",
      "contribution": "Heat conduction and Fourier series.",
      "distance": 10,
      "ancestor": true
    },
    {
      "id": "lagrange",
      "name": "Joseph-Louis Lagrange",
      "contribution": "Analytical mechanics and calculus of variations.",
      "distance": 11,
      "ancestor": true
    },
    {
      "id": "euler",
      "name": "Leonhard Euler",
      "contribution": "Euler’s method for ODEs and equations for inviscid flow.",
      "distance": 12,
      "ancestor": true
    },
    {
      "id": "weierstrass",
      "name": "Karl Weierstrass",
      "contribution": "Rigorous foundations of analysis.",
      "distance": 8,
      "ancestor": true
    },
    {
      "id": "kummer",
      "name": "Ernst Eduard Kummer",
      "contribution": "Algebraic number theory.",
      "distance": 8,
      "ancestor": true
    },
    {
      "id": "schwarz",
      "name": "Hermann Amandus Schwarz",
      "contribution": "Complex analysis and domain decomposition methods.",
      "distance": 9,
      "ancestor": false
    },
    {
      "id": "fejer",
      "name": "Lipót Fejér",
      "contribution": "Harmonic analysis and Fourier series.",
      "distance": 10,
      "ancestor": false
    },
    {
      "id": "neumann",
      "name": "John von Neumann",
      "contribution": "Applied mathematics and foundations of computing.",
      "distance": 11,
      "ancestor": false
    },
    {
      "id": "erdos",
      "name": "Paul Erdős",
      "contribution": "Combinatorics and number theory.",
      "distance": 11,
      "ancestor": false
    },
    {
      "id": "cantor",
      "name": "Georg Cantor",
      "contribution": "Set theory and transfinite numbers.",
      "distance": 9,
      "ancestor": false
    },
    {
      "id": "hausdorff",
      "name": "Felix Hausdorff",
      "contribution": "Topology and set theory.",
      "distance": 8,
      "ancestor": false
    },
    {
      "id": "lindemann",
      "name": "Ferdinand von Lindemann",
      "contribution": "Proof of the transcendence of π.",
      "distance": 8,
      "ancestor": false
    },
    {
      "id": "hilbert",
      "name": "David Hilbert",
      "contribution": "Foundations of mathematics and functional analysis.",
      "distance": 9,
      "ancestor": false
    },
    {
      "id": "minkowski",
      "name": "Hermann Minkowski",
      "contribution": "Geometry of numbers and the spacetime formulation.",
      "distance": 9,
      "ancestor": false
    },
    {
      "id": "sommerfeld",
      "name": "Arnold Sommerfeld",
      "contribution": "Atomic physics and quantum theory.",
      "distance": 9,
      "ancestor": false
    },
    {
      "id": "heisenberg",
      "name": "Werner Heisenberg",
      "contribution": "Quantum mechanics and the uncertainty principle.",
      "distance": 10,
      "ancestor": false
    },
    {
      "id": "pauli",
      "name": "Wolfgang Pauli",
      "contribution": "The exclusion principle in quantum mechanics.",
      "distance": 10,
      "ancestor": false
    },
    {
      "id": "herzfeld",
      "name": "Karl Ferdinand Herzfeld",
      "contribution": "Kinetic theory and molecular physics.",
      "distance": 10,
      "ancestor": false
    },
    {
      "id": "wheeler",
      "name": "John Archibald Wheeler",
      "contribution": "Nuclear physics and general relativity.",
      "distance": 11,
      "ancestor": false
    },
    {
      "id": "feynman",
      "name": "Richard Feynman",
      "contribution": "Quantum electrodynamics and path integrals.",
      "distance": 12,
      "ancestor": false
    }
  ],
  "edges": [
    {
      "from": "loula",
      "to": "volpatto",
      "kind": "doctoral",
      "sources": [
        "lncc"
      ]
    },
    {
      "from": "bevilacqua",
      "to": "loula",
      "kind": "doctoral",
      "sources": [
        "loula-thesis"
      ]
    },
    {
      "from": "lee",
      "to": "bevilacqua",
      "kind": "doctoral",
      "sources": [
        "bevilacqua-cv",
        "acacia"
      ]
    },
    {
      "from": "timoshenko",
      "to": "lee",
      "kind": "doctoral",
      "sources": [
        "stanford",
        "lee-memorial"
      ]
    },
    {
      "from": "prandtl",
      "to": "timoshenko",
      "kind": "historical",
      "sources": [
        "timoshenko"
      ]
    },
    {
      "from": "foppl",
      "to": "prandtl",
      "kind": "historical",
