Interstellar space travel, video conferencing, cyber security, net banking — these words have become a part of common parlance. These seemingly ordinary operations are made possible because of numbers and the calculations that go with it.
It is not just the domain of researchers with dishevelled hair cooped up in rooms with books, pieces of chalk and blackboards. Maths is in use in almost every virtual and real application we use today. The application of Maths in various fields of science, technology, engineering and medicine is what makes the stuff of great innovations.That is where the role of mathematical research institutes in the country becomes significant. On the outskirts of Chennai in Siruseri, spread over five acres of land in the SIPCOT IT park, Chennai Mathematical Institute (CMI) is one such institute.
The subject of Mathematics either evokes an image of terror-stricken students splitting their hair to memorise a bunch of formulas in fear of a strict, uptight teacher or a bunch of number-crunchers having eureka moments solving one mystery after another for the sheer love of numbers. For those who suit the latter image, CMI is just the place to be.
“In our schools, Mathematics is taught like the ‘tricks of the trade’. You memorise the formulas and try your hand at certain tricks. But that is not how it’s done. That’s a small part of Mathematics. The core of Mathematics is to understand the background of the subject,” says mathematician, psephologist and Professor Rajeeva Karandikar, Director, CMI.
“The exciting aspect about Maths, let’s say Trigonometry is that you can measure the height of a building without even going close to it. It may seem elementary, but what stays is that aspect, not the complicated formulas that are the focus in our school system,” he continues. The gist of Mathematics is logical thinking and analytical reasoning, and a lot of it has to do with hard work and application of the mind, he says.
Founded in 1989, CMI is a centre of excellence for teaching and research in Mathematics, Computer Science and Physics. The institute has undergraduate, postgraduate and doctoral programmes to offer in all the three subjects. These teaching programmes are run in cooperation with the Institute of Mathematical Sciences (IMSc), Chennai.
In 2006, CMI was recognised as a university enabling it to award BSc and MSc degrees on its own. It offers BSc (Honours) in Mathematics and Computer Science; Physics; and Mathematics and Physics.
The main areas of research in Maths include Algebra, Analysis, Differential Equations, Geometry and Topology. In Computer Science, areas of research are Formal methods in the Specification and Verification of Software Systems, Design and Analysis of Algorithms, Computational Complexity Theory and Computer Security. In Physics, research is being carried out mainly in Quantum Field Theory, Mathematical Physics and String Theory.
Research in Mathematics has social utility value, Karandikar says, that cannot be seen on a short-term basis but can be of use in the long run. “Computer applications are not just about coding and programming, they involve algorithms. For example how does Google give you relevant results on your first page of search? How does it make suggestions even before we complete typing something in the search box? These are applications of very sophisticated ideas in Mathematics. Students can study Mathematics for the subject or for its relevance in other areas of life,” he explains.
With ideas in Mathematics being increasingly translated to real life, it has formed the core of many exciting areas like Analytics, Big Data, Decision Science and Data Science. “Those who approach these areas with a solid Mathematics background are playing on a strong wicket. Otherwise, even an IT major is handicapped. It’s like you know how to read and write but you don’t know what those words mean. One can code the solution but somebody has to solve the problem first, then it can be translated into a code. This is where a solid foundation in Mathematics comes in,” he says.
Unlike other colleges that offer undergraduate courses in pure sciences, CMI’s students have the advantage of being taught by active researchers. Students are acquainted with the process of scientific discovery early in life, when others of their age are cooped up with straightjacketed syllabi that offer little opportunity for exploration. The students are also taught by distinguished visiting scientists from academic institutions like Tata Institute of Fundamental Research, Mumbai; the Indian Statistical Institute, Bangalore; Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam; IIT Madras; the Inter-University Centre for Astronomy and Astrophysics, Pune and the Ecole Normale Supérieure, Paris.
CMI has had sponsored research projects with Honeywell Technology Solutions Laboratory and Siemens’ Corporate Technology Research Centre, Bangalore, and Tata Research Development and Design Centre, Pune. It actively supports conferences, workshops and activities that contribute to the growth of Mathematics and Computer Science in the country.
As the quality of teaching and research output at CMI compares only with a few other institutes in the country, the academic calibre required of a student at CMI is understandably high. Admission to UG programmes of CMI is through a national entrance test. Students who perform exceptionally well in the national Science Olympiad are eligible for direct admission.
There are currently about 75 undergraduate students, 75 postgraduate and 50 PhD students on roll, and 37 faculty members. The parental pressure to take up technical courses instead of core sciences is one of the reasons for low intake of institutes like CMI.
Fees and scholarships
For the BSc programme the tuition fee is currently `750 per semester. A limited number of scholarships are available. A full scholarship consists of a tuition waiver and a monthly allowance of `5,000. A half-scholarship consists of tuition waiver only.
Currently, the amount payable for hostel and mess per semester is `19,600. (`4000, `13,200 and `2,400 towards hostel, mess and establishment charges respectively). These charges are adjusted periodically to account for inflation.
While Mathematics does not require high-end research infrastructure, Physics students perform basic experiments at the in-house laboratory in CMI.
In addition, students have an intensive laboratory programme at IGCAR for undergraduate
Application of Research
Talking about research in CS, Karandikar says, “Low end programming is not Computer Science, it’s not just about learning C++ and Java. Those skills are required but that is not the end of it. That’s why theoretical CS research is important. Today there’s a craze about Analytics and Big Data. IT majors provide huge chunks of data, and we are the ones who advise them on how to work on it.”
