August 27, 2010 History of Mathe- On the footprints of Opinions 3 5 matics in India 7 Indians Among the Exalted at ICM 2010 he presence of Indian number theory, combinatorial number theory, of current interest in statistics. His work in Tamong the plenary and invited speakers elliptic curves and cryptography. In 1986, he multivariate analysis related to developing at ICM 2010 has been significantly more than solved the Waring problem for fourth powers geometric notions of multivariate quantiles is in the past. To be invited to deliver a plenary in collaboration with J-M. Deshouillers and F. considered a major breakthrough in the area or an invited lecture at an ICM is considered Dress. of multivariate nonparametric inference. More highly prestigious. recently, he has developed methods that en- Prof. Venkataramana has made significant able one to discover statistically significant While Prof. R. Balasubramanian of the Insti- contributions to algebraic groups and discrete features in the income distribution in different tute of Mathematical Sciences (IMSc), Chen- subgroups. He proved the positive character- populations. nai, delivered a Plenary Talk, Profs. V. istic version of the Margulis super-rigidity the- Srinivas and T. N. Venkataramana of the Tata orem and obtained important results on Prof. Arup Bose has made significant re- Institute of Fundamental Research (TIFR, cohomology of locally symmetric varieties. search contributions in resampling plans, se- Mumbai), Probal Chaudhuri and Arup Bose of quential analysis and asymptotics, statistics the Indian Statistical Institute (ISI), Kolkata, Prof. Srinivas has done significant work in as- of diffusion processes, rates of convergence, and V. Suresh of the University of Hyderabad pects of algebraic and commutative multinomial selection problems and strong delivered Invited Talk. In fact, Prof. Balasub- algebra. His interests include algebraic cycles laws. His work in resampling provides a deep ramanian's Plenary Talk is the first ever at an on singular algebraic varieties, projective and powerful impact on areas such as time ICM by an Indian . Prof. Suresh modules, Hilbert functions and multiplicity and series, linear models, general dependent is from a university and the last Indian math- on aspects of algebraic geometry in positive models and nonparametric estimates. ematician from a university to a give an In- characteristic. An important work by him, done vited Talk in an ICM was Minakshisundaram in collaboration with D. Cutkosky, is the solu- Prof. Venapally Suresh has made outstanding in 1958. tion of Zariski's problem (Riemann-Roch prob- contributions to the theory of quadratic forms. lem for surfaces). His work on Galois cohomology and u-invari- Prof. Balasubramanian is a world-renowned ants over function fields of p-adic curves is es- number theorist. His research interests en- Prof. Probal Chaudhuri has made outstanding pecially important and regarded quite compass a wide spectrum of topics in analytic contributions in a number of important areas fundamental. !"#"$%&%'(!)*%+% ,$!(-"./

R. Balasubramanian T. N. Venkataramana V. Srinivas

Probal Chaudhuri Arup Bose V. Suresh

REFLEXIONS August 27,Friday India and Evolution of

!"#"$%&'!()%*% +,!'-"./ im Leslie Plofker is a well-known historian a place value system that is also fully inte- Kof mathematics. Currently a Visiting Pro- grated with arithmetic, is definitely Indian. It is fessor of Mathematics at the Union College, part of this trend, this mainstream in Indian USA, she is the author of the recently pub- mathematics, which is producing the sophis- lished Mathematics in India. Plofker has also ticated arithmetic and algebra that we are contributed a chapter on seeing in the medieval period. And as to ac- in The Mathematics of Egypt, Mesopotamia, tually when that happened is a tough call. I China, India and Islam, which she has also think we can see that this place value system co-edited. She has also contributed to A De- of zero is clearly fully established at least in scriptive Catalogue of the Sanskrit Astronom- the scientific use in India by maybe around ical Manuscripts preserved at the Maharaja 3rd century of this era. Man Singh II Museum in Jaipur, India. She co- edited the volume Studies in the History of the Prof. S. R. Sharma has made some interest- Exact Sciences in Honour of David Pingree. ing arguments in favour of the idea that the place value system, including zero, may have Prof.Kim Leslie Plofker completed her PhD from Brown Uni- been developed in that era. So somewhere versity on ‘Mathematical Approximation by of course the remarkable methods that you around then is when integration of zero into a Transformation of Sine Functions in Medieval see by the Kerala School with infinitesimal number system gets going in the Indian tradi- Sanskrit Astronomical Texts’ under the super- quantities and various operations with infinite tion. vision of David Pingree. Much of the work series. Plofker and Pingree did was founded on the When did Indian mathematics become vis- great early Indian textual scholars of Sanskrit I think one of the things that we may have to ible and how? tradition like Sudhakar Trivedi and Bapudevan thank Indian mathematics for more than we Certainly mathematics is something involving Sastry. realise is the structure of the organisation of various types of calculations. There is a lot of mathematical knowledge; this distinction be- awareness about it in Indian contexts, all the She gave a Plenary Talk at the ICM 2010 titled tween arithmetic as the computation of known way back, when you have hints to the num- ‘Indian rules, Yavana rules: foreign identity quantities and algebra as a parallel type of bers in tens to hundreds to thousands and so and the transmission of mathematics’. In her computation but with unknown quantities is on, and the importance of calculation is defi- talk she discussed the encounter of two cul- something that appears very early in the San- nitely recognized. The other two cultures start tures of mathematics, namely Yavanas and skrit tradition. to understand something about Indian math- Indians, and the reactions of the