| Steven George Krantz | |
|---|---|
| Born | February 3, 1951 San Francisco, California |
| Residence | U.S. |
| Nationality | U.S. |
| Fields | mathematician, writer, scholar |
| Institutions | UCLA, Princeton University, Penn State, Washington University in St. Louis |
| Alma mater | University of California at Santa Cruz, Princeton University |
| Doctoral advisor | Elias M. Stein, Joseph J. Kohn |
| Doctoral students | Gerardo Aladro Marco Peloso Daowei Ma Estela Gavosto Chen Zhenhua Xiaojun Huang Siqi Fu Fausto Di Biase Judy Munshower Tristan Nguyen Bao Luong Lynn Apfel Seth Howell Lina Lee Jiye Yu Dylan Retsek Bennett Standeven Baili Min Liwei Chen (in process) Bingyuan Liu (in process) |
| Known for |
Several Complex Variables |
| Spouse | Randi Ruden (m. 1974–present) |
Steven G. Krantz (born 3 February 1951 in San Francisco, California) is an American mathematician of Hungarian, Austrian, French, and Sicilian descent who teaches at Washington University in St. Louis.[1] He has also taught at UCLA, Princeton, and Penn State. He is Editor-in-Chief of the Notices of the American Mathematical Society for the period (2010–2015).[2] Krantz is also Editor-in-Chief of the Journal of Mathematical Analysis and Applications and Managing Editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society. Krantz is a noted author, editor, and mathematical scholar. He is famous as a mathematics teacher and expositor.
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Steven Krantz attended Roosevelt Elementary School, where he benefitted decisively from the attention and support of Principal Milam Tackitt. Tackitt arranged for Krantz to be skipped ahead two grades. Krantz himself vetoed a third skip, as he feared problems with social adjustment. Krantz graduated from Sequoia High School in Redwood City, California in 1967. He was recently inducted, along with Gordon Moore and Ray Dolby, into the Sequoia High School Hall of fame. Professor Krantz received his bachelor's degree in mathematics from the University of California at Santa Cruz in 1971 (where he graduated Summa cum Laude), and his Ph.D. in mathematics from Princeton University in 1974 (under the direction of E. M. Stein).[3] Krantz was also considerably influenced by his teachers Joseph J. Kohn, Frederick Almgren, Robert Gunning, and Edward Nelson. He has been profoundly affected by the ideas of Charles L. Fefferman, John Erik Fornaess, and Nessim Sibony. Krantz has written papers with Stein and Fornaess.
Among his research interests, about which he has written extensively, are: several complex variables, harmonic analysis, partial differential equations, differential geometry, interpolation of operators, Lie theory, smoothness of functions, convexity theory, the corona problem, the inner functions problem, Fourier analysis, singular integrals, Lusin area integrals, Lipschitz spaces, finite difference operators, Hardy spaces, functions of bounded mean oscillation, geometric measure theory, sets of positive reach, the implicit function theorem, approximation theory, real analytic functions, analysis on the Heisenberg group, complex function theory, and real analysis.[4] He has worked on applications of wavelet analysis to plastic surgery, creating a powerful new piece of software for facial recognition.[5] Krantz has also written important and widely used software for the pharmaceutical industry.
Among other things, Krantz is famous for a book review that was very critical of fractal geometry--see Mathematical Intelligencer, vol. 11, no. 4, December, 1989, pp. 12–16 (the article was originally slated to appear in the Bulletin of the American Mathematical Society but, under pressure from Mandelbrot, the editor reversed his decision and decided not to publish the article). In this article Krantz points out that the Mandelbrot set was not invented by Mandelbrot, but rather by Brooks and Matelski. Also the celebrated fractal images were not an idea of Mandelbrot; they were invented by John Hubbard. The now-famous ideas about the length of the coastline of England were anticipated in work of Lewis Fry Richardson prior to 1953. Finally, the idea of fractal dimension is a weak transmogrification of the classical and more precise and powerful idea of Hausdorff dimension. Felix Hausdorff invented the idea of fractional dimension. Mandelbrot took considerable umbrage with Krantz's review. He wrote a stern rebuttal. And Krantz rebutted that.
Krantz also wrote a noted book review that was critical of Stephen Wofram's book A New Kind of Science. He observes in this review that, in an attempt to reach a very broad and undifferentiated audience, Wolfram has written 1286 pages with virtually no solid content. There are a lot of pictures and vague descriptive passages, but little scientific analysis. Wolfram seems to think that if a cellular automaton generates a picture of a physical phenomenon then it is in fact the cause, or the explanation for, that physical phenomenon. This reasoning is plainly specious, and certainly unsupported by scientific evidence. Wolfram was quite outspoken in disavowing Krantz's review. Contrary to Wolfram's assertions, his ideas about cellular automata are not being widely adopted and not taught in the schools.
Krantz is respected for his work on the inhomogeneous Cauchy-Riemann equations (he obtained the first sharp estimates in a variety of nonisotropic norms), on separate smoothness of functions (most notably with hypotheses about smoothness along integral curves of vector fields), on analysis on the Heisenberg group and other nilpotent Lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables, on partial differential equations, on complex geometry, on the automorphism groups of domains in complex space, and on the geometry of complex domains. Krantz's work with Robert E. Greene, Alexander Isaev, and Kang-Tae Kim on automorphism groups of domains opened up a whole subject area. His work with Song-Ying Li on the harmonic analysis of several complex variables opened up a whole subject area. His work with Marco Peloso has developed several subject areas in harmonic analysis, the inhomogeneous Cauchy-Riemann equations, Hodge theory, and the analysis of the worm domain. Krantz's work on the inhomogeneous Cauchy-Riemann equations and nonisotropic estimates opened up a subject area. His work on smoothness of functions, based on smoothness along integral curves, created a new subject area. Krantz's recent definitive book on the geometry of complex domains, joint with Robert E. Greene and Kang-Tae Kim, appeared in 2011.
