2014 Chern Medal Awarded

On August 13, 2014, the Chern Medal prise the world over through his extensive work on Award was presented at the open- science policy, through his leadership of the Insti- ing ceremonies of the International tute for Advanced Study for more than a decade, and Congress of (ICM) through his work on behalf of science in the developing in Seoul, Korea. The awardee was world. To have contributed at such a high level to Phillip Griffiths of the Institute so many different aspects of mathematical and for Advanced Study “for his ground- scientific life is truly extraordinary. breaking and transformative develop- Right after he received his Ph.D. from Princeton ment of transcendental methods in University in 1962, under the direction of Don- complex , particularly his ald Spencer, Griffiths went to the University of seminal work in and California Berkeley, where he was a Miller Fellow. periods of algebraic varieties.” There he came into contact with Shiing-Shen Chern Photo courtesy of IMU. The Chern Medal Award was insti- (1911–2004). One of the towering figures of twen- Phillip Griffiths tuted in 2010 in memory of the out- tieth-century , Chern was a geometer standing Shiing-Shen of wide interests and deep insights. He also had Chern. It is awarded jointly with the Chern Medal a profound sense of responsibility for developing Foundation (CMF) to an individual whose lifelong the culture and community of mathematics. He outstanding achievements in the field of math- made a lasting impression on the young Griffiths. ematics warrant the highest level of recognition. The two became collaborators and lifelong friends. Shiing-Shen Chern devoted his life to mathemat- In his mathematics research, Griffiths is known ics, both in active research and education, and not so much for having proved big theorems or for in nurturing the field whenever the opportunity things named after him, though he certainly has arose. He obtained fundamental results in all the both. Rather, he is known more for pioneering new major aspects of modern geometry and founded approaches or strategies that have proven very the area of global . Chern fruitful, for developing connections between areas exhibited keen aesthetic tastes in his selection of that had previously seemed unrelated, and for problems, and the breadth of his work deepened opening new lines of research that he and others the connections of modern geometry with different then pursued. Robert Bryant of , areas of mathematics. who served as chair of the 2014 Chern Medal selec- The award consists of a medal and a monetary tion committee, noted that Griffiths has the ability, prize of US$500,000. It is required that half of despite the formidable technical machinery used the award be donated to organizations of the in his work, to hold fast to the intuitive heart of recipient’s choice to support research, education, the problem at hand. “Even when mathematicians outreach, or other activities to promote mathemat- discuss very abstract geometric concepts, they ics. Chern was generous during his lifetime in his often speak as though there are tangible objects personal support of the field, and it is hoped that being represented and attach an almost physical this philanthropy requirement for the promotion sense to them,” said Bryant. “Exactly how this sort of mathematics will set the stage and the standard of metaphorical sense contributes to our under- for mathematicians to continue this generosity on standing of the concepts is mysterious, but it is a personal level. The inaugural Chern Medal was frequently the hallmark of great insight. Griffiths awarded in 2010 to Louis Nirenberg. has an amazingly strong ability to invoke those Phillip Griffiths is a singular figure in math- kinds of intuitions and to communicate them to ematics. For more than fifty years he has been a others.” leader in research, making contributions at the One of Griffiths’s great contributions has been to perceive this intuition in the work of past highest level in several areas, most notably alge- mathematical masters and reinterpret it in mod- braic geometry and differential geometry. He has ern terms. For example, mathematicians looked also been an outstanding teacher and mentor for askance at the work of the Italian school of alge- young people entering mathematics. His exposition braic geometry of the late nineteenth and early has garnered accolades, and his books have had twentieth centuries because the work did not a lasting influence. On top of these contributions conform to new standards of rigor that arose af- to the field of mathematics, Griffiths has had a terward. The Italian algebraic geometers neverthe- substantial impact on the entire scientific enter- less had a genius for geometric intuition. Griffiths DOI: http://dx.doi.org/10.1090/noti1178 imbibed this intuition and made it precise, using

