CMI's goal is to evolve into an institution on the lines of the great universities in Europe and USA. These institutions, founded on a tradition of learning and scholarship over the past few centuries, attract students by the presence of outstanding academic persons on their faculties.

Excellence in research and teaching go together. Faculty who are research oriented can present the material they teach from fresh perspectives. This gets students involved in the process of scientific discovery and opens the eyes of bright young minds to the joy of doing science.

The teaching programme at CMI began in 1998, when the Institute arrived at an arrangement with the Madhya Pradesh Bhoj Open University (MPBOU), Bhopal, to offer accreditation for a BSc Honours course in Mathematics and Computer Science at CMI. In 2001, the BSc programme at CMI was augmented to include separate MSc programmes in Mathematics and Computer Science. In 2003, CMI expanded its BSc programme to include a course in Physics. A new MSc course in Applications of Mathematics will begin in 2010. Since December 2006, CMI has been recognized as a university (under Section 3 of the UGC Act 1956), and it now awards BSc, MSc and PhD degrees directly.

The students who study at CMI are among the brightest in the country. Selection is through a national entrance examination. Students who perform exceptionally well in the national Mathematics, Informatics and Science Olympiads are eligible for direct admission.

Students who have graduated from CMI are pursuing higher studies at the most prestigious institutions around the world: Caltech, Chicago, Johns Hopkins, MIT, Princeton, Rutgers and Yale in USA, the Ecole Normale Superieure in Paris, the University of Paris-Sud and the University of Bordeaux in France, the Max Planck Institutes in Saarbruecken and Bonn in Germany, ETH in Zurich, not to mention CMI, IMSc, HRI, IITs, ISI and other institutions in India.

The teaching programme at CMI has benefitted greatly from the active participation of faculty from the Institute of Mathematical Sciences, Chennai (IMSc). CMI also attracts visiting faculty from other research institutes around the country, many of whom stay for a semester to teach courses and participate in the research activities of the Institute. In addition, CMI has a regular exchange programme with the Ecole Normale Superieure (ENS) in France, one of the leading academic institutions in the world.

In July, 2009, CMI became one of three non-European partners joining the Erasmus Mundus Master Programme ALGANT (ALgebra Geometry And Number Theory), funded by the European Union. The ALGANT programme allows students to pursue Masters and Doctorate degrees across the institutions participating in the programme.