cultures to ematics (well that’s something I talked about each other. Yavanas (In Sanskrit means Which do you think is the most remarkable in my Plenary presentation), and certainly as Greeks or any Western visitor) came into con- development? far as the West is concerned, after the incur- tact with Indians by crossing the Himalayas The work on the infinitesimal series in the Ker- sions of Alexander. So, the Alexander expedi- and travelling across the Arabian Sea. ala School about fourteenth century is just a tion gets as far as India and gets home but really amazing synthesis of so much work -- that means that there is a sense of link be- In a conversation with Richa Malhotra, not just infinite mathematical concepts they tween Greek culture and Indian culture. From Plofker threw light on ancient Indian mathe- evolved but also the astronomical problems then on Greek and other Western sources -- matics and her engagement with it. Excerpts by people who were masters of all aspects of first in the classical theory -- then in the Mus- from the interview: mathematical sciences and thought very orig- lim and then the modern European started to inally of it. report back on what they understand as “In- What are the iconic contributions of an- dian mathematics” and what things these for- cient Indian mathematics? What is the correct story about India and eign people – the Indians -- are doing in Well, first of all, what everybody knows about the origin of zero? Indian mathematics. is the decimal place value number system, It is a very long story. It is hard to know exactly which is now the universal number system. all the details of the origin of zero. Prof. R. C. Do you think it is important to recognise Though it wasn’t the first place value system Gupta, who will be receiving the [Kenneth O.] “who invented what” in mathematics? to be devised, it was the first that is definitely May Medal for has Well of course we don’t want it just to degrade the ancestor of the universal decimal place written a very good article called ‘Who in- into a priority dispute and argue about a few value numbers. That has really made a differ- vented the zero?’ In that he makes some cru- centuries or years here and there. But like ence to not just mathematics in general and cial distinctions between different concepts of everything else what we want to know or un- practical mathematics but the progress of sci- zero. Are we thinking of zero as just a place derstand is how concepts developed, how ence by enabling calculations more effec- holder in a place value system as there is an things were transmitted, how they evolved. I tively. The place value system had a great empty digit of zero? Or we are still thinking of think a thoughtful adaptation of foreign con- impact on Indian science and then, as it zero as something that plays a certain role in cept is historically just as interesting as the spread, had a great impact on doing science computations? Or are we thinking of zero fully original development. So it is important to elsewhere in the world. integrated as a number, something on which know who did what and when in the sense it you can perform arithmetic operations? If we is important to get all of the history right. Per- But that’s one of the best known examples but go back to the first idea of zero as a place haps we were little over-influenced by the some others, I think, are equally interesting. holder we do see that developing already in modern notion of priority, saying that the first These are things that were Indian develop- Babylonian texts although somewhat late -- who did it is better somehow, they deserve a ments that may not have directly contributed. sometime in the first millennium before the medal. This isn’t really how it worked. These were things that were developed in common era. When you have a base 60 num- India and then later rediscovered or inspired ber, written out in a form the way they did, and In the pre-modern world everybody was bor- and then redeveloped in other contexts. For if you have got a missing digit then there is a rowing everybody’s ideas in mathematics and example, the very sophisticated rules for deal- place holder and they put a mark to indicate at that point that it was all very open source; ing with algebra, computations with unknown that. everything went into a common pool of knowl- quantities and symbolic notations for working edge and you pulled it out and, if you thought with equations, the concept of equation [etc.]. When Greek mathematics and astronomy it was interesting, you contributed it to your All of these appear in India by at least in the took over the Babylonian place value units for understanding. As regards the source where first millennium of this era and equivalence measuring things like time and angles – all of it came from, you didn’t feel you were barred structures are being worked out in a similar which were base 60 units – they took over a from adopting it just because somebody else way in the West until about a thousand years form of that place holder notation. But the in- thought of it first. later. So that’s something very important. And tegration of zero as a number being a part of ...continued on page 7

REFLEXIONS August 26, Thursday On the Footprints of Emmy Noether Emmy Noether’s mathematics has been de- Let us take this opportunity to recall also the scribed as ‘abstract, original and deep’ by awesome persona of Emmy Noether. Mythily Ramaswamy. Noether herself is por- trayed as ‘solid and earth-bound’. She was Amalie Emmy Noether was born on March 23, one of the greatest mathematicians of the 1882 in Erlangen, Germany. Her father was twentieth century, surmounting innumerable Max Noether, a professor of mathematics at obstacles to pursue her love of mathematics the University of Erlangen. In Emmy’s time, and in the process made significant contribu- this University would not admit women stu- tions to abstract algebra. She was a towering dents and she had to obtain special authori- presence, with mathematicians from all over zation to work there as an auditor from 1900 the world visiting Göttingen and coming under to 1902. She passed an