The mega mathematical event – the ICM 2018 – which was the 28th episode of the International Congress of Mathematicians (ICM) was recently held – 1August to 9 August , 2018 – in Rio de Janeiro (Brazil) under the auspices of the International Mathematical Union (IMU). An event which happens to be one of a kind in terms of its 125 odd year history was attended by about 3500 delegates drawn from each single country of the world including a reasonably large contingent from India comprising about 160 mathematicians drawn from different states and universities/research institutions in the country. It was at the ICM-1900 held in Paris that David Hilbert set out a road map for mathematics for the next century by proposing a list of 23 outstanding problems that had remained open at that point in time. It is a measure of the progress and development of mathematics that followed thereafter in the 20th century that most of these problems have been settled since they were proposed for the first time then. The prestige that accompanies the event derives not only on account of the many awards/prizes being given away during the event to those amongst the most outstanding mathematicians for their ground breaking work, but also equally importantly in view of the feast of mathematics that is on offer through a series of plenary and invited talks by an array of distinguished mathematicians which happens to figure among the most prominent features of the Congress. The awards given away at the Congress include the Fields Medal which is considered to be the equivalent of the Nobel Prize but considerably more difficult to earn in view of the stringent conditions attached to it that include an upper limit of 40 years of the potential winner.
Who can attend the Congress!
One of the unique features of the ICM is that apart from those who are well known to have left an indelible impact on mathematics through their ground breaking research and leadership, all those who claim to have a ‘reasonable’ interest in mathematics can attend the Congress, of course as long as he/she can arrange travel/living support on his/her own. However, the funding agencies both in India and elsewhere chiefly support those applications for assistance which show evidence of the applicant being involved in a sort of an activity that would foster the advancement of mathematics as an important part of the human endeavour- through research, teaching, math education/history of mathematics and reach out activities involving popularisation and public awareness of mathematics.
The reason for this openness on the part of the IMU to encourage participation of a substantial cross section of all those involved in the enterprise of mathematics in a reasonable sense of the term is informed by the understanding that an exposure to the highest level of mathematics being talked about by those who have presided over the transformation of the subject would ignite the fire amongst the participants to do better and to give their best short in their area of research. The fact is that apart from certain stray cases involving individual islands of excellence, the absence of a culture of excellence in our universities, especially in mathematics, for the most part, has to do with a lack of exposure to those who are the best in the business. ICM offers the best platform for such an exposure towards sundry areas of research in mathematics and to the vast array of mathematicians of repute who are in attendance at the Congress.
Important features of the Congress
The main take-away from the ICM’s has been the incredibly high level of plenary talks by world class mathematicians besides those by the Field Medallists and MOST of the invited talks. Apart from being a uniquely humbling experience, these talks have all along been an intellectual feast on offer at the ICM’s, including at the ICM in Rio de Janeiro. The lectures by this year’s Field Medallists, the 2002 Field Medallist Laffrogue, the 2010 Field Medallist Cedric Villani and the Field Medallist/Abel Laureate Sir Michael Atiyah were some of these very fascinating lectures that were featured during the event. However, it is also a fact that the ICM’s are structured in a way where one is witness to how it takes the rough with the smooth. This because whereas on the one hand the level of short communications in many cases comes across as below par, on the other hand alongside the front ranking mathematicians from all over the world who turn up at the event, there are many times more of those who happen to end up at the event just for fun, as they are seen to spend most of the time outside the venue and away in the shopping malls of the city, oblivious to the need to benefit from the academic feast that is on offer at the event.
Besides the four Fields Medals which were awarded this year to Peter Scholze (MPI, Germany), Caucher Birkar (Cambridge), Akshay Venkatesh (Princeton) and Alessio Figalli (ETH, Zurich), there are many more awards that are given away at the ICM. These include the Nevanlina prize for theoretical computer science (Constantinos Daskalisis, MIT), the Gauss prize (David Donoho, Stanford), the Chern medal (Masaki Kashiwara, Kyoto) and the Leelavati prize, with the last one having been conceived and funded by the Infosys India. This year the Leeavati prize was awarded to Nesin Ali of Turkey for his contribution in the development of mathematics and the immense efforts he and his collaborators have invested in the creation of a mathematics village in Turkey. His speech at the ICM sought to provide a glimpse into the inhospitable conditions that he had to contend with in the accomplishment of his mission to see this institute coming to fruition. It was a story of undying commitment to his passion, perseverance, dedication and above all his love for mathematics that had finally carried the day for him against such heavy odds that had even landed him in jail for persisting with the idea of the maths village which somehow did not find favour with the political establishment in Turkey. His has been a saga of dogged will, indefatigable enthusiasm and the ultimate sacrifice for a cause that should be an inspiration for all those who are constrained to work against such heavy odds.
Some interesting comparisons of ICM’s with other important world events
There are in witness unmistakable similarities between the Oscar award ceremony and the opening ceremony of the ICM where the winners of Field Medals in mathematics are announced. In either case, whereas the winners are already in the loop having been told in advance of the award having been decided to be conferred upon them, the audience is, as is to be expected, completely unaware of who the winners are going to be till their names are announced at the event. And equally intense is the extent of the accompanying excitement and expectation underlying these two events.
Another striking similarity comes from an altogether different world involving the breath taking scenes one encounters at the Arafat during the Haj pilgrimage in Mecca. And this pertains to the spectacle of getting melted away-literally- in the sea of humanity that turns up at the Arafat where one is left to fend for oneself in a state of Nafsi Nafsi while even momentarily losing track of those accompanying the pilgrim as co-travellers. On the same analogy, here at the ICM except during a brief spell of media limelight being focussed on the Field Medallists during the inaugural function, one soon witnesses an Arafat like scene where all the participating mathematicians, both big and small, including the award winners are soon seen to be lost in the milling crowds, standing in long queues for coffee, meals at the venue and travelling to the hotels in overcrowded buses, invariably even without a seat to sit upon.
