The Genealogy of CAAM

Jay Raol

History and CAAM?

History in the wider sense is all that has happened, not merely all the phenomena of human life, but those of the

natural world as well. It includes everything that undergoes change; and as modern science has shown

that there is nothing absolutely static, therefore the whole universe, and every part of it, has its history

-1911 Encyclopædia Britannica

Sources

• The Mathematics Genealogy Project– http://www.genealogy.ams.org/index.html

• Biographical sketches– http://www-history.mcs.st-andrews.ac.uk/

Academic Genealogy

• Tree of advisors and their students

Robert BixbyCornell 1972

7/12Composition and Decompostion of

Matroids and Related Topics

Louis BilleraCUNY 1968

19/46On Cores and Bargaining Sets for N-Person Cooperative Games Without

Side Payments NameInstitution Year

# of students/decedentsThesis

Academic Genealogy

• Things to consider …– Pedigree– How are specialized fields created?– What’s the relationship between an advisor’s

thesis and his/her student’s thesis

Edward HydeCal Tech 2003

Fast, High-Order Methods for Scattering by Inhomogeneous

Media

Oscar BrunoNYU 1989

3/3The Effective Conductivity of an Infinitely Interchangeable

Mixture

Robert KohnPrinceton 1979

18/25New Estimates for

Deformations in Terms of Their Strains; I) Estimates of Wirtinger Type for Nonlinear Strains; II) Functions Whose

Linearized Strains are Measures

Frederick Almgren, Jr.Brown 1962

20/66The Homotopy Groups of the

Integral Cycle Groups

Herbert Federer U.C. Berkeley

9/107Surface Area

Anthony Perry Morse Brown 1937

15/147Convergence in Variation and

Related Topics

Clarence Adams Harvard 1922

8/222The General Theory of the Linear Partial q-Difference Equation and of the Linear

Partial Difference Equation of the Intermediate Type

George David Birkhoff U Chicago 1907

46/4120Asymptotic Properties of Certain

Ordinary Differential Equations with Applications to Boundary Value and

Expansion Problems

E. H. MooreYale 188531/9568

Extensions of Certain Theorems of Clifford and

Cayley in the Geometry of n Dimensions

Michel Chasles École Polytechnique 1814

2/12269perçu historique sur l'origine et

le développement des méthodes en géométrie

Siméon Denis PoissonÉcole Polytechnique 1800

2/32908

“Life is good for only two things, discovering

mathematics and teaching mathematics.”

Joseph Louis Lagrange

3/55590

Leonhard EulerUniversität Basel 1726

Johann and Jacob Bernoulli

Gottfried Leibniz Universität Altdorf 1666Disputatio Inauguralis De

Casibus Perplexis In Jure

Richard TapiaUCLA 1967

34/52A Generalization of Newton's Method with an Application to the Euler-Lagrange Equation

Magnus HestenesU Chicago 1932

35/154Sufficient Conditions for the General Problem of Mayer with Variable End-Points