examination in 1903 the influence of her mathematics! which enabled her to become a doctoral stu- dent at the University of Göttingen which was open to woman students. In 1907, she ob- `Emmy Noether was the centre of the tained her doctorate after which she assisted most fer le circle of research at her father in giving lectures at Erlangen, as there were no university positions open for that me in Go"ngen' women. She taught at the University of Erlan- gen but was not paid for her services. ‐ Constance Reid Amalie Emmy Noether Noether started publishing her research work. The IMU General Assembly (GA) held at Her first major work in theoretical physics in Shanghai in 2002 passed a resolution recom- 1915 was a relationship between symmetries mending continuing the tradition of the 1994, in physics and conservation principles ‒ Noe- `When I explained the founda ons of 1998, 2002 ICMs by holding an Emmy Noe- ther’s theorem. This work made Hilbert and class field theory, he got very ther lecture at the next two ICMs (2006 and Klein invite Noether to join them at the Univer- 2010) with selections of the speakers made enthusias c and said, "But, that is ex‐ sity of Göttingen in their research work on the tremely beau ful, who has by an IMU-appointed committee. The Emmy general theory of relativity. The University op- Noether Lecture Committee for 2010 is posed this saying ‘How can it be allowed that created it?", and I had to tell him that chaired by Prof. Cheryl Praeger (University of a woman become a Privatdozent? Having be- it was he himself who had Western Australia, Australia). She pointed out come a Privatdozent, she can then become a laid the founda on and envisaged that that the ICM Emmy Noether lectures were in- professor and a member of the University beau ful theory' stituted to honour women who made funda- Senate. Is it permitted that women enter the mental and sustained contributions to the Senate? What will our soldiers think when mathematical science. She said that possibly they return to the university and find they are ‐Hasse about Hilbert. the first woman to give a lecture at an ICM expected to learn at the foot of a woman?’ was Emmy Noether in 1928. In the 1932 ICM, Hilbert argued: ‘I do not see that the sex of the she gave a plenary talk and was definitely the candidate is an argument against her admis- first woman to do so at an ICM. The next "Yesterday I received from Miss Noe‐ sion as Privatdozent. After all, we are a uni- ther a very interes ng paper on woman mathematician to give a plenary lec- versity and the Senate is not a bathing ture in an ICM was Karen Uhlenbeck in 1990. establishment.’ invariant forms. I am impressed that one can comprehend these ma!ers From 1994 onwards an ICM Emmy Noether Although the University did not grant permis- from so general a viewpoint. It would lecture was instituted. The first three speakers sion for Noether to enter as a Privatdozent, were Olga Ladyzhenskaya (1994), Cathleen not have done the old guard at Hilbert announced her lectures as his, with Gö"ngen any harm had they picked Synge Morawetz (1998) and Hesheng Hu her as his assistant. In 1919, Noether became (2002). Following the Shanghai GA resolution, a Privatdozent but never obtained a position up a thing or two from her" the next two Emmy Noether lecturers were of importance although her research and selected by an IMU committee. Yvonne Cho- teaching were of high quality. Being a Jew ‐Einstein wrote to Hilbert quet -Bruhat was the speaker at the 2006 caused her dismissal in 1933. She joined the ICM. This year’s speaker is Idun Reiten of the Bryn Mawr College in the United States where Norwegian University of Science and Technol- she finally worked as a normal Professor. She ogy, Norway, who is speaking on Cluster cat- passed away on 14 April 1935. egories. The GA only made the resolution that the Emmy Noether lecture should be held It is said about Emmy that ‘she discovered until the ICM in 2010. Praeger indicated that within her the spirit not only to make major it would be good to hold this lecture at each contributions to mathematics, but also to ICM to honour women mathematicians. share her insights with students and col- leagues so that they also made significant Idun Reiten is a well-known Norwegian math- strides in their fields’. Albert Einstein stated: ematician born on January 1, 1942. She got ‘In the judgment of the most competent living her Ph.D. in 1971 from the University of Illinois mathematicians, Fräulein Noether was the at Urbana-Champaign with Robert Fossum. most significant creative mathematical genius Her research interests are in representation thus far produced since the higher education theory, commutative algebra and homological of women began. In the realm of algebra, in algebra. In collaboration with Maurice Auslan- which the most gifted mathematicians have der, she developed what has come to be been busy for centuries, she discovered known as Auslander-Reiten theory. In 2007, methods which have proved of enormous im- Reiten was awarded the Möbius prize. In portance in the development of the present 2009, she won Fridtjof Nansen reward for day younger generation of mathematicians’. successful researchers, and the "Nansen Her paper in 1921 on the theory of ideals in medal for astonishing research. She speaks rings is an essential contribution to modern al- on `Cluster Categories' in the Emmy Noether gebra. Idun Reiten lecture this year. Geethanjali Monto

