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Home , Louis Nirenberg, Mathematician

August 21, 2010 Remembering Daughter’s reminis- Panel discussion on Chern 2 cences on Chern 3 school 4 The Legacy of Shiing-Shen Chern

he Chern Medal Award was established of study. He obtained fundamental results Tin 2009 in the memory of the outstand- in all the major aspects of modern geometry ing Chinese Shiing-Shen and founded the of global differential Chern (1911 – 2004). It was awarded for geometry. His work exhibited keen aes- the first time yesterday at the 2010 Interna- thetic tastes in his selection of problems tional Congress of (ICM and in his breadth exemplified the intercon- 2010) at Hyderabad, India. It will subse- nectivity of modern geometry and all of its quently be awarded every four years at the aspects. quadrennial ICMs. Today, these aspects have become funda- The Award will be given to an individual mental to many of mathematics and whose accomplishments warrant the high- The face of the genius even theoretical with the concepts est level of recognition for outstanding of ‘Chern Classes’ and ‘Chern-Simons In- achievements in the field of mathematics. of Courant Institute of variants’ becoming highly significant in All persons, regardless of age or vocation, Mathematical , Univer- gauge theory and string theory. are eligible for the Medal. The award con- sity (NYU). There was a separate ceremony sists of a gold medal and a cash prize of on August 20, to commemorate S. S. Prof. Chern’s name has an earlier Indian US$ 250,000. In addition, each Medalist Chern, who devoted his life to mathematics, connection as well. In the late 1940s, Homi may nominate one or more organizations to both in active and education, and Bhabha had made an offer of faculty posi- receive funding totaling US$ 250,000, for in nurturing the field whenever the opportu- tion at the Tata Institute of Fundamental Re- the support of research, education, or other nity arose. search (TIFR) to Prof. Chern.This was at outreach programmes in the field of mathe- the initiative of Prof. D. D. Kosambi, himself matics. This is called the “Organization Prof. Chern was one of the greatest geome- an eminent geometer those days before he Award”. The prize is jointly awarded by the ters of the 20th century. In the 1930s and moved to other areas of study. But appar- International Mathematical Union (IMU) and the 40s, Prof. Chern took the then dominant ently Prof. Chern declined that offer and the Chern Medal Foundation (CMF). The field of , which deals moved to the University of Chicago in 1949 CMF funds the award. with the mathematical description of geo- where he served till 1960 before moving to metrical shapes, including those in many University of California, Berkeley, where he The Chern Medal for 2010 was awarded to , and turned into a vibrant area remained till 1979. Accolades Paid to Chern at Congress n event of the morning of August 20 was divoted to paying trib- presentation, May Chu made another small video presentation Aute to S.S Chern and his work. Speaking on the Chern Medal where many other mathematicians as well as friends and family Award, László Lovász said that this Award lays emphasis on the members reminisced about Chern. This part of the event ended achievement of the awardee and puts those mathematicians who with a lecture by Prof. Robert Bryant on the mathematical work of are worthy of this as an example to the world. The Chern Award Chern especially highlighting some parts which are no as well- was instituted by Chern’s family. It’s a financial grant of half a million known. dollars split into two parts ‒ half of which is a gift to the recipient of the prize and the other half at his disposal for philanthropic pur- Chern’s publishing career according to Bryant spread across six poses and for supporting good causes in mathematical life. May decades. Chern, as is well-known is a foundational figure in 20th Chu, Shiing-Shen-Chern’s century mathematics. He also high- daughter, thanked Simons for his lighted that Chern’s work is rooted financial support (which is two- “Chern was one in classical differential geometry thirds of the amount) and for his of the founda‐ and that Chern provided excellent steady and warm guidance in ideas that led to the development making this Medal a reality. onal fathers of global topology and analysis. of 20th century Chern made contributions to sev- Simons was unable to be pres- eral branches like integral geome- ent at this ICM but spoke with the mathemacs” try, , Riemannian delegates through video in the - Robert Bryant geometry and Finsler geometry form of a conversation with Den- which is not as well appreciated as nis Sullivan. After Simons's video some of his other work. REFLEXIONS August 21,Saturday James Harris Simons – mathematician, money manager and munificent millionaire !""#$%&'%()*+,&#, here was a brief period I thought I mons Foundation’ which backs research in ‘Tmight like to be a Rabbi, but it fortu- basic and mathematics.The foun- nately came and went.’ (James Simons’ in dation financed two-thirds of the investe- an interview with Seed magazine) ment towards the Chern prize. A new program has been launched in 2009 with a James Harris Simons was born in 1938 in funding of US$ 40 million per year, to sup- Massachusetts and is a mathematician who port ‘research in mathematics and theoret- became the founder and CEO of ‘Renais- ical aspects of areas related to sance Technologies Corporation’ in 1982. In mathematics’. Seventy Simons Postdoc- October 2009, he announced his retirement Chern Simons toral Fellowships were created. The Foun- as of 01 January 2010 from active manage- dation also funds autism research. ment of the firm in order to focus more on During these few years I was working on his philanthropic pursuits. minimal varieties, when I had something Simons has been instrumental in creating that of being global, I would call him up – Avalon Park, a nature preserve in Stony He is known for his collaboration with math- another global theorem...’ Brook. Nepalese health care is supported ematician S. S. Chern in creating the by the Nick Simons Institute. Simons also Chern-Simons theory which has applica- Simons’ highly successful founded ‘Math for America’ in 2004 which tions in theoretical physics also. The Chern Technologies investment fund employs focuses on improving public schools’ math Medal Award was presented for the first mathematical models to analyze and exe- education, and supports and trains math time in this International Congress of Math- cute trades. The company employs people teachers. ematicians, at the opening ceremony on from various countries irrespective of August 19, in memory of Shiing-Shen- whether they are from academia or industry. The donation to the Simon Center for Chern. Simons has also worked on the It has made Simons one of the world’s rich- Geometry and Physics at the Stony Brook Poincaré conjecture, which was solved by est men – he uses this fortune to support University is reported to be the ‘largest ever Grigori Perelman. research. gift to any public college or university in New York state’. Simons’ belief was that the At a conference, Simons is reported to have He and his wife are the founders of ‘The Si- new center will give many of the world’s talked on his relationship with Chern: best mathematicians and physicists ‘When I was there (at Berkeley), he the opportunity to work and interact in was always very encouraging and later an environment and an architecture on, when I proved some theorem in carefully designed to enhance minimal varieties I called him and progress. showed him this theorem. He said, “Oh, global! Global theorem is very These are just a few of the achieve- good. It’s rare to have a nice global ments of this multifaceted personality. theorem.” Boy that was very very en- Only the future will reveal what the couraging. I just wanted to run home ‘minister for math’ still has up his and prove a million global theorems. sleeve. Chern – Your Memory! People Reminisce imons: I was at Berkeley. cided to leave mathematics, but with a large head! SIn walked a tall Chinese Chern said, “After all, he’s not Some tidbits about Robert Bryant: He was just with a tweed jacket. I asked David Hilbert”! In the fall of Chern someone who that was and you 1972, when Chern came to the able to see lots of calculations! could have knocked me down IAS and was leaving for Berke- Chern knows calligraphy. In Philip Griffiths: Elie Cartan with a feather when I learnt it ley, he asked me to drive him to Weil's book ` theory: was the leading geometer of was Chern. I had supposed the airport instead of Andre an approach through history early 20th century and his tra- that Chern was short for Cher- Weil, saying that we could keep dition was continued by Chern. From Hammurapi to Le- nofsky or something! talking on the way and that Weil gendre', there is a frontispiece could come behind with the Calvin C.Moore: It is impossi- of a warhorse from the tomb In 1968, I stumbled upon a bags! ble to imagine differential of emperor Tai-Zong and a three- invariant and geometry without Chern and calligraphy by Chern which showed it to Chern who said, I met Chern last in September the Gauss-Bonnet theorem for means something like `the old “That is a special case. We can 2001, and thought that it was surfaces. horse knows the way'. make it more general”. Chern good I met him before it was saw a big generalization and too late. Maybe Chern was Rob Kirby: He had a pres- Chern once told someone, “if then we started working to- thinking the same thing about ence, a gravitas! People just lis- you do one thing that's good, gether in spite of Chern being me too! tened to him! that's all you can expect in a at Berkeley and I at Stony lifetime”. A.Weinstein: He had infinite Brook. There were no email fa- Susan Chern (daughter-in- patience and time. cilities at that time. When I de- law): He was reasonably tall B.Sury

