Mazur and Golomb Awarded National Medal of Science

On December 21, 2012, President Obama an- new ideas and techniques into number theory that nounced the recipients of the National Medal of have changed the direction of the subject. With Science for 2011. Among the twelve honorees are Swinnerton-Dyer he was the first to introduce two mathematicians: Barry Mazur of Harvard p-adic L-functions for modular forms, a subject University and Solomon Golomb of the University that has received enormous attention ever since. of Southern California. His 1977 Eisenstein ideal paper marked a turning point in the number theoretic applications of the Barry Mazur detailed arithmetic algebraic geometry of modular Barry Mazur was honored for “original and land- curves. In the mid-1980s Mazur introduced the mark contributions to differential topology, num- deformation theory of Galois representations, a ber theory, and arithmetic algebraic geometry, simple, but extremely powerful, idea that trans- where, among other applications, his work was formed number theory. This proved to be key to foundational to Wiles’ proof of Fermat’s last Wiles’ proof of Fermat’s last theorem. A few years theorem and for his dedication to communicating later, with Coleman, he introduced many new subtle mathematical ideas to the broader public.” p-adic families of modular forms (‘the eigencurve’), The Notices asked which continue to be a major topic of research. As D. Kotschick of Ludwig- important as Mazur’s mathematical contributions Maximilians-Universität are his remarkable contributions as a mentor. München and R. L. Taylor He has advised dozens of graduate students and of the Institute for Ad- postdocs, including many of the most successful vanced Study to comment number theorists of the last thirty-five years.” on the work of Mazur. Barry Mazur was born in New York City and, They responded: “Barry under the direction of Ralph Fox, received his Ph.D. Mazur is a mathematician from Princeton University in 1959. At the time he of extraordinary breadth received his degree, he had already proven the and originality. He started

Photos: Ryan K. Morris/National Science generalized Schoenflies conjecture in geometric his career in topology, topology. He was a research fellow at the Institute & Technology Medals Foundation. where he discovered what for Advanced Study from 1958 to 1959, and in Barry Mazur and President are now called Mazur man- 1959 he published his first four papers. He was Obama at National Medal ifolds. His achievements a Junior Fellow at Harvard from 1959 to 1962. ceremony, December 2012. include a proof of the He became an assistant professor at Harvard in generalized Schoenflies 1962 and is currently the Gerhard Gade University theorem and a proof of the s-cobordism theorem. Professor and a Senior Fellow. His other honors in- Mazur was the first to formalize certain arguments clude the Veblen Prize (1965), the Cole Prize (1982), using infinite repetitions, which are designed to the Chauvenet Prize (1994), and the Steele Prize push difficulties off to infinity. This is now referred (1999). He was elected a member of the National to as the ‘Mazur swindle’. Academy of Sciences in 1982 and of the American “In the late 1960s Mazur’s interests evolved Philosophical Society in 2001. He is the author toward number theory. Here he made a series of of the book Imagining Numbers (Particularly the fundamental contributions, such as his work on Square Root of Minus Fifteen) (Farrar, Straus and Katz’s conjecture, his classification of the possible Giroux, 2003), and coauthor of Universal Extensions rational torsion points on an elliptic curve, and his proof (with Wiles) of the main conjecture of and One Dimensional Crystalline Cohomology with Iwasawa theory. Mazur has repeatedly introduced William Messing (Lecture Notes in Mathematics, Springer, 1974) and of Kolyvagin Systems with Karl DOI: http://dx.doi.org/10.1090/noti1020 Rubin (Memoirs of the AMS, 2004).

758 Notices of the AMS Volume 60, Number 6 Solomon W. Golomb mathematician and later Golomb was honored with the National Medal of supervisor of the research Science for his “pioneering work in shift register group and assistant chief of sequences that changed the course of communi- the Telecommunications Re- cations from analog to digital and for numerous search Section. In the latter innovations in reliable and secure space, radar, position he played a key role cellular, wireless and spread-spectrum commu- in formulating the design of nications.” deep-space communications The Notices asked Alfred W. Hales to comment for the subsequent lunar on the work of Golomb. Hales is a professor emeri- and planetary explorations. tus at the University of California Los Angeles and He joined the University of is currently with the Center for Communications Southern California in 1963. Research of the Institute for Defense Analyses. In 1992 he received the Solomon Golomb and President Hales responded: “For the past fifty-plus years, medal of the U.S. National Obama. Solomon Golomb has been a world leader in the Security Agency for his re- search. He has also been the recipient of the Lo- development and application of mathematics for monosov Medal of the Russian Academy of Science communications and coding theory, especially and the Kapitsa Medal of the Russian Academy of digital and space communications. In his remark- Natural Sciences. His honors from the IEEE include able career, first at the Jet Propulsion Laboratory the Shannon Award (1985) and the Richard W. and then at the University of Southern California Hamming Medal (2000) for his exceptional con- (in electrical engineering and mathematics), his tributions to information sciences and systems. research contributions have ranged over a wide He was awarded the USC Presidential Medallion in spectrum of science and technology. Perhaps he is 1985. He has been a major contributor in coding best known for his mathematical analysis of shift and information theory for more than forty years register sequences in his classic book with that and is recognized for his ability to apply advanced title and in numerous journal publications—such mathematics to problems in digital communica- sequences are ubiquitous in radar, space commu- tions. His books include Shift Register Sequences nications, cryptography, cell phones, etc. Other (Holden-Day, 1967), Polyominoes (Princeton Uni- noteworthy contributions in this direction include versity Press, 2nd ed., 1996), and Signal Design for Golomb (entropy) coding, Golomb rulers, and the Good Correlation (coauthored with Guang Gong, Golomb construction for Costas arrays. For all this Cambridge University Press, 2005). He is a member work the IEEE has honored him with both its Ham- of the National Academy of Engineering, the Insti- ming Medal and the Shannon Award in Information tute of Electrical and Electronics Engineers (IEEE), Theory. Golomb’s Harvard Ph.D. was in analytic the American Association for the Advancement number theory, and he has extensive (and seminal) of Science (AAAS), and a fellow of the AMS. He publications in number theory, combinatorics, became a foreign member of the Russian Academy algebra, and various other fields (including even of Natural Science in 1994. molecular genetics). He is also a noted expert in mathematical game theory (polyominoes were his About the Medal invention), and he continues to publish a number The National Medal of Science is the country’s of puzzle columns in various journals. In addi- highest distinction for contributions to scientific tion to his many research contributions, Golomb research. According to a news release from the has had a great influence on future generations Office of Science and Technology Policy, “The through his generous and insightful mentoring of National Medal of Science honors individuals young people—his students, postdocs, and many for pioneering scientific research in a range of others.” fields, including physical, biological, mathemati- Solomon Golomb was born in Baltimore, Mary- cal, social, behavioral, and engineering sciences, land. He received his B.A. from Johns Hopkins that enhances our understanding of the world University and his Ph.D. in mathematics from and leads to innovations and technologies that Harvard University in 1957 under the direction of give the United States its global economic edge.” David Widder. He is currently professor of elec- The National Science Foundation administers the trical engineering at the University of Southern award, which was established by Congress in 1959. California and is best known to the general public and fans of mathematical games as the inventor — Elaine Kehoe of polyominoes, the inspiration for the computer game Tetris. While he was working toward his Ph.D. he held a Fulbright Fellowship at the University of Oslo. He worked at the Jet Propulsion Laboratory at the California Institute of Technology from 1956 to 1963, where he was a senior research

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