Career
In 1959 Traub joined the Research Division of Bell Laboratories in Murray Hill, NJ. One day a colleague asked him how to compute the solution of a certain problem. Traub could think of a number of ways to solve the problem. What was the optimal algorithm, that is, a method which would minimize the required computational resources? To his surprise, there was no theory of optimal algorithms. (The phrase computational complexity, which is the study of the minimal resources required to solve computational problems was not introduced until 1965.) Traub had the key insight that the optimal algorithm for solving a continuous problem depended on the available information. This was to eventually lead to the field of information-based complexity. The first area for which Traub applied his insight was the solution of nonlinear equations. This research led to the 1964 monograph Iterative Methods for the Solution of Equations, which is still in print.
In 1966 he spent a sabbatical at Stanford where he met a student named Michael Jenkins. Together they created the Jenkins-Traub Algorithm for Polynomial Zeros. This algorithm is still one of the most widely used methods for this problem and is included in many textbooks.
In 1970 he became a professor at the University of Washington and in 1971 he became Head of the Carnegie Mellon Computer Science Department. The Department was quite small including Gordon Bell, Nico Haberman, Allen Newell, Raj Reddy, Herbert A. Simon, and William Wulf. Just prior to 1971 many faculty had left the Department to take positions elsewhere. Those professors who remained formed a core of world-class scientists recognized as leaders of the discipline. By 1978 the Department had grown to some 50 teaching and research faculty.(See Joseph Traub digital archive at Carnegie Mellon.)
One of Traub's PhD students was H. T. Kung, now a chaired professor at Harvard. They created the Kung-Traub algorithm for comparing the expansion of an algebraic function. They showed that computing the first terms was no harder than multiplying two -th degree polynomials. This problem had been worked on by Isaac Newton who missed a key point.
In 1973 he invited Henryk Woźniakowski to visit CMU. They pioneered the field of information-based complexity, co-authoring three monographs and numerous papers. Woźniakowski is now a tenured professor at both Columbia and the University of Warsaw, Poland.
In 1978, while on sabbatical at Berkeley, he was recruited by Peter Likins to become founding Chairman of the Computer Science Department at Columbia and Edwin Howard Armstrong Professor of Computer Science. He served as chair 1979-1989.
In 1980 he co-authored A General Theory of Optimal Algorithms, Academic Press, with Woźniakowski. This was the first research monograph on information-based complexity. Greg Wasilkowski joined Traub and Woźniakowski in two more monographs Information, Uncertainty, Complexity, Addison-Wesley, 1983, and Information-Based Complexity, Academic Press, 1988.
In 1985 Traub became founding Editor-in-Chief of the Journal of Complexity. This was probably the first journal which had complexity in the sense of computational complexity in its title. Starting with two issues and 285 pages in 1985 the Journal now publishes six issues and nearly 1000 pages. Traub continues as Editor-in-Chief.
In 1986, he was asked by the National Academies to form a Computer Science Board. The original name of the Board was the Computer Science and Technology Board (CSTB). Several years later CSTB was asked to also be responsible for telecommunications so it was renamed the Computer Science and Telecommunications Board, preserving the abbreviation CSTB. The Board deals with critical national issues in computer science and telecommunications. Traub served as founding chair 1986-1992 and is again serving as chair starting in 2005.
In 1990 Traub taught in the summer school of the Santa Fe Institute(SFI). He has since played a variety of roles at SFI. In the nineties he organized a series of Workshops on Limits to Scientific Knowledge funded by the Alfred P. Sloan Foundation. The goal was to enrich science in the same way that the work of Gödel and Turing on the limits of mathematics enriched that field. There were a series of Workshops on limits in various disciplines: physics, economics, and geophysics. Currently he is an External Professor at SFI.
Starting in 1991 Traub has been co-organizer of an international Seminar on "Continuous Algorithms and Complexity" at Schloss Dagstuhl, Germany. The ninth Seminar was held in September 2006. Many of the Seminar talks are on information-based complexity and more recently on continuous quantum computing.
Traub was invited by the Accademia Nazionale dei Lincee in Rome, Italy, to present the 1993 Lezione Lincee. He chose to give the cycle of six lectures at the Scuola Normale in Pisa. He invited Arthur Werschulz to join him in publishing the lectures. The lectures appeared in expanded form in Complexity and Information, Cambridge University Press, 1998.
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. This involved the numerical approximation of a number of integrals in dimensions. To the surprise of the research group Paskov reported that QMC always beat MC for this problem. 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 . Paskov and Traub reported their results to a number of Wall Street firms to considerable initial skepticism. They first published the results in Paskov and Traub Faster Evaluation of Financial Derivatives, Journal of Portfolio Management 22, 1995, 113-120. The theory and software was greatly improved by Anargyros Papageorgiou. Today QMC is widely used in the financial sector to value financial derivatives. QMC is not a panacea for all high dimensional integrals. Research is continuing on the characterization of problems for which QMC is superior to MC.
In 1999 Traub received the Mayor's medal for Science and Technology. Decisions regarding this award are made by the New York Academy of Sciences. The medal was awarded by Mayor Rudy Giuliani in a ceremony in Gracie Mansion, the home of New York City's mayor.
Moore's law is an empirical observation that the number of features on a chip doubles roughly every 18 months. This has held since the early 60s and is responsible for the computer and telecommunications revolution. It is widely believed that Moore's law will cease to hold in 10–15 years using silicon technology. There is therefore interest in creating new technologies. One candidate is quantum computing. That is building a computer using the principles of quantum mechanics. Traub and his colleagues decided to work on continuous quantum computing. The motivation is that most problems in physical science, engineering, and mathematical finance have continuous mathematical models.
In 2005 Traub donated some 100 boxes of archival material to the Carnegie Mellon University Library. This collection is being digitized.
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