Mathematical Genealogy

My Ph.D. is in economics, not in mathematics, but I did write a master’s thesis in differential topology, some of which was published in: Transversality and the Inverse Image of a Submanifold with Corners. Mathematica Scandinavica 49 (1981), 211-221.

My thesis advisor was Vagn Lundsgaard Hansen, then at the University of Copenhagen, now at the Technical University of Denmark. Through him, I trace my mathematical ancestry back to Birkhoff, and possibly all the way back to Poisson, Lagrange, Euler, Johan and Jacob Bernoulli, and, finally, Leibnitz.

Apart from being my advisor, Lundsgaard Hansen was also my teacher in first-year undergraduate mathematical analysis. The course started with an unforgettably vivid exposition of the topology of metric spaces — pulling back open and closed sets and mapping compact sets forward and so on. Later on I took his course in algebraic topology, where the main agenda was to use category theory to translate topological questions into easier algebraic ones.

Category theory was apparently invented by Samuel Eilenberg together with Saunders Mac Lane.

Samuel Eilenberg

Samuel Eilenberg

This bust of Samuel Eilenberg stands in the corner of the Faculty Lounge in the Columbia Mathematics Department. Eilenberg was a professor in the department from 1947 and until his retirement in 1982.

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