The primary objective of the School of Mathematics TIFR has been to carry out research at the highest level in Mathematics. The need to continue such research cannot be over-emphasized. It has of late become a danger that the technologically advanced countries want to have all basic research done on their soil. The claim is that `ivory tower' or `blue sky' research is not affordable for developing countries like India. This is a false notion. If India hopes to retain (and advance) its position in the world then its control over its own culture and technology is essential. Basic research in Mathematics is a big component in this. It is an area in which India has taken the lead in the long distant past and there continues to be a strong tradition of talent and admiration for this area among Indians. If this activity is not supported on Indian soil then our talents in this area will form part of a brain drain---a phenomenon which is already quite harmful to Indian Science and Technology. Hence the first point in the Vision of the Mathematics in the year 2020:
The School of Mathematics,TIFR is one of the strongest research groups in Mathematics in the world in 2020. It attracts the best Mathematical talent in the country and the world for research and study.
One of the objectives of the TIFR was that it should spread the culture of good scientific research all over the country--the filtering down effect. Partly due to the difficulties involved in setting up a centre to begin with and also partly due to entrenched forces which pulled in other directions this has not happened. However, we now see that a number of sister institutions like MatScience, Madras and MRI, Allahabad are also growing to be good centres for mathematical research. This should continue and the cooperation between these institutes should also grow. Hence the second point in the Vision of Mathematics in the year 2020:
There are a number of Research centres around the country where excellent research in Mathematics is being done. The joint conference (and its proceedings) held by these institutes is eagerly awaited by people around the world.
In a similar vein the job of teaching and exposition is one area where the School of Mathematics, TIFR has not contributed much as yet. Now that its strength has built up over the years it can make a dent here too. There are already schools every year where members of the School teach some of the important and interesting concepts in Mathematics. This program should expand to include Lecture series, Graduate texts and Quality improvement programs. Hence the third point in the Vision of Mathematics in the year 2020:
There are a number of universities where one can obtain a quality education in mathematics in 2020. The teachers in these universities are scholars with wide interests---no recent mathematical development is entirely outside their reach. Every year one of the top researchers from the research institutes comes to these institutes to give a course on some currently expanding area. Lecture notes from these course are published as a regular series.
One of the disturbing aspects of Mathematics education in India and also the rest of the world is that of the lack of mathematical sophistication in the education provided to non-mathematicians. Most of the mathematics taught to non-mathematicians centers around the developments of the previous century. Engineers are often taught to use mathematics like a black-box. Recent developments in Theoretical Physics, Computer Science and Engineering areas have shown that this is an erroneous approach. Thus it is important that the non-mathematical community be brought up-to-date on recent developments in mathematics---not only `Applied Mathematics' but even `Pure Mathematics'. Towards this purpose is the final point in the Vision of Mathematics in the year 2020:
Every year a number of mathematicians and non-mathematicians gather to discuss some aspect of current mathematics. There are courses by mathematicians on the developments in these areas while the non-mathematicians provide intuitive understanding for some of the concepts from a physical/engineering perspective.
Of course some of these goals may sound too ambitious but it won't hurt to try to achieve them.