      "sources": [
        "foppl-tum",
        "prandtl-mactutor"
      ]
    },
    {
      "from": "klein",
      "to": "foppl",
      "kind": "disputed",
      "sources": [
        "foppl-mgp",
        "foppl-biography"
      ]
    },
    {
      "from": "bruns",
      "to": "foppl",
      "kind": "disputed",
      "sources": [
        "foppl-mgp",
        "foppl-biography"
      ]
    },
    {
      "from": "wiedemann",
      "to": "foppl",
      "kind": "historical",
      "sources": [
        "foppl-biography"
      ]
    },
    {
      "from": "plucker",
      "to": "klein",
      "kind": "doctoral",
      "sources": [
        "klein"
      ]
    },
    {
      "from": "lipschitz",
      "to": "klein",
      "kind": "doctoral",
      "sources": [
        "klein"
      ]
    },
    {
      "from": "gerling",
      "to": "plucker",
      "kind": "doctoral",
      "sources": [
        "plucker"
      ]
    },
    {
      "from": "gauss",
      "to": "gerling",
      "kind": "doctoral",
      "sources": [
        "gerling"
      ]
    },
    {
      "from": "gauss",
      "to": "riemann",
      "kind": "doctoral",
      "sources": [
        "riemann"
      ]
    },
    {
      "from": "dirichlet",
      "to": "lipschitz",
      "kind": "doctoral",
      "sources": [
        "lipschitz"
      ]
    },
    {
      "from": "fourier",
      "to": "dirichlet",
      "kind": "historical",
      "sources": [
        "dirichlet"
      ]
    },
    {
      "from": "lagrange",
      "to": "fourier",
      "kind": "historical",
      "sources": [
        "fourier"
      ]
    },
    {
      "from": "euler",
      "to": "lagrange",
      "kind": "historical",
      "sources": [
        "euler-lagrange"
      ]
    },
    {
      "from": "weierstrass",
      "to": "bruns",
      "kind": "doctoral",
      "sources": [
        "bruns"
      ]
    },
    {
      "from": "kummer",
      "to": "bruns",
      "kind": "doctoral",
      "sources": [
        "bruns"
      ]
    },
    {
      "from": "bruns",
      "to": "hausdorff",
      "kind": "doctoral",
      "sources": [
        "bruns"
      ]
    },
    {
      "from": "weierstrass",
      "to": "cantor",
      "kind": "doctoral",
      "sources": [
        "weierstrass"
      ]
    },
    {
      "from": "weierstrass",
      "to": "schwarz",
      "kind": "doctoral",
      "sources": [
        "schwarz"
      ]
    },
    {
      "from": "kummer",
      "to": "schwarz",
      "kind": "doctoral",
      "sources": [
        "schwarz"
      ]
    },
    {
      "from": "schwarz",
      "to": "fejer",
      "kind": "doctoral",
      "sources": [
        "schwarz"
      ]
    },
    {
      "from": "fejer",
      "to": "neumann",
      "kind": "doctoral",
      "sources": [
        "fejer"
      ]
    },
    {
      "from": "fejer",
      "to": "erdos",
      "kind": "doctoral",
      "sources": [
        "fejer"
      ]
    },
    {
      "from": "klein",
      "to": "lindemann",
      "kind": "doctoral",
      "sources": [
        "klein"
      ]
    },
    {
      "from": "lindemann",
      "to": "hilbert",
      "kind": "doctoral",
      "sources": [
        "lindemann"
      ]
    },
    {
      "from": "lindemann",
      "to": "minkowski",
      "kind": "doctoral",
      "sources": [
        "lindemann"
      ]
    },
    {
      "from": "lindemann",
      "to": "sommerfeld",
      "kind": "doctoral",
      "sources": [
        "lindemann"
      ]
    },
    {
      "from": "sommerfeld",
      "to": "heisenberg",
      "kind": "doctoral",
      "sources": [
        "sommerfeld"
      ]
    },
    {
      "from": "sommerfeld",
      "to": "pauli",
      "kind": "doctoral",
      "sources": [
        "sommerfeld"
      ]
    },
    {
      "from": "sommerfeld",
      "to": "herzfeld",
      "kind": "historical",
      "sources": [
        "herzfeld"
      ]
    },
    {
      "from": "herzfeld",
      "to": "wheeler",
      "kind": "doctoral",
      "sources": [
        "herzfeld"
      ]
    },
    {
      "from": "wheeler",
      "to": "feynman",
      "kind": "doctoral",
      "sources": [
        "feynman"
      ]
    }
  ],
  "sources": [
    {
      "id": "lncc",
      "title": "LNCC · Relatório de gestão de 2023",
      "url": "https://www.gov.br/lncc/pt-br/acesso-a-informacao/auditorias/relatorio_tcg_2023.pdf",
      "note": "Record of Volpatto’s doctorate and Loula’s supervision."