Krantz has written a number of papers that have received wide attention. The paper based on his thesis established sharp estimates for the inhomogeneous Cauchy-Riemann equations. His boundary Schwarz lemma with Dan Burns was an important piece of work. The automorphism semicontinuity theorem with Robert E. Greene is widely quoted. The work with Song-Ying Li on bounds for the Lusin area integral is an important paper. The papers with Alexander Isaev on automorphism groups of Reinhardt domains are definitive.
Steven Krantz has written several important monographs, including Function Theory of Several Complex Variables, Complex Analysis: The Geometric Viewpoint, A Primer of Real Analytic Functions (joint with Harold Parks), The Implicit Function Theorem (joint with Harold Parks), Geometric Integration Theory (joint with Harold Parks), and The Geometry of Complex Domains (joint with Kang-Tae Kim and Robert E. Greene). His book The Proof is in the Pudding: A Look at the Changing Nature of Mathematical Proof is a unique look at the evolving nature of the proof concept. Krantz's latest book, A Mathematician Comes of Age, to be published by the Mathematical Association of America, is the first exploration in book form of the concept of mathematical maturity.
Krantz has written several incisive books with Harold R. Parks. These include A Primer of Real Analytic Functions, The Geometry of Domains in Space, The Implicit Function Theorem, and Geometric Integration Theory. They are currently preparing a book, The Mathematical Experience, which will explain the life of a mathematician to the lay reading public.
Professor Krantz is author of many textbooks[1] and is an accomplished expository writer. His calculus book, jointly authored with Brian Blank, is quite successful. His books Mathematical Apocrypha and Mathematical Apocrypha Redux are collections of anecdotes about famous mathematicians.[3] His influential text How to Teach Mathematics is the best-selling of his works. It is used in mathematics departments and other academic departments around the world. His book Handbook of Typography for the Mathematical Sciences is the most detailed and modern book on the subject. His book A Primer of Mathematical Writing is widely quoted. Krantz's book An Episodic History of Mathematics: Mathematical Culture through Problem Solving is an unusual blend of history and problem solving. A Mathematician's Survival Guide and The Survival of a Mathematician are about how to get into the mathematics profession and how to survive in the mathematics profession. Krantz has an Erdős number of 1. He is listed in Who's Who and in American Men and Women of Science.
Krantz is widely considered to be a charismatic and galvanizing teacher. Many students consider him to be the best mathematics teacher that they have ever had. Krantz has been a mentor to many other developing teachers. He was awarded the UCLA Alumni Foundation Distinguished Teaching Award in 1979. He wrote the definitive book on the teaching of mathematics, called How to Teach Mathematics, published by the American Mathematical Society. He has given presentations all over the country about the teaching of mathematics.
Krantz has organized many important conferences, including the Summer Workshop in Several Complex Variables held in Santa Cruz in 1989 and attended by 250 people. He is a frequent principal speaker at conferences organized by others. Krantz was the principal lecturer at a CBMS conference at George Mason University in 1992.
Krantz is Associate Editor of three scholarly journals and Managing Editor of three others. He is the founder and Managing Editor of The Journal of Geometric Analysis. He is or has been the Consulting Editor for several book series. Krantz is the President of Mathematica Josephina, Inc.
Steven Krantz has been awarded several notable prizes, including the Chauvenet Prize of the MAA, the Beckenbach Book Award of the MAA, the Kemper Prize, the Washington University Faculty Mentor Award, and the UCLA Alumni Foundation Distinguished Teaching Award. Krantz has been the Frontiers Speaker at Texas A&M University, the Richardson Fellow at Australian National University, a CBMS speaker at George Mason University, the Nagle Memorial Lecturer at the University of South Florida, the Court Lecturer of the MAA, the Arvid Longseth Lecturer at Oregon State University, the Friends of Mathematics Lecturer at Kansas State University, and the Buckingham Scholar at Miami University of Oxford, Ohio.
In May, 2011, an international conference was held at Washington University in St. Louis to honor Steven Krantz for his 60th birthday and John Erik Fornaess for his 65th birthday. It was attended by more than 85 people from countries as far as China, Korea, Italy, Australia, India, and France.
Krantz has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. He has served as Chair of the latter department. He has been a visiting faculty member at a number of institutions around the world, including the Institute for Advanced Study, the University of Paris, the University Autonoma Madrid, Pohang Institute of Science and Technology, the Mathematical Sciences Research Institute, Australian National University (as the Richardson Fellow), Texas A&M (as the Frontiers Lecturer), the University of Umeå, Uppsala University, the University of Oslo, Politecnico Torino, the University of Seoul, Université Paul Sabatier, and Beijing University. He has directed 18 Ph.D. students and 9 Masters students. Among his students are Marco Peloso at the University of Milan, Siqi Fu at Rutgers University, Xiaojun Huang at Rutgers University, and Lina Lee at the University of California at Riverside. Krantz has published more than 170 scholarly articles and more than 65 books.
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