A brief digression
The 9-day mathematical extravaganza which was attended by more than 3500 delegates from all over the world came to a simple but glorious end today on the 9th of Aug. Amongst so many features of the event, the one that stands out as unique is the sheer diversity of mathematics that is on offer for all those who turn up at the event: from the highest level involving the frontiers of mathematics which engage the efforts of the best minds in the world to the other extreme involving the kind of mathematics that for a substantial number of those who turn up there merely happens to be not more than a source of living for them. There also are those who get benefited by attending events devoted to recreational maths, math education, history of mathematics, women in mathematics or the growth and development of maths in the third world. It’s this smorgasbord of the human endeavour called mathematics that is on offer at the ICM that has the potential to motivate, inspire and engage mathematicians of all kinds present there – serious and not so serious- in a meaningful pursuit of mathematics upon their return home. Which is reason enough why, at least in a large number of cases, influential mathematicians across the world get their governments to chip in to provide substantial funds to facilitate the participation of a reasonable number of mathematicians in their countries in the ICM which is held once every four years in different parts of the world ever since it was held for the first time in 1897 in Zurich- barring a brief hiatus on account of the world war-II. The next ICM in 2022 is slated to be held in Saint Petersberg, Russia.
In contrast with the bewildering variety of mathematics that gets featured at the ICM, there are a whole lot of mini conferences devoted to a particular theme of mathematics which are featured either prior to the commencement or after the conclusion of the Congress. These so called satellite conferences varying between 15 and 25 in each Congress are held in different parts of the host country or in neighbouring countries and attended on an average by around 50-100 participants as opposed to the milling crowds jostling for space in the ICM. One such conference in which I had participated and which was devoted to Banach space theory was held in the Ubatuba town of Sao Paulo during Aug.13th-17th, 2018.
Where does India stand in the world of mathematics?
In spite of the fact that the number of mathematicians per unit population of India is much lower than that of many countries, those Indian mathematicians and working in India whose work has impacted the development of a certain area of mathematics in which they are known to have made significant contributions are reasonably large in numbers so as to earn a prestigious place for India in the overall ranking of ‘mathematically advanced’ countries. The fact that India was chosen to host the 26th ICM in 2010 may be taken to be a tacit recognition of India’s standing in the world of mathematics. Yet another indicator of this recognition is that three invited talks were featured in the ICM 2018 in Rio by Indian mathematicians working in India. All that notwithstanding, the undeniable but unpalatable fact remains that the enormous pool of the mathematical talent in the country largely remains untapped in view of the shambolic state of Indian universities, even as a tiny fraction of that pool gets identified, nurtured and trained in the two dozen odd research institutions in the country which are dedicated to quality research in mathematics (and theoretical computer science/physics).
At this point, it is not out of place to point out that there are problem solvers and theory builders amongst those engaged in the pursuit of mathematics as a profession/passion. It is true but sounds strange that the ingenuity of problem solvers does not lie as much in a deep knowledge of the subject as in the intuition that informs their skill in problem solving. Both these genres of mathematicians are central to the growth and development of mathematics as an important human endeavour. However, apart from these types of mathematicians, a third category consists of those who read, understand, absorb and enjoy a lot of good mathematics but don’t go beyond that. Their role may surely not be terribly vital to the development of mathematics per se, but a willingness on their part to share the excitement of mathematics with their peers or students does indeed go a long way in motivating scores of budding mathematicians to pursue a successful career in mathematics. Come to think of it, a sheer majority (approx. 90%) of those in India involved in teaching/’research’ in mathematics at college/university level come across as those who belong to none of the above stated categories of mathematicians, and so settle for ‘metric-driven’ research which is certainly not going to promote the cause of conducting cutting edge research in the Indian university system! And that is a moment of deep concern indeed.
Dismal scenario of mathematics education in J&K
Back home in my own state of Jammu and Kashmir, the situation regarding pedagogy and research in mathematics remains as pathetic as it ever has been. Barring stray instances of reasonably good research output, there is not much to show for excellence in either of these domains. The need is for improving teaching, especially at the school and college level where teaching is conducted mostly in the run of the mill manner. A lack of interest amongst the school/college students to participate in the regional/national Math Olympiads may be attributed to a lacklustre teaching methodology as it prevails in our educational institutions. Participation in such competitions inspires learning and resurgence of talent in mathematics whereas for those involved in research, the ICM may be seen to provide a unique platform for a wide variety of opportunities that include an exchange of ideas with those who turn up there at the event and thus to explore the possibility of advancing mathematical knowledge through collaboration with those working on similar problems. Equally importantly, there is also this wonderful opportunity at the event of an exposure to the remarkable range of mathematics at the highest level that engage the attention of the best minds in mathematics. Such an exposure can and does provide inspiration to a whole lot of those pursuing a career in mathematics who are thus motivated to give their best shot in their endeavour to do meaningful research. The participation of teachers/researchers in the ICM, at least once during their career, both from the universities and colleges would go a long way in that direction which, however, would not be possible in the absence of liberal funding by the government that would do well to earmark a reasonable budgetary provision for the purpose on a regular basis.
Prof. M. A. Sofi is Professor Emeritus, Department of Mathematics Kashmir University, Srinagar
aminsofi@gmail.com