    },
    {
      "id": "loula-thesis",
      "title": "UFRJ · Tese de Abimael Loula (1979)",
      "url": "https://pantheon.ufrj.br/bitstream/11422/3579/1/152180.pdf",
      "note": "The acknowledgments identify Luiz Bevilacqua as advisor."
    },
    {
      "id": "bevilacqua-cv",
      "title": "Luiz Bevilacqua · Registro curricular",
      "url": "https://www.escavador.com/sobre/3616201/luiz-bevilacqua",
      "note": "Curriculum reproduction recording Erastus H. Lee as advisor; this is not the original Stanford dissertation record."
    },
    {
      "id": "acacia",
      "title": "Plataforma Acácia · Erastus H. Lee",
      "url": "https://www.plataforma-acacia.org/descendants/erastus-h-lee/",
      "note": "Supplementary source for the Brazilian academic lineage."
    },
    {
      "id": "stanford",
      "title": "Stanford · History of Aeronautics and Astronautics",
      "url": "https://web.stanford.edu/~cantwell/History_of_AA_at_Stanford_and_AA_Vision_2008/History_of_Aeronautics%20and%20Astronautics%20at%20Stanford%20-%2050th%20Anniversary%202008.pdf",
      "note": "Identifies Lee among Timoshenko’s doctoral students."
    },
    {
      "id": "lee-memorial",
      "title": "National Academy of Engineering · Erastus H. Lee",
      "url": "https://www.nationalacademies.org/read/12473/chapter/30",
      "note": "Biographical memorial on Lee’s education and work."
    },
    {
      "id": "timoshenko",
      "title": "Stanford · Timoshenko’s formative years",
      "url": "https://timoshenko.stanford.edu/formative",
      "note": "Timoshenko’s stay with Prandtl in Göttingen; study, not doctoral supervision."
    },
    {
      "id": "foppl-tum",
      "title": "TUM · August Föppl",
      "url": "https://www.mae.ed.tum.de/en/lww/history/foeppl-august/",
      "note": "Working and mentoring relationship between Föppl and Prandtl."
    },
    {
      "id": "prandtl-mactutor",
      "title": "MacTutor · Ludwig Prandtl",
      "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Prandtl/",
      "note": "Distinguishes Föppl’s support from the thesis examination and describes the lack of formal supervision."
    },
    {
      "id": "foppl-mgp",
      "title": "Mathematics Genealogy Project · August Föppl",
      "url": "https://www.mathgenealogy.org/id.php?id=71565",
      "note": "Attributes supervision to Bruns and Klein. Retained as a disputed attribution rather than historical certainty."
    },
    {
      "id": "foppl-biography",
      "title": "Deutsche Biographie · August Föppl",
      "url": "https://www.deutsche-biographie.de/gnd11663510X.html",
      "note": "Describes study with Wiedemann and a doctorate based on previous work; does not confirm the joint supervision listed by MGP."
    },
    {
      "id": "klein",
      "title": "Mathematics Genealogy Project · Felix Klein",
      "url": "https://www.mathgenealogy.org/id.php?id=7401",
      "note": "Plücker and Lipschitz as advisors; Lindemann as a student."
    },
    {
      "id": "plucker",
      "title": "Mathematics Genealogy Project · Julius Plücker",
      "url": "https://www.mathgenealogy.org/id.php?id=7402",
      "note": "The Gerling–Plücker relationship."
    },
    {
      "id": "gerling",
      "title": "Mathematics Genealogy Project · Christian Ludwig Gerling",
      "url": "https://www.mathgenealogy.org/id.php?id=29642",
      "note": "The Gauss–Gerling relationship."
    },
    {
      "id": "riemann",
      "title": "Mathematics Genealogy Project · Bernhard Riemann",
      "url": "https://www.mathgenealogy.org/id.php?id=18232",
      "note": "Gauss’s supervision; Riemann appears as a collateral branch in this selection."
    },
    {
      "id": "lipschitz",
      "title": "Mathematics Genealogy Project · Rudolf Lipschitz",
      "url": "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=19964",
      "note": "The Dirichlet–Lipschitz relationship."
    },
    {
      "id": "dirichlet",
      "title": "Mathematics Genealogy Project · Dirichlet",
      "url": "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=17946",
      "note": "Lists Fourier and an honorary doctorate; the link is treated here as historical."
