Department of Mathematics

The Department of Mathematics at MIT seeks to improve upon its top ranking in both research and teaching by aggressively hiring the very best faculty, with special attention to the recruitment of top women and underrepresented minority candidates, and by continuing to serve the broad and varied educational needs of its graduate students, the mathematics majors, and all undergraduates of the Institute.


During the academic year 2002–2003, there were 375 undergraduates majoring in mathematics, 327 in Course 18 Mathematics and 48 in Course 18-C Mathematics/Computer Science. Bachelor of science degrees, including double majors, were awarded to 120 students, 108 in Course 18 and 12 in Course 18-C. There were a total of 120 graduate students in mathematics, all in the PhD program. This year, 20 students received the doctoral degree.

Faculty Changes

Professor emeritus Francis B. Hildebrand, who served on the mathematics faculty from 1940 to 1984, died in November 2002 at the age of 87. Professor Hildebrand was internationally recognized as an educator and publisher of curricular and reference texts in applied mathematics. In the 1940s, he developed the MIT subject Advanced Calculus for Engineers, and he subsequently published a text of the same title. These standardized the mathematics curriculum for the engineering and computational sciences, and they were adopted and emulated in top engineering departments worldwide. His text Methods in Applied Mathematics (1952) became a widely used reference, and his Introduction to Numerical Analysis (1956) was influential in positioning that study in the early stages of computer design.

Professor Peter W. Shor (from AT&T Labs-Research) will join the department as professor of applied mathematics. A recipient of the 1998 Nevanlinna Prize and the 2002 King Faisal International Prize in science, Professor Shor is a major figure in quantum computing and computational geometry.

Associate professor Lars Hesselholt received tenure; he specializes in algebraic topology and K-theory.

Assistant professors Martin Bazant (fluid dynamics), Hubert Bray (differential geometry), András Vasy (geometric analysis), and Santosh Vempala (theoretical computer science) were promoted to associate professor.

CLE (Core Language Engine) Moore instructor Jason Starr (algebraic geometry) was promoted to assistant professor, and Dr. Kiran Kedlaya will join the department as assistant professor. Specialized in arithmetic algebraic geometry, Dr. Kedlaya is currently a visiting assistant professor at UC Berkeley.

Associate professor Sara Billey resigned from MIT for a faculty position at the University of Washington.

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These facultywill continue to chair the following committees: Professor Michael Artin as chair of the Undergraduate Committee, associate professor Pavel Etingof as chair of the Graduate Student Committee, Professor David Jerison as chair of the Pure Mathematics Committee, Professor Ruben Rosales as chair of the Applied Mathematics Committee, and Professor Michael Sipser as chair of the Committee of Advisors.

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Here are a few snippets from the great range of research underway in the department.

Professor Steven Kleiman, with Eduardo Esteves, established Jouanolou's conjecture of 1979 that, for any Pfaff system of algebraic differential equations, even if not completely integrable, the singular set meets the solution set in a nonempty subset of co-dimension 1.

Professor Gerald Sacks is continuing work on necessary properties of counterexamples of Vaught's conjecture by attempting to extend them to weakly scattered theories.

Professor Daniel Stroock's book, Markov Processes from K. Itô's Perspective, appeared as volume 155 in the Annals of Mathematics Studies series, published by the Princeton University Press.

Professor Gang Tian has continued to develop the regularity theory for the Yang-Mills equation, proving with T. Tao a sharp removable singularity theorem for Yang-Mills connections in any dimension. In addition, together with X. H. Zhu, he proved the uniqueness of Kahler-Ricci solitons on any compact Kahler manifold. With J. Cheeger, he proved that the singular set of a solution of the Einstein equations with special holonomy has co-dimension at least 4. This is a fundamental result.

Associate professor John Bush—with graduate students David Hu (mathematics) and Brian Chan (mechanical engineering)—has discovered how one of the most common water-walking insects, the water strider, propels itself along the water surface. Their experimental study, conducted in the Applied Math Laboratory, changes the previously accepted understanding by showing that the principal momentum transfer is in subsurface vortices rather than waves. This work will appear in the August 7 issue of Nature.

Assistant professor Martin Bazant created the Dry Fluids Laboratory for experiments on granular flows and the Applied Mathematics Computational Laboratory for large-scale simulations. With these resources, he has been developing a mathematical theory of diffusion in dense granular flows. He also discovered a new physical phenomenon—induced-charge electro-osmosis—which has useful microfluidic applications.

Assistant professor Santosh Vempala found that the hit-and-run random walk "mixes rapidly," starting from any interior point of a convex body (in n-dimensional Euclidean space). This is the first geometric random walk known to have this property.