Karandikar, who has often been seen on television during the 2014 general elections offering insights into voting patterns, says opinion polls are something that he talks about when he visits schools and colleges. “How does one convey the mood of the nation in an opinion poll by just talking to 20,000 people? There’s very simple
Mathematics behind that.
“Probability Statistics is an integral part of the interface between Mathematics and society,” says Karandikar, who has specialised in the area of probability theory. In 2000, he developed a secret block cipher for the defence department. In 2005, he was also consulted by the CBI in a case involving cheating in a multiple choice examination.
In real life, one is always trying to optimise operations, minimise cost and maximise benefits, where Mathematics is involved. There is also a level of uncertainty where probability statistics come into picture. In Psephology, complex mathematical and statistical models need to be built. Statistical analysis used in surveys like the National Sample Survey have a direct bearing on policy making in the country. Hence, Mathematics seeps into our daily lives in invisible and intangible ways beyond our imagination.
KV Subrahmanyam, Professor of CS at CMI says, “We offer very high-level CS, Maths and Physics. This is not something you will get in Engineering, not even in the IITs. You may learn problem-solving there but here you learn a lot of theory and the way to go about it; on how to get the solution on your own.”
The professor opines that there is a culture to thinking in Maths. “There is a way to think in Mathematics, appreciate it and analyse it. This can only be taught by someone doing research. It is not available in textbooks. You may know Linear Algebra but may not know that it appears in Topology, Differential Geometry appears in calculations there. To know that Mathematics plays a central role in other subjects is crucial,” he says.
He says Mathematics is a subject where applications come much later and that is because of the nature of the Science itself. “But the tools and techniques used in verification have applications in subjects like Embedded Systems (an embedded system is a computer system with a dedicated function within a larger electrical system, often with real-time computing constraints). You can use these tools in top-notch industries that develop mircochips for validating how they work,” he adds.
As a practitioner of Maths and CS, he explains that software companies these days only ‘maintain’ existing software and that very few are into developing products. “A good background in theory helps in such a scenario. This is not something that is taught in run-of-the-mill colleges,” he points out.
One of CMI’s core strengths, he feels, is that 75 per cent of its students go on to do PhDs and contribute later through academic positions or industry positions. “This is not common in most institutes in the country. This is our 16th year of teaching. A number of alumni have begun their own startups, either in India or abroad. A lot of them have joined finance and insurance companies, like many of those from mainstream colleges, but they contribute to the industry at a much higher level commensurate to their depth of study,” he says.
CMI alumni Arul Shankar was acknowledged in Fields Medal winner Manjul Bhargava’s citation this year. The Fields Medal is the equivalent of a Nobel Prize in Mathematics. Bhargava was awarded for his pioneering work in number theory.
In 2013, Shiladitya Banerjee won the APS Award for Outstanding PhD Thesis in Biological Physics. Shiladitya studied the mechanics and shape of living cells and developed theoretical models to describe active stress generation in cells, tissues and their underlying cytoskeleton. He graduated with BSc (Hons) in Physics from CMI in 2008.
Sourav Chakraborty, Associate Professor, Computer Science, who was a student here in 2003 and later became a faculty in 2010 says the course-structure at CMI is geared towards research. “It’s not that if you want to work after this you won’t get a job but such is the nature of this course,” he says.
Emphasising that the student-teacher ratio is amazing at 6:1, he adds that the faculty is always accessible to the students. Echoing the sentiments of Karandikar, he says, “We should stop our super fascination with engineering. People working in places like TCS and elsewhere are not even practising engineering. They’re programmers. Programming is not engineering. The eminent scientist, CNR Rao, once said we are not producing engineers we’re producing clerks. Do what you love. For students to take up basic sciences, mindsets should change.”
VV Sreedhar, Professor of Physics at the institute, says his subject is the youngest discipline there. He guides students pursuing research in String Theory, Quantum Field Theory, Mathematical Physics, Quantum Gravity, Gravitation Theory and Applied Knot Theory.
“We have a niche market for students. For someone who is straight out of school and doing a high-level BSc here, the learning curve is steep. It is unique to the Indian context because universities are primarily relegated to teaching or research; either this or that. We are closer to the American or French model where students come face to face with the researcher while being taught by him,” he says.
Prof A Vijayakumar, Mathematics, Cochin University of Science and Technology, who has coordinated many regional-level Maths Olympiad exams, says that in a survey he did among his students, not many knew about CMI. “Even if you go to rural areas, students would have heard about IITs. But they don’t know about CMI. It should work more on its PR,” says Vijayakumar whose research areas include Discrete Mathematics, Graph Theory, Network Modelling and Mathematical Chemistry.
CMI’s programme is fully residential. All students are accommodated in the hostel on campus. The institute has a regular transportation arrangement for students to visit the city for shopping and other activities.
The use of Mathematics in telecommunication, computers, space science and many other subjects is infinite. The opportunities and possibilities it offers are unlimited. Unlike countries like the US where there are separate departments of the State devoted to promoting high-end research in Maths as well as higher education in the subject, in India it is individual efforts of selected institutes that spread awareness about the subject and the avenues it opens. For India to produce more Field Medalists in Mathematics more institutes like CMI should come up in the near future, nurturing the spirit of Maths and the joy of discovering Science.