REFLEXIONS August 27,Friday Twelve Year-Old Girl, A Mathematical Pearl aavya Jayram is 12 years old First of all, I came last December Well, two things I guess. There is Kand is taking third year and visited people in IMSc, TIFR, It started this way. When my dad the question of when p(n) is even courses in the undergraduate etc. and there, they told me that I went to a conference, Manindra and when it is odd and the other mathematics programme at Stan- could take courses if I go there. Agarwal was there in IIT Kanpur. is the 3n+1 problem. ford University. She was a partic- I heard about his primality result ipant in the ICM 2010 as well as How does it feel socially? and, we basically stayed up until Do you like combinatorics in the ICWM held for the first time. You mean friends and stuff like midnight with him explaining the also? In the ICWM, she presented a that? I have older people like pro- result. Next day, I went to a book- Next to number theory my paper on the partition function fessors with whom I discuss math store there and got a bunch of favourite is combinatorics. Then which is to be published in the In- but there are also others home books on primality and ever since algebra and the least favourite is ternational Journal of Number schoolers who are part of a book I have got hooked on to math and geometry. I liked algebraic topol- Theory. Kaavya also plays the vi- club and a chess club. I have number theory in particular. ogy. There is a lot of combina- olin and is a voraceous reader. friends from the book club. torics in it. I took Prof. Diaconis's On the 25th August 2010, she What age was that? course on combinatorics. He is a talked to Richa Malhotra and B. When did you finish high That was 2006; I was 8. wonderful teacher. Sury. school? When I was 7. There is the bay When were you born? How did you get to learn vio- You have written a paper on area math association and they July 3, 1998. lin? partition theory. Have you met would invite professors who Kaavya's mother: For a silly rea- Prof. Andrews? would give talks. After school, for Do you know Prof. Jaikumar son. This violin teacher was the Yes, he is here and I have also one year I would attend such lec- Radhakrishnan at TIFR Bom- nearest to home. The teacher met him in Florida when I went for tures. During that time, they bay? thought she has a natural bent a one-week conference in num- would give problems over email. Yes, yes. My dad and he had and a knack to advance her ca- ber theory. I kept in touch with the profes- been together in Rutgers. We reer in this line. sors. After that I started taking went to TIFR. There, we met Prof. Have you met other precocious classes at San Jose State Univer- Raghunathan, Prof. Sujatha, and How long are you going to be kids there in the U.S. where sity. I took classes for 2 quarters. Prof. Parimala was there on Ra- in India? you live? Are you friendly with After that Prof. Soundararajan manujan Day. One and a half years. We will be any of them? !"#"$%&'!()%*% +,!'-"./ in Bangalore and will keep shut- Well, there are plenty of home- tling to Chennai to meet Prof. Bal- schooled kids who take part in “Basically my par‐ asubramanian. these math olympiads. ents or profesors Do you want to say anything? What are your other interests? aren't pushing or Did you find things are much Outside of mathematics, I partic- easier in the US than in India? ularly like reading, especially pressurising me In India, I guess things like home Jane Austen and the Bronte sis- schooling are not as easily ac- ters; I re-read them often. My or anything but cepted and younger people join- favourite book is Jane Eyre. I ing college, etc. also are not as like to read non-fiction also and they are only fa‐ easy; but I don't know really. have learnt the violin since I was 5 years old. During the ICWM, I cilitating things.” Sometimes when you are too played 3 pieces. grown up at your age, some Kaavya people try to take advantage of Are you also interested in com- What are you going to do now? your talents in some way and puter science? asked me to take classes at Stan- Do you have any plans? try to get things out of you Not very much. My father is a the- ford. I am going to keep doing math. I without giving you credit? Did oretical computer scientist but it am going to apply to go to the uni- you experience such a thing? doesn't interest me that much. Kaavya's mother: It came to a versity full time next year. Either Not really. I don't think I have ex- state where she exhausted all Stanford or Berkeley. There is perienced that. What about physics? that San Jose had to offer in pure also the issue about dorms – I I like doing it maybe just as a mathematics. They said she don't want to stay in a dorm. I will Do you feel pressurised at all? hobby. could get a degree in a year. But, stay somewhere nearby. No, I don't. It's basically that my she didn't want to take that op- parents or professors aren't push- Have you met Prof. tion. She won't have time to do Since you just took some ing me or anything but only facili- Soundararajan? her research. courses at Stanford without en- tating things. Yes, I took a lot of classes with tering it full time, did you get Prof. Soundararajan at Stanford; Shobha Madan: How did you time to solve problems in Have you read anything written he gives me problems to work on. discover your mathematical topology, etc. or just studied by Ramanujan? ability? from a book? (Laughs) yes, I read a couple of Did you attend the talk of Kaavya's mother: Home school- Well, what I mean by saying I papers by ramanujan. I also read Fields Medalists here at the ing is where the child leads the took the courses is that I solved a couple of papers by Dyson ICM? Did you understand what path and parents just follow. Ini- problems and took the exam etc. about cranks. The crank features they said? tially, she just changed her mind I am not in a rush to join university in my work a lot. I also read a I could get a general sense but often. Her interest in math is her full time. Prof. Soundararajan couple of papers by Prof. not the details. own. At 7, she became solely also told me that I should not join Soundararajan and Prof. Ono. committed to math. Earlier she'd full time until I am 14 at least. How does it feel to be so young go to science meetings; for in- Kaavya's mother: Prof. Who is your role model? and attending college already? stance, she went to NASA. She Soundararajan is a kind of a men- I have several male math. Role I am not yet registered full time was exempted many things in tor. models - Prof. Soundararajan, but took some courses. bay area. Prof. Ono, Ramanujan etc. But I Is there any particular problem am always looking for a female How do you plan to spend time Shobha Madan: I am so happy to in number theory that fasci- role model. So far I found Prof. in India? know you! nates you? Parimala.

