# [Book Review] What is Mathematics?

Standard

This mid-sem recess I read : What is mathematics? by Balkrishna Shetty.

As many of you may know and have read the old classic by same title What is mathematics? by Richard Courant and Herbert Robbins. But both have completely different genre. One starling difference between these books is that Courant & Robbins have arranged their book in chapters as in a textbook where as Shetty has arranged his book on popular math topics. Though both books requires high school mathematics as prerequisite. I am not going to comment o the classic by Courant & Robbins.

Shetty has his focus on modern inter disciplinary aspects of mathematics. Shetty has written in a story telling form. A kind of Panchtantras genre. More of philosophical treatment of mathematics by drawing analogies which I don’t understand. There are mythological stories (Indian as well as western) at beginning of each section but I didn’t find much relation between the mathematical concept being explained and the story being told as a motivation for that concept. Shetty has tried to prove to common man that we all are mathematicians since mathematics is all around us. The book also consists the “Life Blood of Mathematics” i.e. Problems & Puzzles in form of Notes towards end of the book. Almost all famous recreational problems have been touched in form of notes in this book.

Shetty is not an active researcher. Actually he is a retired Indian diplomat who served as India’s Ambassador to Sweden, Latvia, Bahrain, Senegal and Mali. But before becoming a diplomat he was a researcher in Mathematics at the Tata Institute of Fundamental Research, Mumbai, he joined the Indian Statistical Service in 1973 and was Assistant Director, dealing with Industries and Trade Statistics in Central Statistical Organisation, Government of India, New Delhi.  Thus his style of writing may not at all appeal a person like me who is interested in pure & abstract beauty of mathematics. People like me don’t care much about physical existence of object to describe its beauty. But Shetty has tried to describe mathematics by attaching a physical meaning to it. Towards end of his book he discussed applications of mathematics in various fields (which is source for funding of abstract ideas of mathematicians).

I know that, $\sqrt{1+\sqrt{1+\sqrt{\ldots}}}=\phi$ where $\phi$ is our famous golden ratio. But there is a theorem concerning series:
If $\sum_{n=1}^\infty a_n$ converges then $\lim_{n \to \infty} a_n = 0$
But to be able to check validity of this theorem I should be able to find $a_n$ which seems to be non-existent for nested radical sequences.