Gilbert BlissU Chicago 1900

54/558The Geodesic Lines on the

Anchor Ring

Oskar Bolza Universität Göttingen 1886

10/648Über die Reduction

hyperelliptischer Integrale erster Ordnung und erster

Gattung auf elliptische, insbesondere über die Reduction durch eine

Transformation vierten Grades

C. Feilx Klein Universität Bonn 1868

55/21910 Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen

Linien-Koordinaten auf eine kanonische Form

Julius Plücker Universität Marburg 1823

1/21911Generalem analyeseos

applicationem ad ea quae geometriae altioris et mechanicae basis et

fundamenta sunt e serie Tayloria deducit

Christian GerlingUniversität Göttingen 1812

1/21912Methodi proiectionis

orthographicae usum ad calculos parallacticos

facilitandos explicavit simulque eclipsin solarem die

Carl GaussUniversität Göttingen 1799

7/29159Demonstratio nova theorematis omnem

functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus

resolvi posse

Abraham KaestnerUniversität Leipzig 1739

6/30607Theoria radicum in

aequationibus

Johann PfaffUniversität Göttingen

1786 2/29681

Commentatio de ortibus et occasibus siderum apud

auctores classicos commemoratis

Christian Hausen Universität Halle-Wittenberg 1713

2/30594De corpore scissuris figurisque non

cruetando ductu

Johann Wichmannshausen Universität Leipzig 1685

1/30595Disputationem Moralem De Divortiis

Secundum Jus Naturae

Otto Mencke Universität Leipzig 1665

2/30597Ex Theologia naturali -- De Absoluta Dei

Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo

Conspicuam

C. Feilx Klein Universität Bonn 1868

55/21910 Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen

Linien-Koordinaten auf eine kanonische Form

Rudolf Lipschitz Universität Berlin 1853

55/21911 Determinatio status magnetici viribus inducentibus commoti

in ellipsoide

Gustav Dirichlet Universität Bonn 1827

4/22680 Partial Results on Fermat's

Last Theorem

Jean Fourier École Polytechnique

4/22682

Steven CoxRPI 1988

Extremal Eigenvalue Problems for Composite Membranes

Joyce McLaughlinU.C. Riverside 1968

12Sturm Separation and

Comparison Theorems for Ordinary and Partial

Differential Equations

Joaquin Basilio Diaz Brown 1945

29On a Class of Partial

Differential Equations of Even Order

Lipman Bers Charles University 1938

218Potential/Harmonic Theory

Charles Loewner Charles University 1917

21/332Geometric Function Theory

Georg Alexander Pick Universität Wien 1880

4/336Über eine Klasse abelscher

Integrale

Leo Königsberger Universität Berlin 1860

35/436De motu puncti versus duo fixa

centra attracti

Ernst Kummer Halle-Wittenberg 1831

51/10910De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum

multiplicium evolv

Karl Weierstraß Universität Königsberg 1854

41/9348Zur Theorie der Abelschen

Functionen

Kummer and Weierstrass

• Nicolai Bugaev (1527)• Georg Cantor• Georg Frobenius (3780)• Lazarus Fuchs (3603)• Hermann Schwarz (3383)

• Carl Runge• Friedrich Shur

• Both men were originally teachers working as amateur mathematicians

• Both men descended from Gauss• Who did they advise?

A thought for the faculty

• Kummer's popularity as a professor was based mot only on the clarity of his lectures but on his charm and sense of humour as well. Moreover, he was concerned for the well-being of his students and willingly aided them when material difficulties arose...

-Biermann

Danny Sorensen U.C. San Diego 1977

4/336Updating the Symmetric

Indefinite Factorization with Applications in a Modified

Newton's Method

James Bunch U.C. Berkeley 1969

10/11On Direct Methods for Solving Symmetric Systems of Linear

Equations

Beresford Parlett Stanford 1962

25/43Bundles of Matrices and the Linear Indepence of Their Minors; II. Applications of Laguerre's Method to the

Matrix Eigenvalue Problem

George Forsythe Brown 1941

16/193Riesz Summabilitly Methods of Order r, for R (r) < 0, Cesaro Summability of Independent

Random Variables

Jacob Tamarkin Univ. of St. Petersburg 1917

28/755

Andrei Markov Univ. of St. Petersburg 1884

4/2786On Some Applications of

Algebraic Continuous Fractions

Pafnuty ChebyshevUniv. of St. Petersburg 1849

5/3581On Integration by Means of

Logarithms

Willi FellerUniversität Göttingen 1926

16/571Über algebraisch rektifizierbare

transzendente Kurven

Richard CourantUniversität Göttingen 1910

32/2160Über die Anwendung des

Dirichletschen Prinzipes auf die Probleme der konformen

Abbildung

David HilbertUniversität Königsberg 1885

73/11512Über invariante Eigenschaften

specieller binärer Formen, insbesondere der Kugelfunctionen

We must know, we shall know

C.L. LindemannUniv. Erlangen-Nürnberg 1873

47/14063Über unendlich kleine Bewegungen

und über Kraftsysteme bei allgemeiner projektivischer

Maßbestimmung

Jim Douglas Rice University 1952

41/186I. Two Equivalent Methods for

Sequences on Random Variables. II. The Expansion of

Measures on Series of Orthogonal Measures

Hugh Brunk Rice University 1944

7/240Some Generalizations for

Dirichlet Series of Hadamard's Theorem with Applications

Szolem Mandelbrojt Sorbonne 1923

7/498Some Generalizations for

Dirichlet Series of Hadamard's Theorem with Applications

Jacques Hadamard École Normale Supérieure Paris 1892

5/916Essai sur l'étude des fonctions données par

leur développment de Taylor

Charles PicardÉcole Normale Supérieure Paris 1877

7/3368Applications des complexes lineaires a

l'etude des surfaces et des courbes gauches

Jules TanneryÉcole Normale Supérieure Paris 1874

1/917Proprietes des integrales des equations

differentielles lineaires a coefficients variables

Charles Hermite