REFLEXIONS August 27, Friday I see 'em – How do they see? M.G.Nikhil has enjoyed the wide variety of perts. “At home, we have Na- The organization is doing a great o far the International Con- mathematical topics presented at tional Associations meetings for job in transport and security serv- Sgress of Mathematicians has the Congress. mathematicians but I do not learn ices,” he added. witnessed awe-inspiring lectures For Beatrice Pelloni of the Univer- as much there as I do here,” he Jean M-S Lubuma from Univer- from the distinguished award win- sity of Reading, UK, two events adds. sity of Pretoria, Republic of South ners, panellists and plenary and have been extremely amazing. Africa, is deeply impressed by the invited speakers from across the “Award winner, Cedric Villani’s Dimitri Shlyakhtenko of the Uni- politeness and friendliness of his world. A survey by Reflexions to talk and the lecture on the ‘Life versity of California, Los Angeles, Indian counterparts. “The organi- find out people’s opinions about and Work of Chern’ have been USA, is amazed to see so many zation is doing extremely well the organization and proceedings the best ones so far,” he said. mathematicians together. given its scale and complexity,” at ICM 2010 during its first four Su Ion In of University of Col- Tinne Hoff Kjeldsen of Roskilde he said. He particularly enjoys the days revealed diverse reactions orado at Boulder, USA, is attend- University, Denmark, has thor- talks presented by the laureates that highlighted various aspects ing ICM for the first time. He said oughly enjoyed the special lec- and award winners. “The idea of of the Congress. Here are some that the congress has put to- tures on History of Mathematics, having a specific time everyday excerpts from the views ex- gether great talks and discus- although she complained that the for talks by the laureates is great,” pressed. sions - all under one roof. hall was too small and always he added. packed. According to Geetha Venkatara- Mikhail Shchukin of the Interna- “The entire event is very well or- Mohammed Abdul Rahim from man of the University of Delhi, tional Sakharov Environmental ganised. The lecture halls are Yanbu Industrial College, Saudi just the thought of having 3000 University, Belarus, opined that, very close to each other which is Arabia, was of the opinion that lot mathematicians in one place is “ICM has been a great adventure good because I can get to lec- many talks focus on pure mathe- extraordinary. She believes that it in my life. I am extremely happy tures without much trouble,” ap- matics and only a few on applied is a great opportunity to meet and to be here.” He also thanked the preciated Dragutin Svrtan of the mathematics. “The prayer room interact with distinguished math- organising committee for the invi- University of Zagreb, Croatia. He that has been allotted for us is ematicians. “The presentations tation and the travel grant. is immensely enjoying his experi- probably the most thoughtful ef- by Irit Dinur and Smirnov were “My first acquaintance with Indian ences here at ICM. forts of the organizers.” particularly interesting,” she men- Mathematics was the beautiful Alan Durfee of Mount Holyoke Oluwole Daniel Makinde of Cape tioned. story of Lilavati written by College, USA, has been attend- Peninsula University of Technol- While we do not want to indulge Bhaskaracharya. This story has ing ICM without fail since 1974. ogy, South Africa, opined that in self-praise, we were particu- greatly influenced me in becom- This event is of great importance every lecture and talk has been larly pleased to see that several ing a historian of mathematics,” to him because it helps him learn immensely interesting and educa- participants complimented the ef- remarked Mohammad Baghai of the recent developments in the tive. “It is incredible to see so forts of the Newsletter Commit- the University of Tehran, Iran. He field of mathematics from the ex- much participation in one place. tee! -ICM SNAPS- Highly Composite rof. R. Balasubramanian is a well- contributions of Indian number theo- Pknown number theorist and the rists after Ramanujan. Director of the Institute of Mathemati- cal Sciences, Chennai. He delivered a S. S. Pillai and S. Chowla were two plenary talk in ICM 2010 which was leading figures in number theory in the tantalisingly titled `Highly Composite'. period immediately following Ramanu- This is intended to be the short form jan. Some other Indian number theo- for ‘Highly composite contributions of rists of the post-Ramanujan period the Indian number theorists’. who have made significant contribu- tions are K. Ananda Rau, S. Chowla, In this talk, Prof. Balasubramanian T. Vijayaraghavan, K. Chandrasekha- traced the development of analytic ran Raghavan Narasimhan, K. Ra- number theory in India after Ramanu- machandra, M. V. Subba Rao and R. jan. Balasubramanian. Recently in an ef- fort to bring out the collected works of Number theory is one of the oldest S. S. Pillai, it was realized that some areas of mathematics. With the kind important contributions made by Pillai of fascination that it carries, it is very have not been archived. It was sur- natural that it continues to enjoy the at- prisingly found that there is no good bi- tention of some of the greatest minds ography of Pillai. Many of Pillai's throughout history. India has enor- unpublished manuscripts and corre- mously contributed to the subject with spondences with other mathemati- Ramanujan leading the way. Even cians are now available, thanks to the after his time, the contributions of In- effort of Prof. R. Thangadurai, Harish- dian mathematicians has been very Chandra Research Institute, Alla- significant. However, no good account habad. of these contributions are available. No lecture could possibly give a de- The first half of his lecture recounted tailed account of such a rich history of this rich heritage. The second half of deep contributions spread over sev- his talk was devoted to the deep and eral decades. The purpose of his lec- significant contribution of Ramachan- ture was to bring out some marvellous dra to analytic number theory.