1236 Notices of the AMS Volume 61, Number 10 modern techniques. He also absorbed and revived While no one has yet proved the Hodge Conjec- interest in the work of Elie Cartan (1869–1951) ture, Griffiths’s work has been a potent force in on exterior differential systems. While it was full shedding light on the contours of that problem of tremendous insights, Cartan’s work had been and shaping much of the research that has been neglected because it was difficult to read and had done on it. not been put into a systematic framework. After Often mathematicians are categorized as Griffiths and his collaborators developed and “problem solvers” or “theory builders”; Griffiths expanded on ideas from Cartan’s work, exterior does not quite fit into either group. “He’s an ‘un- differential systems went on to have a significant derstander’,” said Bryant. “He wants to understand impact on the theory of partial differential equa- where an idea can go, its connections to other tions. “There was a kernel of beautiful geometric ideas, and how it might illuminate a problem he’s ideas that ran through these classic works and— considering.” This drive to understand has made once you got through the old-fashioned language Griffiths an excellent communicator, not only and notations—an extraordinary relevance to mod- among fellow researchers but with students as ern problems,” said Mark Green of the University well. He has had twenty-nine Ph.D. students, many of California at Los Angeles. “Griffiths was a great of whom have gone on to outstanding careers believer in the power of deep geometric ideas, and themselves; altogether, he has about four hundred he encouraged his students to engage with these sixty doctoral “descendants.” Griffiths’s math- classic books and papers.” ematical writing is known for its clarity and polish Four volumes of the selected works of Griffiths as well as for the way it opens new directions for have appeared: on analytic geometry, algebraic research. A prominent example is his paper “Peri- geometry, variations of Hodge structures, and dif- ods of integrals on algebraic manifolds,” which ap- ferential systems. There is also ample material for peared in the Bulletin of the American Mathemati- a fifth volume, which is under consideration. This cal Society in 1970 and received the AMS Steele staggering output ranges over an enormous vari- Prize the following year. His books have also had a ety of topics. Nevertheless, one can still perceive wide influence, particularly Principles of Algebraic some unifying and powerful geometric ideas that Geometry, written with his former Ph.D. student run through his work. An example can serve to il- Joseph Harris. Universally known by the shorthand lustrate the nature of these ideas. A fundamental “Griffiths and Harris,” this textbook has become distinction in mathematics is between algebraic a standard reference for generations of students. functions, such as the square root of x, and tran- After his Miller Fellowship at the University scendental functions, such as sine and cosine, of California Berkeley, Griffiths became a faculty which cannot be expressed algebraically. An im- member there. In 1967 he moved to Princeton Uni- portant insight that emerged in versity and in 1972 to Harvard. His appointment in over the course of the nineteenth century is that 1983 as provost of Duke University began his work objects described in terms of algebraic equations in administration, which, surprisingly, did not slow can be productively studied using transcendental down at all his research output. In 1991 he became functions; this gives rise to the subject known as director of the Institute for Advanced Study (IAS) transcendental algebraic geometry. For algebraic in Princeton, one of the world’s foremost research curves in the plane, one aspect of these transcen- centers, particularly in the areas of mathematics dental methods was embodied in a construction and theoretical physics. Under his twelve-year known as the period map. However, when one goes directorship, the IAS launched several new initia- beyond curves to higher dimensions, genuinely tives, including programs in theoretical computer new phenomena occur that no one had anticipated science and theoretical biology. Also during this until the work of Griffiths. He found an innovative time, three new buildings were completed, among way to bring together modern methods, such as them Simonyi Hall, which now houses the IAS deformation theory and Hodge theory, with the School of Mathematics. classic framework. Griffiths has been much sought after for his Not far off from these developments lies one of wise council in matters of science and educational the major challenges in mathematics, the Hodge policy. As Green put it, “He is a person everyone Conjecture, which has been designated as one of trusts to be fair and judicious.” Among the most the million-dollar Millennium Prize Problems of prominent roles Griffiths played was as chair of the Clay Mathematics Institute. W. D. V. Hodge the Committee on Science, Engineering, and Public (1903–1975) noted that to certain objects in al- Policy (COSEPUP) of the National Academies from gebraic geometry—namely, algebraic cycles—one 1992 until 1999. In that time COSEPUP issued two can associate a particular type of object in topol- especially influential reports, one on reshaping ogy, a “Hodge class.” The Hodge Conjecture asks graduate education in science and engineering and whether one can reverse this association: Can one the other on the various facets of being an effective take a Hodge class and find an algebraic cycle mentor in these areas. Griffiths also served on the with rational coefficients to which it is associated? National Science Board, the policymaking body of

November 2014 Notices of the AMS 1237 the National Science Foundation (1991–96), and as secretary of the International Mathematical Union (1999–2006). While director of the IAS, Griffiths got to know James Wolfensohn, president of the World Bank, who at the time served as an IAS trustee. Inspired by this contact, Griffiths launched the Science Initiative Group (SIG), an international team of leading scientists that aims to help developing countries build scientific capacity. Rather than imposing goals and frameworks from outside, SIG helps native-born scientists to identify criti- cal national needs and to build the educational and research infrastructure required to address them. SIG’s first effort was the Millennium Sci- ence Initiative, a research and education program that was funded mainly by the World Bank and that reached developing countries in Africa, Asia, and Latin America. Building on this experience, SIG launched RISE (Regional Initiative in Science and Education), which is funded by the Carnegie Corporation of New York and managed jointly by SIG and the African Academy of Sciences. RISE supports university-based research and training networks in sub-Saharan Africa, with the goal of preparing Ph.D.-level scientists and engineers. RISE has put special emphasis on participation by Afri- can women, who have long been underrepresented in the sciences. At seventy-six years of age, Griffiths shows little sign of slowing down. Now a professor emeritus at the IAS, he remains deeply involved with SIG. Over the past year he has teamed with other US leaders in mathematics and science on a program that aims to effect constructive change in post- secondary mathematics education. And he is still doing research: his most recent paper, written with Mark Green, was posted on the arXiv preprint server in May 2014. With his distinguished legacy in mathematics research, his profound impact on young people in the field, and his contributions to supporting research and education around the globe, Griffiths is an inspiration to many—but not one who is easily emulated, Green noted. To take on as many projects as Griffiths has, “the rest of us would need extra hours in the day.” Phillip Griffiths was born in Raleigh, North Carolina, in 1938. Among his awards are the Dan- nie Heineman Prize (1979), the Wolf Foundation Prize in Mathematics (2008), and the Brouwer Prize (2008). He held a Guggenheim Fellowship from 1980 to 1982 and is a Distinguished Presidential Fellow for International Affairs, National Academy of Sci- ences, a Carnegie Fellow, and a Fellow of the AMS. He is also senior advisor for the Andrew W. Mellon Foundation. He is a member of the National Acad- emy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.

— From an IMU news release

1238 Notices of the AMS Volume 61, Number 10