Prof. Sudhir R. Ghorpade earned his B.Sc. from the University of Bombay in 1982, M.Sc. from IIT Bombay in 1984, and Ph.D. from Purdue University, USA, under the supervision of Prof. Shreeram S. Abhyankar, in 1989. Subsequently, he joined IIT Bombay, where he is currently an Institute Chair Professor in the Department of Mathematics.
During December 2012  December 2015, he was the Head of the Department of Mathematics at IIT Bombay. He has held visiting faculty positions in Denmark, France, Germany and USA, and has given numerous seminar/colloquium talks worldwide. His research interests include algebraic geometry, combinatorics, coding theory and commutative algebra. His research has resulted in enhancing fundamental knowledge and he is widely acknowledged for his contributions. He received an AICTE Career Award for Young Teachers in 1998, IIT Bombay Research Paper Award for 2011 and the Prof. S. C. Bhattacharya Award for Excellence in Pure Sciences from IIT Bombay in March 2014. He is a Fellow of the National Academy of Sciences since 2010, a member of the Apex Committee of the National Center for Mathematics, Mumbai, India since 2013, and has served on the Editorial Board of Resonance during 20032011 as well as the International Journal of Information and Coding Theory during 20072013.
Besides many research publications in reputed international journals, he has coauthored two textbooks on calculus and real analysis with Prof. B.V. Limaye, which have been published in the Undergraduate Texts in Mathematics series by Springer, New York (2006, 2010) and has coedited two monographs, published by the American Mathematical Society (2005) and the Ramanujan Mathematical Society (2013). He was also a guest editor of a special issue of the Journal of Algebra and its Applications (Vol. 9, 2015) in honour of its founding editor late Prof. Shreeram Abhyankar.
Recently, he has been elected as the President of the Indian Mathematical Society for the period April 2018  March 2019.
ET: You are a Professor at the Indian Institute of Technology, widely considered as one of the foremost educational institutions in the world. In your opinion, does Science, Technology, Engineering & Mathematics (STEM) education get enough attention in India?
SG: I think the question does not have simplistic answers. First of all, the question itself can be interpreted in several ways such as whether or not STEM education is getting enough attention in India from (i) people at large, especially parents and the students themselves, and (ii) governments and policymakers. Let me try to address these two stakeholders, leaving aside other possibilities such as industry and media.
I believe most Indian parents are deeply concerned about the education of their children. We often see poor people going through considerable hardships and making sacrifices for their children to get a decent education. Those that are relatively better off are also spending considerable time, energy and resources for providing quality education to their children in India or abroad. These people recognize that Science and Mathematics form an integral component of education. Engineering and Technology are still amongst the top career choices that students and parents consider, even though the sheen may have worn off a bit in the recent past. That said, undue weightage and importance is often given to examinations and marks instead of gaining a thorough understanding of the subject and witnessing the joy of learning.
As for governments and policymakers, at a macro level, I think there is significant support, even though in terms of percentage of GDP, our country seems to spend much less on education than many developed and some developing countries. I am not an expert on this topic, but it is my impression that for pursuing Science, Technology, Engineering and Mathematics at an advanced level, especially at elite institutions such as IITs and CSIR and DRDO laboratories, there is ample funding available. There are generous doctoral and postdoctoral fellowships available for those who can clear some eligibility tests, and for top students wishing to take up studies in Science and Mathematics after 12 years of schooling. There are handsome scholarships available through the INSPIRE programme of the Department of Science & Technology (DST) of the Government of India. On the other hand, funding to universities at large (that are usually supported by state governments) and undergraduate institutions appears to be far from adequate. More than the lack of funds, there has been tremendous bureaucratization, especially in our universities and the bodies that control them such as the UGC and AICTE. This stifles growth and provides fewer incentives for researchers to truly excel in their chosen fields, or even to convey the excitement about their subject to the students whom they teach and guide. The situation in schools that are fully funded by the local bodies such as municipal corporations is even more dismal, especially in mofussil areas. If one compares the amount of money spent per child in public schools in India as opposed to developed countries such as USA, the difference is quite phenomenal.