REFLEXIONS August 27,Friday Hyderabad Hooligan xploring Hyderabad during the Con- national school and the other was somewhere Egress’s off-day on August 23, Shaun in between. I believe I sparked at least a cou- Maguire, a student of Stanley Osher (who ple of kid’s imaginations. All-in-all, I believe gave the invited talk on ‘New Algorithms in the kids enjoyed themselves and have stories Image Science’ at ICM 2010 on August 24) at of a crazy American to bond over. Caltech, had an amazing experience, which is narrated below in his own words. At one point, my new friend “VV” drove his scooter through a mountain of cow dung while Today was our only day off during the nine- he was looking over his shoulder to tell me a day congress. I ate a healthy breakfast, laced- disturbingly profane story. I got SPLAT- up my shoes tight, packed an umbrella and TERED! With regards to the story, this was embarked on what I thought would be a stim- not the only one of this kind that he told me, ulating but standard day of sightseeing. I took but I didn’t want to offend him while sitting on the hour-long bus into the old city, and started Shaun Maguire with Kids the back of his scooter in rural India. We ate walking towards Charminar — a four hundred a delicious south Indian feast for lunch at one year-old mosque whose history explains came confident his proposition was legitimate. of the schools. much of Hyderabad’s existence. Everything was going according to plan. After about 3 km I asked him how often he does this, where the We had the Hyderabad Ramadan special cui- of walking, a dude on a scooter pulled up next last person he picked-up was from, which sine of Haleem for an afternoon snack and to me, from behind, and asked where I was school we will go to first, the name of the prin- feasted on the equally famous Hyderabad from. This guy had a red beard and long hair! ciple there, where he lives, how he makes Biryani for dinner. The latter two didn’t live up “Red” flags were obviously set off. I told him money, etc. I used to play poker, so I applied to the hype, but were still enjoyable. I was the the USA and turned around to start walking the tricks I learned for reading people’s hon- main attraction in a prayer session accompa- again. I am a seasoned backpacker and have esty and checked for common tells, such as nied by about 300 people, including over a a lot of experience brushing-off crazies. momentarily glancing away before telling a lie. hundred dancing children. I was given count- Furthermore, he was quite small and his less trinkets. I gave a high-five to a guy while However, this guy spoke perfect accent-less scooter had at most a 50cc engine, so I felt we were each speeding along on scooters be- English and asked me what I do for a living. confident that I could either tackle him or roll cause he had an awesome custom scooter The question struck me as odd so I told him I off the back of his bike if things got out of horn. Speaking of scooters, I spent at least am a mathematician. He asked if I was in Hy- hand. Anyways, some of the best days of my four hours on the back of VV’s. I saw more derabad for the ICM. Okay, he obviously was- life started similarly and teaching mathematics than I ever could have hoped to. The roads n’t completely insane. We talked for a bit and is always rewarding, so I set off with him are a disaster for daily driving, but have a nice despite the fact that he was nerve-rackingly around 9:45am.I just got back after 13 hours scooter party vibe going on — a nightmare for attracted to me and undeniably sketchy, he with this creep — my first impression was so- residents, but amusing for tourists. But, impor- posed an interesting proposition. He invited lidified over the course of the day. However, I tantly, I finally managed to depart from VV in me to spend the day teaching mathematics to spoke to over 200 students in half a dozen an untraceable way. schoolchildren in the area. I have sponta- classes at three schools. The kids ran the neously done similar things in the past, and I gamut in every sense of the word. One school Interested readers can find more about the in- consider myself to be a talented judge of char- was incredibly poor and in the boondocks an cident in Maguire’s blog at acter so I vetted him for a few minutes and be- hour out of Hyderabad, one was a rich inter- http://lavashaun.wordpress.com Drama in ICM 2010 Sunil Mukhi Cambridge, Ramanujan’s hesita- the mathematics professor ob- that any two distinct continuous he award-winning play “A Dis- tion and later acceptance of the sessed with her formulae and numbers always contain infinitely Tappearing Number” is woven invitation, his trip overseas, his with the life of Ramanujan, the In- many other continuous numbers around the life of the mathemati- joint work with Hardy, his prob- dian-American working in the fu- between them. cal genius . lems with his health and the lack tures market who stumbles into It is a theatrical production with of Indian food, his suicide attempt her classroom by mistake and While Hardy is fascinated solely two interwoven stories, one his- and his return to India as a sick soon proposes to her, and the by Ramanujan’s brilliance and torical and the other modern, and man with tuberculosis, followed string theorist who helps bind the originality at mathematics, the opens with a woman mathemat- by his tragic demise just short of story together. None of the char- other characters constantly inter- ics professor lecturing on a fa- his 33rd birth- acters is espe- act with India in some way or mous formula of Ramanujan. She day. Truth is cer- cially