The fields of work of the seven recipients of the four high global awards at the ongoing International Congress of Mathematicians (ICM) at Hyderabad are indicative of the fast-disappearing boundaries between pure and applied mathematics. The field of mathematics has evolved tremendously since the great G.H. Hardy proclaimed in A Mathematician's Apology that it was the very fact that pure mathematics had no practical applications that made it beautiful and of permanent aesthetic value — as against applied mathematics, which was dull and trivial. It was for the same reason that mathematics did not enter Alfred Nobel's mind when he established the Nobel Prize primarily to honour inventions and discoveries of great practical benefit to humanity. The Fields Medal, the most important of the mathematics awards and regarded as the equivalent of the Nobel Prize, is traditionally given for exemplary achievement like solving an outstanding problem of great significance in pure mathematics. In recent years, this too has begun to recognise mathematical achievements in problems arising in physics and other subjects. This is very much in evidence in this year's awards.
The institution by the International Mathematical Union of awards other than the Fields Medal to recognise significant mathematical achievements in information theory and other technologically important areas is yet another indicator of the increasing relevance of mathematics to diverse fields. The Rolf Nevalninna Prize and the Gauss Prize this year have honoured improved error-correcting codes in communications, which have applications in high speed modems, and the mathematical theory of wavelets, which has resulted in efficient data compression in imaging technologies with applications in digital movies and space-based astronomy. Public-key encryption, which is widely used in data security, is rooted firmly in number theory, Hardy's field of specialisation, which he said was beautiful but of little practical value. Recent developments in theoretical computer science, financial mathematics, and derivative pricing are examples of important emerging applications in mathematics. Indeed, some very important talks in the Hyderabad Congress are in areas of pure mathematics inspired by problems in applied mathematics. It is this wonderful duality of mathematics — the joy of pursuit of pure mathematics for its intrinsic aesthetic experience, and its increasing relevance to real-life problems — that must be projected in greater measure to school and college students. It must become an essential component of mathematics education to promote the idea that successful careers are possible through the pursuit of mathematics.