In short, while much attention is being given to STEM education in India, there is much that can be done by way of putting in more resources and also directing the resources that are already being put in a better and effective manner.
ET: What makes Mathematics important in life and how do we make it attractive for students to learn?
SG: While many of us may not realize it, Mathematics is everywhere in our day to day life, and its importance cannot be overemphasized. Let us take the case of numbers, about that we learn at a very young age. Our understanding of the world, in general, and our finances, in particular, would suffer a great deal if it were not for this fundamental concept. It is such a remarkable abstraction! The number 5, for instance, has no caste, creed, and colour, religious, political or sexual preference! We can equally well talk of 5 apples or 5 stones or 5 persons. We can appreciate this notion, and in particular, the number 0 and the place value system, both of which are said to have originated in India, if we try to perform addition or multiplication using roman numerals, or think of the cave man possessing no knowledge of numbers, but trying to ensure that all his sheep that went out for grazing return to the shelter by night. Notions of number and space are among the most basic in Mathematics and pervade many aspects of Science and daily life. Over the years, Mathematics has developed into a remarkable edifice. While developments in Mathematics have sometimes come about due to practical problems, they have also come about due to internal problems concerned with understanding patterns or symmetry and seemingly devoid of any practical use. Some of these have later found significant practical applications. For instance, the credit card numbers, when sent across electronic media, are encrypted for security using what is called the RSA algorithm which uses prime numbers in an essential way. We enter a movie theatre and see a sign such as "digital Dolby music" without pausing to think that the word digital has to do with digits that we learn in Mathematics. Communication by mobile telephone, deciphering the data sent by satellite, rendering of music digitally recorded on CD players are often aided by error correcting codes that use advanced algebra and related areas of Mathematics.
In order to make Mathematics attractive for students to learn, they could be told about some of the uses of Mathematics, but more importantly, students should be encouraged to ask questions, think on their own and develop a clear understanding. Mathematics is one subject that students cannot hope to master by mere memorization or rote learning. Once they understand something well, they are more likely to enjoy the subject and develop a liking for it. There are many books and videos that do an admirable job of explaining the basics of Mathematics and conveying the excitement of learning Mathematics. These can be made available to the students in the school library or pointers could be provided by teachers to some of the nice things about Mathematics available on the Internet.
ET: Besides standard accounting, in what parts of business does Mathematics play a central role? And, is this role likely to expand with the emergence of Big Data, Artificial Intelligence, etc.?
SG: The areas of human endeavour, in general, and business, in particular, where Mathematics plays a central role are perhaps too numerous to list here. I will just mention a few.
Mathematics and statistics are used in a significant way in data analytics so much so that in recent decades, a whole new branch has emerged, called Financial Mathematics. This uses advanced methods from partial differential equations and stochastic processes that are well beyond what is usually studied in undergraduate courses.
Mathematics of linear programming enters into efficient scheduling of airlines and human resources, and a good algorithm can save the industry millions of Dollars.
Advanced notions and results in linear algebra are used in the algorithm that Google uses to decide the order in which pages relevant to your search are lined up.
One does expect that the role of Mathematics is likely to expand with the advent of big data, AI, etc. Already, questions about efficient storage and retrieval of huge data by companies such as Facebook have led to newer questions and concepts in the theory of error correcting codes to which I alluded to in the answer to the previous question. Some of the keywords here are codes with locality or locally repairable codes. Newer and stronger algorithms for cryptosystems will be required if and when a quantum computer is actually realized. Already many advanced notions and results from classical areas of Mathematics (for instance, algebraic geometry) are used in relatively recent areas such as cryptography and coding theory. This could well expand in the future. Thus, there are exciting times ahead!
ET: Shortly you assume the role of the President of the Indian Mathematical Society. In your experience, what are the challenges in encouraging people to pursue a career in Mathematics?
