Reflections On The Philosophy of Mathematics (An Old and Rare Book)

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Dr. D. Chatterjee, a renowned mathematician and educationist, had his earlier education from St. Xavier's College, Calcutta University and Indian Statistical Institute. Being invited he visited the International Centre for Pure and Applied Mathematics, France and later joined the Technical University of Vienna in the 'Chair for Analysis' on sabbatical leave. As Reader in Mathematics he has written several text books on Mathematics and Statistics for the undergraduate and post- graduate levels and has to his credit nearly thirty research papers published in inter- national journals of repute. He is associated with many universities and learned bodies in different capacities and has been actively contributing in various fields of knowledge over the last two decades.

Mrs. S. Chatterjee, wife of Dr. Chatterjee, had her education in Philosophy from Calcutta University. She then opted for a research career in the Philosophy of Science at the Rabindra Bharati University. Her research work was largely supported by Professor Rama Ranjan Mukherjee and Dr. Amarnath Bhattacharyay and received wide applause from many in India and abroad. She has several research papers to her credit and is actively engaged in researches on scientific aspects of Tantra Philosophy.

The spectacular growth of scientific knowledge in the last two centuries has called for an introspection as to its necessity and relevance. By this time the nature and character of a subject have also undergone a radical change resolving the often artificial distinction between different subjects and their fields. The questions of survival and values have thus gained importance in the context of various overlapping theories. A review of the old system of thoughts in relation to the new has become a call of the age. This monograph is an interesting evaluation of various philosophical aspects of mathematics in the said direction. The discussion starts with the nature of mathematics in the changed perspectives and winds its path through the philosophical schools, space and time, intuition in mathematics, crises in mathematics right upto the future of mathematics.

The title of this study is 'Philosophy of Mathematics'. The usual meaning of philosophy is the use of reasoning in seeking truth and reality and knowledge of reality, especially of causes and nature of things. This agrees rather well with the explanation given by the authors when they state that the aim of the philosophy of mathematics is to find its relevance to human existence analysing its basic concepts, its meaning and essence, to put mathematics on a strong foundation. This means that use will be replete with abstract notions as is natural with mathematics, as the authors say "Mathematics is a formal discipline, abstract and symbolic without reference to meaning."

The authors have made an exhaustive and critical study of the works of mathematicians through the ages, starting with the Greek and Vedic period from the 4th century B.C. right to the most recent mathematics of the present age.

The essence of life is the quest for knowledge and this world is a wonderful place that reveals at each corner of its vast domain unexpected new beauty and grace that is called knowledge. So the kingdom of knowledge is infinite and ever- green with fascinating ideas that surprise anyone with a serious mind. Eventually we, while walking down the road of life entered into a new world, namely, the Philosophy of Science whose firmament is studded with innumerable glittering stars. Astounded we looked up and then bathed in di- vine grace, we resolved to share our joy with others. This monograph is a gentle expression of our joy that we want to share. If anyone gets pleasure in reading this, that would be our best reward.

The theme essentially circles round and round one arch- idea the essence of Mathematics and it is arranged so as to enable the reader roam comfortably and happily over our reflections, except for the last article which is little involved. Our musing on different aspects of the life of Mathematics has manifested itself mainly through philosophical overviews, introspections and conclusions of different chapters. Many may differ from us and that is natural but no realisation can be nullified by controversies. Only data can be rectified. Arguments and counter-arguments enrich knowledge but not wisdom. Mistakes are inevitable, more so for persons like us with humble means and ability. All responsibilities in this regard are ours and we beg no excuse for this but will be glad to receive comments and criticisms from all.