    },
    {
      "id": "fourier",
      "title": "Mathematics Genealogy Project · Joseph Fourier",
      "url": "https://www.mathgenealogy.org/id.php?id=17981",
      "note": "The link to Lagrange is interpreted as historical training, not a modern doctorate."
    },
    {
      "id": "euler-lagrange",
      "title": "TU Wien · Notes on academic genealogy",
      "url": "https://dmg.tuwien.ac.at/goldstern/www/really.html",
      "note": "Caveats about historical genealogy; Euler–Lagrange denotes correspondence and intellectual influence, not formal supervision."
    },
    {
      "id": "bruns",
      "title": "Mathematics Genealogy Project · Heinrich Bruns",
      "url": "https://www.mathgenealogy.org/id.php?id=9712",
      "note": "Weierstrass and Kummer as advisors; Hausdorff as a student."
    },
    {
      "id": "weierstrass",
      "title": "Mathematics Genealogy Project · Karl Weierstrass",
      "url": "https://www.mathgenealogy.org/id.php?id=7486",
      "note": "Supervision of Cantor and Schwarz."
    },
    {
      "id": "schwarz",
      "title": "Mathematics Genealogy Project · Hermann Amandus Schwarz",
      "url": "https://www.mathgenealogy.org/id.php?id=7487",
      "note": "Weierstrass and Kummer as advisors; Fejér as a student."
    },
    {
      "id": "fejer",
      "title": "Mathematics Genealogy Project · Lipót Fejér",
      "url": "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7488",
      "note": "Supervision of von Neumann and Erdős."
    },
    {
      "id": "lindemann",
      "title": "Mathematics Genealogy Project · Ferdinand von Lindemann",
      "url": "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7404",
      "note": "Links to Hilbert, Minkowski and Sommerfeld; these are collateral branches in this selection."
    },
    {
      "id": "sommerfeld",
      "title": "Mathematics Genealogy Project · Arnold Sommerfeld",
      "url": "https://www.mathgenealogy.org/id.php?id=31357",
      "note": "Supervision of Heisenberg and Pauli. The relationship with Herzfeld is qualified separately by the biographical memoir."
    },
    {
      "id": "herzfeld",
      "title": "National Academy of Sciences · Karl Ferdinand Herzfeld",
      "url": "https://www.nationalacademies.org/read/10269/chapter/10",
      "note": "Herzfeld earned his doctorate with Hasenöhrl, not Sommerfeld; he studied with Sommerfeld later and supervised Wheeler."
    },
    {
      "id": "feynman",
      "title": "MacTutor · Richard Feynman",
      "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Feynman/",
      "note": "Wheeler’s supervision; Feynman is a collateral connection, not an ancestor of Volpatto."
    },
    {
      "id": "gauss-quadrature",
      "title": "NIST DLMF · Gauss quadrature",
      "url": "https://dlmf.nist.gov/3.5#v",
      "note": "Reference for the Gauss highlight on numerical quadrature."
    },
    {
      "id": "gauss-least-squares",
      "title": "MacTutor · Gaussian elimination and least squares",
      "url": "https://mathshistory.st-andrews.ac.uk/Miller/mathsym/matrices/",
      "note": "Historical context on Gauss’s work on least squares; this does not imply sole authorship of the method."
    },
    {
      "id": "euler-ode",
      "title": "Jiří Lebl · Notes on Diffy Qs",
      "url": "https://www.jirka.org/diffyqs/diffyqs.pdf",
      "note": "Section 1.7: numerical integration of ODEs using Euler’s method."
    },
    {
      "id": "euler-fluids",
      "title": "Euler Archive · Principes généraux du mouvement des fluides",
      "url": "https://scholarlycommons.pacific.edu/euler-works/226/",
      "note": "Euler’s original paper on the equations of fluid motion."
    },
    {
      "id": "dirichlet-biography",
      "title": "MacTutor · Lejeune Dirichlet",
      "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Dirichlet/",
      "note": "Work on harmonic functions, boundary-value problems and potential theory."
    },
    {
      "id": "fourier-biography",
      "title": "MacTutor · Joseph Fourier",
      "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Fourier/",
      "note": "The heat diffusion equation and its solution using trigonometric series."
    },
    {
      "id": "lagrange-biography",
      "title": "MacTutor · Joseph-Louis Lagrange",
      "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Lagrange/",
      "note": "Contributions to calculus of variations and analytical mechanics."
    }
  ],
  "locale": "en",
  "license": "CC BY 4.0",
  "interpretation": "Distances are calculated within this graph only. Paths through Klein or Bruns depend on the disputed attribution for Föppl. Euler–Lagrange denotes correspondence and intellectual influence. This is not a uniform chain of doctoral supervision."
}