 Patrick Lincoln
(Stanford University, 1992), Computational Aspects of Linear Logic
 John Mitchell
(Massachusetts Institute of
Technology, 1984), Lambda Calculus Models of Typed Programming
Languages
 Albert Meyer
(Harvard University, 1972), On Complex
Recursive Functions
 Patrick Fischer
(Massachusetts Institute
of Technology, 1962), Theory of Provable Recursive Functions
 Hartley
Rogers, Jr. (Princeton
University, 1952), Some Results on Definability and Decidability in
Elementary Theories
 Alonzo
Church
(Princeton University, 1927), Alternatives to Zermelo's
Assumption
 Oswald
Veblen
(The University of Chicago, 1903), A System of Axioms for
Geometry
 Eliakim
Moore (Yale University, 1885), Extensions of Certain Theorems of
Clifford and Cayley in the Geometry
of n Dimensions
 Hubert
Anson Newton (Yale University, 1850). Newton may have never
properly completed a Ph.D., though he taught at Yale, was head of
the math department for many years, and published in higher
mathematics. Michael Chales has been claimed as a mentor of Newton,
but there is scant concrete evidence of an actual studentadvisor
relationship. So the remainder of this list is somewhat speculative.
 Michel
Chasles (École Polytechnique in Paris 1814)
 SiméonDenis
Poisson (École Polytechnique in Paris 1800)
 JosephLouis
Lagrange (could argue that PierreSimon Laplace was advisor of Poisson)

Leonhard
Euler (Universitt Basel 1726) Dissertatio physica de sono

Johann
Bernoulli (Universität Basel 1690/1694)
Dissertatio de effervescentia et fermentatione; Dissertatio Inauguralis
PhysicoAnatomica de Motu Musculorum
 Jacob
Bernoulli, (Universität Basel, 1684) Solutionem tergemini
problematis arithmetici, geometrici et astronomici

Gottfried Wilhelm Leibniz
, (Universitt Altdorf, 1666)
Disputatio Inauguralis De Casibus Perplexis In Jure

Christiaan Huygens , (Universit d'Angers 1647, 1655)

Frans van Schooten, Jr , (Universiteit Leiden 1635)
 There is a chain of claimed other studentadvisor relationships
on the mathematics genealogy project that continues:
Jacobus Golius (1612), Thomas Erpenius (1608), Joseph Justus Scaliger
(1563), Adrien Turnebe (1532), Jacques Toussain (1521), Guillaume Bude
(1486), Janus Lascaris (1472), Demetrios Chalcocondyles (1452), etc.
However, any genealogy dating back to the dark ages becomes vague.
(Sources: The
Mathematics Genealogy Project and MacTutor History
of Mathematics archive and
Brian Howard's home page)