Today I heard Prof. M S Raghunathan on Mathematics: art that would rather be science? (pdf): his thesis was that mathematicians develop mathematics driven by their fascination with its beauty than usefulness; however, they tend to align themselves with scientists than artists. However, I found it curious that Hardy was not mentioned (I might be wrong about this since I came a bit late to the talk; for all I know he might have started with Hardy; but there was no reference to Hardy after I entered the hall — which was, at worst, after the first five minutes).
Prof. Raghunathan’s talk set me thinking about a couple of things that I find fascinating about mathematics: (a) Why do many people find mathematics hard (because, it is easy to make mistakes and hard to cover them up — I probably heard this first in Terence Tao’s blog) (b) Why do people have tendency to use too much of mathematics, unnecessarily (ostensibly to make a piece of work more respectable!).
On the whole, it was an enjoyable talk; and, I found some of his answers to questions (Are Indians more mathematically talented? Why do not we have a good programme to identify and nurture mathematical talent) quite sharp and funny!
Entertaining Research 
August 27, 2011 at 7:35 am |
Whether it is art or science probably depends on the practioner. For many pure mathematicians, it is probably like an art because of the freedom to built without bothering about immediate applications. But for people like Newton or anybody who is interested in understanding nature, it is like a science. If there is no known math. to handle the problems they try to build the necessary math., considered the language of science. Possibly whatever human being do tends to have some tenuous connection with reality; may be that is why some math. built purely for aesthetic pleasure has been useful later (including some of Hardy’s work), sometimes after centuries.
Finally I do not really know whether mathematics is hard or not. I found caluculus hard when I started. At some stage I felt that math was not based on just calculations but ideas were also imporatant and started understanding and appreciating the ideas, it became less hard but never completely easy. But now my interests have shifted and I find that eventhough I can still do some math. it no longer thrills me.
August 27, 2011 at 9:09 am |
Dear Swarup:
Prof. Raghunathan did speak about natural scientists who started with physical problems and proceeded according to the dictates of mathematical beauty (Weyl, Dirac, …). He also talked about Grotherndieck and his loss of interest in mathematics later in his career after revolutionising a couple of areas of mathematics.
I agree with you about the tenuous connection part — Prof. Raghunathan quoted Darwin who apparently said that the only way any progress in science can be made is via mathematics; mathematics being a language, and one in which complex ideas can be expressed very neatly, it is no wonder that any mathematics that is developed will be used by people later to explain their own physical observations.