Seven MIT undergraduates participated with four mathematics graduate-student mentors in the department's sixth Summer Program in Undergraduate Research, which offers a six-week program of full-time research experience, culminating in written papers and lectures to faculty.

Summer 2002 was the tenth year of the Mathematics Department's participation in the Research Science Institute (RSI) program for gifted high school students, in which seven mathematics graduate students and one visiting faculty member mentored 13 high school students from the United States and abroad for a five-week period. Two of the mentored students went on to become third- and sixth-place finalists in the Intel Science Talent Search for 2002, and a third was the first-place winner of the national Siemens Westinghouse Competition in Math, Science and Technology. The projects submitted to these competitions by these finalists were based on their work in RSI.

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Honors, Prizes, and Awards

Professor Victor Guillemin received the Leroy P. Steele Prize for Lifetime Achievement of the American Mathematical Society. The citation reads, in part, for "fundamental contributions to microlocal analysis, symplectic group actions, and spectral theory of elliptic operators on manifolds."

Professor George Lusztig was awarded the Romanian National Order "Faithful Service" grade of commander for his contributions to mathematics.

Professor Richard Stanley received the 2003 Rolf Schock Prize in mathematics of the Royal Swedish Academy of Sciences "for his fundamental contributions to combinatorics and its relationship to algebra and geometry."

Professor Gilbert Strang was selected as chair of the US National Committee on Mathematics, 2003–2004, which "represents U.S. interests in the International Mathematical Union (IMU) and promotes the advancement of the mathematical sciences in the United States and throughout the world."

Associate professor Daniel Spielman was jointly awarded the 2002 Information Theory Society Paper Award for his publication in the February 2001 IEEE Transactions on Information Theory special issue on "Codes on Graphs and Iterative Decoding."

Assistant professor Alexander Postnikov received an Alfred P. Sloan Research Fellowship.

Turning to graduate students, the Housman Graduate Student Teaching Award was presented to Peter Clifford, Alberto De Sole, and Peter McNamara for their exceptional skill and dedication to teaching. Vasiliy Dolgushev and Peter McNamara were awarded the Charles W. and Jennifer C. Johnson Prize for an outstanding research paper accepted in a major journal by a graduate student in mathematics. The Clay Mathematics Institute selected Alberto De Sole and Eun Soo Lee for its Liftoff postdoctoral research program for summer 2003. Mohammad Mahdian was selected as a Microsoft fellow for the next two years and offered a 12-week paid internship with Microsoft Researchers.

Senior Ivan Petrakiev was awarded the Jon A. Bucsela Prize in mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, 32 were elected to Phi Beta Kappa.

The MIT Mathematics team, comprised of sophomore Reid Barton, junior David Pritchard, and sophomore Nikolay Andreev, finished among the top 10 teams in the William Lowell Putnam Intercollegiate Mathematical Competition. Reid Barton and senior Deniss Cebikins were among the five highest ranking individuals in the competition and were therefore designated Putnam fellows. MIT had 2 other individual scores in the top 23, and another 10 individuals were given Honorable Mention for finishing in the top 66.

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The project "Computer Aided Teaching of Mathematics," developed by Professors David Jerison, Haynes Miller, and Gilbert Strang with the support of the D'Arbeloff Grant, is making considerable progress and setting a high standard for mathematics courseware design. The goals are twofold: to broaden the active learning experiences of the classroom through visualization tools that can be student manipulated and to design tools to interact closely with other MIT courses so that students can use them throughout their MIT educational careers.

A new laboratory-style subject is being developed, modeled partly on a similar subject given at Cambridge University, and it will be offered for the first time next spring. Students will perform experiments on topics selected from an authorized list, typically using computer models, and write up the results as laboratory reports, presenting at least one report orally.

The Mathematics Department has developed an exciting plan for implementing the new Communications Requirement. We expect that roughly 150 students will enroll in communication-intensive (CI) mathematics subjects each year. Several subjects already in place qualify for CI status: our writing tutorial, three undergraduate seminars, and subject 18.413 Error-Correcting Codes Laboratory, given for the first time last year. These subjects serve approximately 60 students each year. The remaining students will be served by three additions to our program: an increase from three to five or six in the number of undergraduate seminars that we offer each year, the laboratory course mentioned above, and some subjects that emphasize writing of mathematics that will be offered concurrently with the subjects 18.100A, 18.100B Analysis, and 18.310 Principles of Applied Mathematics.

David A. Vogan Jr.
Department Head
Professor of Mathematics

More information about the Mathematics Department can be found on the web at


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