[4] Traub was the author or editor of ten monographs and some 120 papers in computer science, mathematics, physics, finance, and economics.
[8] From 1971 to 1979 Traub headed the Computer Science Department at Carnegie Mellon during a critical period.
From 1986 to 1992 he served as founding Chair of the Computer Science and Telecommunications Board, National Academies and held the post again 2005–2009.
[9] Traub was founding editor of the Annual Review of Computer Science (1986–1990)[10] and Editor-in-Chief of the Journal of Complexity (1985–2015).
[4] Traub attended the Bronx High School of Science where he was captain and first board of the chess team.
After graduating from City College of New York he entered Columbia in 1954 intending to take a PhD in physics.
In 1955, on the advice of a fellow student, Traub visited the IBM Watson Research Lab at Columbia.
)[12][4] In 1959, Traub joined the Research Division of Bell Laboratories in Murray Hill, NJ.
Traub had the key insight that the optimal algorithm for solving a continuous problem depended on the available information.
[13] In 1966 Traub spent a sabbatical year at Stanford University where he met a student named Michael Jenkins.
[14][1] In 1970 Traub became a professor at the University of Washington and in 1971 he became Head of the Carnegie Mellon Computer Science Department.
[2] In the nineties he organized a series of Workshops on Limits to Scientific Knowledge funded by the Alfred P. Sloan Foundation.
[26] Starting in 1991 Traub was co-organizer of an international Seminar on "Continuous Algorithms and Complexity" at Schloss Dagstuhl, Germany.
The lectures appeared in expanded form as Complexity and Information, Cambridge University Press, 1998.
[28][29] In 1994 he asked a PhD student, Spassimir Paskov, to compare the Monte Carlo method (MC) with the Quasi-Monte Carlo method (QMC) when calculating a collateralized mortgage obligation (CMO) Traub had obtained from Goldman Sachs.
People in finance had always used MC for such problems and the experts in number theory believed QMC should not be used for integrals of dimension greater than 12.
Paskov and Traub reported their results to a number of Wall Street firms to considerable initial skepticism.
Moore's law is an empirical observation that the number of features on a chip doubles roughly every 18 months.
[4] The U.S. patents US5940810 and US0605837 were issued to Traub et al. for the FinDer Software System and were assigned to Columbia University.
These patents cover an application of a well known technique (low discrepancy sequences) to a well known problem (valuation of securities).