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Every mathematician begins as an apprentice (graduate student) and has a teacher (his/her advisor). An apprentice then becomes a teacher and has his/her own apprentices. This forms a chain, a mathematical genealogy. Here is my mathematical genealogy from The Mathematics Genealogy Project. (To the right are the university and the year the person earned his Ph.D.)
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Erhard Weigel (Universitat Leipzig 1650)
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Gottfried Leibniz (Universitat Altdorf 1666)
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Jacob Bernoulli
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Johann Bernoulli (1694)
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Leonhard Euler (Universitat Basel 1726)
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Joseph Louis Lagrange
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Simeon Denis Poisson
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Michel Chasles (Ecole Polytechnique 1814)
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Hubert Anson Newton (B.S. Yale University 1850)
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Eliakim Hastings Moore (Yale University 1885)
& Oswald Veblen (University of Chicago 1903)
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Robert Lee Moore (University of Chicago 1905)
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John Robert Kline (University of Pennsylvania 1916)
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Donald Alexander Flanders (University of Pennsylvania 1927)
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Jacob Wolfowitz (New York University 1942)
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Jack Carl Kiefer (Columbia University 1952)
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Lawrence D. Brown (Cornell University 1964)
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T. Tony Cai (Cornell University 1996)