REFLEXIONS August 21,Saturday S.-S. Chern: The Daughter Speaks

!"#"$%&'!()%*% +,!'-"./ Obviously, if you listen to the do what I wanted to. He was not talks in mathematics, they are an overdoting father by any very different. It is not easy to means. understand and mathemati- cians, among themselves don’t What initiatives were taken to necessarily understand the honour Prof. Chern, besides other areas of mathematics. So instituting the Chern Medal? my math went up to upper level Well, for instance the Math Insti- (university level) and occasion- tute at Nankai University was ally in the past when I was renamed as Chern Institute of young, I would ask him for help Mathematics and I think that is with problems and things like recognition of all of the effort that. But obviously, I do not un- and financial support that he derstand any of what he did gave to the institute over the (laughs). years. In addition to that the Mathematical Sciences Re- Prof. May Chu How was Prof. Chern as a fa- search Institute at Berkeley has ther? certain portions of it also, with rof. May Chu is the daugh- -off situation where somebody I think he was pretty much self- my father’s names in it. It is Pter of one of the greatest gets one award and it’s done! made, he didn’t have a very recognition of his contributions. mathematicians, Prof. Shiing Our thought process is to have strict father and mother who There is also a Chern Chair and Richa Shen Chern. She talks to something which is ongoing. forced him to study all the time, a Chern–Simon Chair in the Malhotra about her father and Like there is still the Nobel Prize he did things on his own and University of California, Berke- the award instituted in his name. named after Alfred Nobel; spent a lot of time in his younger ley. So, there are these kinds of maybe the Chern Medal (we days with his grandmother who things that are associated with How did the idea of instituting hope) would still be in existence probably spoiled him as much his name. the Chern Medal evolve? 100 years from now and re- as she could. He didn’t really It has almost evolved from a garded. If that’s the case I think think that people needed a very Next year Prof. Chern’s birth selfish standpoint, obviously. then the family has done its strict environment. He thought Centenary is being cele- The family has a tremendous work. I think that mathematics at that people should find their brated. What initiatives are amount of respect for my father that point will still be ongoing own way, understand what they being planned? and his accomplishments within and active, and I hope that like to do, just automatically do The preparations are ongoing mathematics and his relation- mathematical community be a things they like and enjoy and for one year. The Executive ships to mathematicians world- very congenial kind of a place to be very good at it. But I kept on Committee has been formed. wide, and his support for the work and that the Chern Medal telling him, in his later life, there The two venues have been de- field of mathematics. So we has contributed in some way to is really a very special group of cided upon - the universities in wanted to keep his legacy going that. people who need a lot of disci- China and Berkeley have al- and one of the ways of doing pline in order to be succeeding ready decided upon the dates. that is to do something which Did you discuss mathematics in life but my life was extremely So, I think they should be pretty can continue, not just be a one problems with your father? carefree in the sense he let me well-established. Mathaloon

-Arghya Mondal

REFLEXIONS August 21,Saturday Making Sense of School Mathematics Sidharth Varma / Nikhil MG Photo: Rahul V Pisharody elation between the discipline and school mathematics was Rthe issue around which the panel discussion took place on the second day of ICM. , who chaired the discussion said that the discussion would broadly re- volve around mathematics at school and research level.