compelling, other, bringing out a complexity gets carried away by her enthusi- tainly stranger but together they and diversity that provides a nice asm and starts to scribble formu- than fiction here do manage to foil to Ramanujan’s traditional lae all over the board. In the and the play convey a sense background as a poor Brahmin. meanwhile an actor, who will later quite appropri- of the excitement Several globalised Indian charac- play a physicist working in an ately presents of mathematics. ters play a key role in these inter- area of particle physics called the events liter- While the audi- actions including the hedge-fund string theory, addresses the audi- ally and in se- ence does not manager and the string theorist ence to point out that everything quence. There end up much but also a call-centre operator they are seeing – the set, the are no revela- wiser about how and a chambermaid at a London mathematics professor, the props tions for anyone A Scene from the Play a sum of infinitely hotel. – is fake, except the mathemat- already ac- many positive ics, which is real. quainted with Ramanujan’s life, numbers can add up to -1/12 (a The use of Indian dance forms, but for others the narration should subtle result due to Ramanujan tabla music and rhythmic chants In the course of the play the main quite effectively convey this mov- that has actually played an impor- at critical moments in the play recorded events in the life of Ra- ing and remarkable true story of tant role in string theory), there also brings the Indian context into manujan are surveyed – his letter an incomparable genius. are several musings about the the unfolding events in a novel to Cambridge mathematician G. nature of infinity that stimulate a way, as do the hilarious cinematic H. Hardy presenting a series of What makes this an effective sense of wonder. Infinity is pre- projections of Chennai traffic and astonishing mathematical formu- piece of theatre is the interweav- sented in two distinct contexts: a more poignantly the shimmering lae without proof, Hardy’s swift re- ing of the historical account with sequence of whole numbers that river in front of which Ramanujan action to invite Ramanujan to a tale about fictional characters: increase without limit, and the fact finally passes away.

REFLEXIONS August 27,Friday The Flip Side of Impact Factors Richa Malhotra mpact Factor is the most widely used metric in evaluating scientific Speaking at the Round Table Prof. José-Antonio de la Peña pointed Iresearch but is it a true indication of the quality of journals? Prof. out the various uses and abuses of evaluating science. He considers Douglas Arnold doesn’t seem to agree. “Impact Factor” he said, “is the impact factor as a completely ill-conceived concept. easy to use, but is fatally flawed...It is a highly skewed distribution and a flawed statistics”. One of the rea- Prof. Malcolm MacCallum high- sons for this, he pointed out, is the The impact factor was created in the 1960s as a way to meas‐ lighted the use of metrics other manipulation of citations by the edi- ure the value of journals by calculang the average number than impact factor, such as the tors of some ‘high-impact’ mathemat- of citaons per arcle over a specific period of me. [Garfield bibliometric measures whose ics journals. Prof. Arnold was 2005] The average is computed from data gathered by Thom‐ use was not found flawless ei- speaking at a Round Table discus- son Scienfic (previously called the Instute for Scienfic In‐ ther. But MacCallum likes the sion on ‘The use of metrics in evalu- formaon), which publishes Journal Citaon Reports. use of impact factor as it serves ating research’. Thomson Scienfic extracts references from more than 9,000 as a useful measure of how the journals, adding informaon about each arcle and its refer‐ journal is competing with other This special meeting was a follow-up ences to its database each year. journals. on the June 2008 report Citation Sta- tistics prepared by the International (Citaon Stascs, June 2008, p. 6) Citation data is inadequate due Mathematical Union (IMU) in associ- to several causes – self-citation ation with the International Council of Industrial and Applied Mathe- by authors, neglect of some papers, reputation of the author, gender matics (ICIAM) and the Institute of Mathematical Statistics (IMS). bias, etc. Prof. Frank Pacard gave an overview of the situation in France and highlighted that money for mathematics research is allo- To quote from the Executive Summary of the Report: “Using citation cated by the French Government and is then distributed to the Depart- data to assess research ultimately means using citation-based statis- ments on the basis of citations of the various departments of science. tics to rank things—journals, papers, people, programs, and disci- plines. The statistical tools used to rank these things are often Sir John Ball mediated the discussion. After the discussion people misunderstood and misused.” from Australia, Chile, Kenya and India, shared their experiences in their respective countries. Sanskrit: Effective Transmitter of Mathematics

