This year, the Meera Trust invited TIFR mathematician Professor M.S. Raghunathan to deliver this public lecture, and he chose to speak on The Queen of Sciences: Her Realm, Her Influence and Her Health.
In his talk (delivered yesterday at the Indian Institute of World Culture, Bangalore), Raghunathan started with what really sets mathematics apart from the other sciences. The answer, he said, lies in what their practitioners are after: a mathematician's primary quest is for higher levels of abstraction and beauty, while other scientists' primary motivation is to 'crack' -- understand -- a 'real' phenomenon. While 'unreasonably effective' connections between math and physics (or other sciences) may exist or emerge, they are purely incidental to the mathematician's quest.
The way mathematics develops is mostly determined by an internal dynamic, the imagination of the mathematician. It does every now and then draw upon natural sciences for inspiration, but even when that happens, the new mathematics that is born takes on a life of its own and often charts a path that has little relevance to its origins: the mathematician's imagination takes over.
Raghunathan peppered this part of the talk with interesting episodes from the history of mathematics. Here's one of them:
It would appear that great mathematicians tend to set greater store by mathematics that is concerned with its own constructs rather than mathematics that enlists itself into the service of other disciplines. ... When admonished by Joseph Fourier, a major figure of eighteenth century mathematics for pursuing useless mathematics, his greater contemporary Carl Gustav Jacobi responded with “A savant like Fourier ought to know that the sole end of science is the glory of the human mind and under that title, a question about numbers is worth as much as a question about the system of the world”.
The second part of his talk was an extended detour into some of the greatest mathematicians who had wide interests and / or led colourful lives. The idea, I believe, was to dispel the stereotype that mathematicians -- with their heads filled with 'cold logic,' as it were -- are socially inept nerds.
Raghunathan then turned to the 'health' of Indian mathematics. He expressed his deep concern about the state of mathematics education -- especially at the school level. He ended with a plea for making teaching an attractive profession for our bright young people.