SG: Classically, pursuing a career in Mathematics means either becoming a researcher and making original contributions to the subject, or to focus primarily on teaching Mathematics at a basic level especially at undergraduate institutions. Of course, the two activities can overlap. Each of these is fraught with unique challenges and I will try to convey my personal impressions here.
Those aspiring to do research in Mathematics have an opportunity to create something permanent that can possibly last for generations to come, and leave a definitive footprint on the sand of time. In his charming little book, A Mathematician's Apology, G. H. Hardy (the English mathematician who arranged for Ramanujan to go to Cambridge) emphasized the permanence of mathematical achievement by saying "What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men....In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all." Hardy goes on to write "Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean." I could be digressing here and indulging in some rhetoric, but the point is that for a young person genuinely interested in Mathematics, there is no dearth of motivation to pursue a career in Mathematics as a professional researcher.
But let us turn to some pragmatic considerations. The challenges that I see, especially in the Indian scenario, is the shortage of role models  researchers working at a sufficiently high level that can personally guide young students to do world class research and have a meaningful career. For a variety of reasons, mediocrity has set in and there is a tendency to pay scant regard to quality. Hiring and promotions at many institutions are decided merely on the basis of numerical indicators of academic performance and this, in turn, has led to a spurt of spurious journals where it is possible to publish just about anything provided one is willing to pay. What is particularly sad is that our young doctoral students may get the wrong ideas about how research is done. Of course, the situation is better at the socalled elite institutions. But for India to grow and be counted as a scientific powerhouse to reckon with, our universities at large have to prosper and be seen as places where vibrant and high quality research thrives. However, I do see some silver linings as well. There are isolated instances of top class researchers in some universities. The ATM (Advanced Training in Mathematics) schools organized by the National Centre for Mathematics (NCM) are attempting to ensure that doctoral students across the country have a strong foundation in the basic areas of Mathematics and a good exposure to some advanced topics. The MATRICS (Mathematical Research ImpactCentric Support) scheme of DST now provides for a modest, but useful and flexible, support to a large number of researchers in a manner that is free from bureaucratic impediments. Thus there is hope!
Those who are teaching Mathematics in colleges and predominantly undergraduate institutions have an invaluable opportunity to shape the minds of young students, and they have a very important role to play. In my younger days, I was blessed to have some dedicated teachers in my college who aroused my curiosity, helped to develop a good understanding of the subject, and encouraged me to take up higher studies. Perhaps they did not earn a whole lot of money, but were highly respected for their dedication and knowledge. Today, the salaries of college teachers are quite good, but for their professional growth, they are expected to do research. This seems a little unfair to me given the amount of teaching they do. A narrowminded insistence on all college teachers to do research is inevitably leading to many of them adopting unsavoury means to satisfy the requirement, at least on paper, and thereby losing focus on the scholastic abilities that can make them effective and inspiring teachers. This is also a challenge, in my opinion, especially since systemic changes are not easy to make.
ET: What is your advice to professionals who are overwhelmed by the fear of numbers?
SG: Fear is often a result of improper understanding of the relevant matter. As was mentioned earlier, numbers are important to our daytoday living and in fact, it is difficult to imagine life without numbers. Mathematics is a peculiar subject in that it evokes extreme emotions among people at large. Often, when I meet people in other walks of life and tell them what I do, they respond by telling how they hated Mathematics (and sometimes, how they loved it and were particularly good at it in school). There seems to be nothing inbetween. I mean, one doesn't usually tell a musician or a painter how we hated music or painting (even if we were not particularly good at it). Perhaps this has a lot to do with personal experiences and the kind of teachers one has had at a young age. For those interested in overcoming their fear of numbers and learning something about Mathematics, there is a wealth of resources available in a good library or perhaps more easily, on the internet. They just need to look up! And of course not everyone has to become a Mathematician!
To read the complete issue click here.