Carlos Bosch, Instituto Technologico Autonomo de Mexico, who spoke about the scenario in the Latin American countries of Brazil, Chile and Mexico said, “After the mandatory school, the majority of students lack the ability to solve problems and use algorithms.” He expressed concern about the unqualified and under qualified training given to the teachers and that the teaching pool is inade- Mathematicians takes part in the Panel discussion. quate. Speaking of the good practices in teacher training in Latin presentation focused on ‘Live Mathematics and classroom America, he referred to the La Ciencia en tu Escuela (Science in processes’. Through his experiences with school children he con- your school) project in Mexico which aims at changing the existing cluded that there is a big gap between school mathematics and attitudes towards mathematics and science. In recent times, inter- mathematics as a discipline. He added that in many countries peo- net is being used to teach teachers, but access to computers and ple have begun to question the role of mathematics in compulsory operational knowledge is hampering the progress. In the Chilean school education. He also suggested a need for re-orientation of perspective lack of relationship between disciplinary knowledge classroom textbooks and systematic education. By engaging stu- and training techniques is the barrier. dent’s attention, every child can be made interested in mathemat- ics. Ivan Yashchenko from the Moscow Centre for Continuous Mathe- matical Education, Russia, pointed that training future research W. McCallum said, “The goal is to teach mathematics and not to mathematicians should not be the only purpose of teaching math- get to the solution.” He said the biggest problem in terms of atti- ematics at the school level. The researchers and the students of tudes of the people is that they think school mathematics is di- middle and high school work together in Russia, resulting in the vorced from reality. He also said that Math Circles have taken off level of mathematics being very high in general. Speaking of the in the U.S. similar to that in Russia and teachers work in an envi- current trends in the Russian Mathematical syllabus, he pointed ronment solving problems given by researchers. out that there has been a decrease in calculus and theoretical geometry, and increase in discrete mathematics. Majority of the audience shared the opinion that there is a need to have good textbooks. Researchers’ engagement in writing text- Presenting the three perspectives of mathematical education in books or proofreading textbooks written by others is significant in Germany, H. Steinbring (University of Duisburg-Essen, Germany) teaching the teachers and students, besides the public. Steinbring elaborated on the various aspects of the learning and development also believed that teaching changes with economic and social con- process. “There is a difference between cultural conditions of pro- ditions of the place. In response to a question from the floor, he fessional mathematical research practice and in the school instruc- said that change must come not only in the textbooks/curriculum, tion of mathematics,” he opined. but also in the teaching, learning and understanding of the teacher. In conclusion, Gowers described the need of a continuous path R. Ramanujam (Institute of Mathematical Sciences, India) had his from school mathematics to university mathematics.

!"#$!%!$!&$'(!% Photo: Rahul V Pishoarody 0!%'&"& 7&!"8 $&9: !'$' LILAVATI - Traditions of Professor M. Sal Moslehian’s Natya, Kavya, Ganita – 1989. talk entitled Refinements of Conceived and Choreo- operator Jensen’s inequality graphed by Chandralekha. scheduled for 26 August (17:00‒17:15 hrs) has been Show Timings: 18:00-19:00 shifted to 21 August and 19:15-20:15 (19:00‒19:15) in Room No. T3 Room No. G01+G02 %%"$%''%# ('*'##',&.' Participants of the ICM R.Ramachandran 2010are requested to prepare, B.Sury in the form of a pdf file, and Geethanjali Monto print the participation certifi- Richa Malhotra cate at Beautiful display of Indian arts, literature and the Shastras, by a Midhun Raj U.R group of classical dancers choreographed by C.V Chandrashekhar Mohammed Anvar T and Jaya Chandrashekhar, with a central theme of ”Panchama- mathstat-uohyd.ernet.in/icm2010/cert Rahul V Pisharody habhutam”- Jala, Vayu, Agni, Akas and Prthvi- filled the atmos- Sidharth Varma phere at HICC’s packed auditorium on Friday, August 20, the using their access key. second day of the ICM 2010 Nikhil MG