...continued from page 2 in the US have to study Sanskrit, tracted me]. The focus of Sanskrit to the way Indians studied many fall in love with it, especially is on orality in languages, in mathematics and astronomy? How did you come to learn when you have a mathematical speech and in some scriptures These counterfactuals are bit Sanskrit? mind, because it is such a logical put together deliberately. But how hard. How else would Indian It was a complete accident and language. For those of us who do you use that when you are mathematicians have done? San- just goes to show what happens only learn ABCD which has al- thinking of these rules, these skrit helped them. In some ways when you start taking courses. I most no linguistic rhyme or rea- mathematical concepts, the texts I suppose, like anything else, it had always thought that India son to it, Sanskrit is a revelation as things that are supposed to be might have had its advantages was interesting while growing up and I loved it but at that time I re- very concise. and disadvantages. The focus on in , in the United alized that I wanted to get into the orality may have meant this idea States in the 1960s and 70s. I history of mathematics and sci- With different meanings of verses that the text is supposed to be didn’t have any particular contact ence. I also didn’t want to give up that are nonetheless supposed to composed in verses. with it. I came out of my under- Sanskrit. So I told convey knowl- graduate degree in mathematics my Sanskrit This is so different edge – how do The idea of having a text that is and I went to work as a computer teacher that this you handle that? very dense and concise may programmer in the Boston area. I is my situation, is from the kind of This is so differ- have been very hard for people to thought just for continuing the ed- there some place pedantic Euclid- ent from the kind understand sometimes. On the ucation -- we had a lot of that where I can study of the very other hand, that very difficulty adult education -- where you can the history of sci- ean tradition as pedantic or Eu- may have evoked people to con- just take a class or something. ence? Is there laid out in a step clidean tradition tinue to tackle the text who would The extension mathematics or by step sequence. as laid out in a have the ability to do it. school was offering night classes science in San- step by step se- and I wanted to study a language skrit. We had no quence. We think What other languages besides that I haven’t studied before and idea that in the history of math of that as normal and it has some Sanskrit and Hindi do you which has something I hadn’t books Sanskrit was important. My definitive advantages for explain- know? seen. teacher knew about David Pin- ing things. But it seems to me that I have learnt some Arabic, Per- gree at Brown University. in the classical Indian tradition in sian, Latin and a little bit of Greek. One of the courses being offered mathematics, one must be able to I picked up French and Dutch, at Harvard was Sanskrit and I had What attracted you to ancient have that understanding without and some amount of German, no idea what it was, except that it Indian mathematics? having every little thing spelled only for reading and conversing has got something to do with Well the fact that usable Sanskrit out for you. purposes. I am not a literary ex- India. But I took it. and it happens text is written in verse and how pert in any of those languages but to many people. I don’t know if the textual and pedagogical tradi- Do you think Sanskrit as a lan- I can read the math texts written that happens here, when people tion had to accommodate that [at- guage was particularly helpful in those languages. REFLEXIONS August 27,Friday

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(From left) A. Narne, G. Misra, R. Roy, T. Amarnath, R.Tandon, M.S. (From left) Richa Malhotra, B. Sury, Rahul V. Pisharody, Midhun Raj Raghunathan, S. Kumaresan, G. Rangarajan, R. Balasubramanian, U., Geethanjali Monto, R. Ramachandran, Gadadhar Misra (sitting), S. Kesavan and D. Singh Nikhil M. G., Sidharth Varma and Mohammed Anvar T.

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Viswanathan Anand shares a light moment with his opponents during Delegates are reading Reflexions, the newsletter of ICM 2010. the game. !"#$#%&'(&)*"+,&-&!.%"*/#0( Kenneth Prize for R. C. Gupta Richa Malhotra The award was presented to Prof. Grattan-Guinness at the 23rd In- ternational Congress of History of Science and Technology held in Budapest, Hungary. Prof. Gupta could not attend the Budapest Congress and will receive the award in his home country, India at the Closing Ceremony of the ICM on 27 August 2010.

Prof. Gupta's major contributions in the field include work on the history of development of trigonometry in India. He au- The 2007-2010 IMU Executive Committee at the Abel thored the chapter 'Historiogra- Prize Banquet on May 22, 2007 in Oslo. adha Charan Gupta is the phy of Mathematics in India' in the Rfirst Indian to be awarded the book Writing the History of Math- From left ro right: Z. Ma, Sir John Ball, M. Grötschel, C. Praeger, L. Kenneth O. May Prize for his con- ematics: Its Historical Develop- Lovász, M. de León, R. Piene, V. Vassiliev, S. Baouendi, M. Viana, C. tributions to the history of mathe- ment. He was the President of the Procesi matics. Prof. Kim Plofker, the Association of Mathematics +,,-.,/!*!,% !"#$!%%!&'(!)* author of 'Mathematics in India', Teachers of India from 1994 until will present the award to Prof. recently. He also founded the R.Ramachandran Gupta on behalf of the Interna- Volume 1 of the ICM journal Ganita Bharati (meaning B.Sury tional Commission on the History “Indian Mathematics”) and has 2010 Proceedings will Geethanjali Monto of Mathematics (ICHM). Prof. written several articles in the jour- Gupta was chosen for the 2009 nal. be sent separately, in Richa Malhotra prize jointly with Prof. Ivor Grat- Midhun Raj U.R tan-Guinness of UK by the ICHM. the form of a DVD, to Mohammed Anvar T all the delegates when Rahul V Pisharody See You, Seoulmates! it is ready. Sidharth Varma Nikhil MG