The Mathematical Trinity

The book discusses nine popular propositions in Mathematics: “The Consistency Theorem” from Logic; “Isosceles Triangle Theorem” and “Pythagorean Theorem” from Geometry; “Ordered Pair Proposition” and “Mathematical Induction Principle” from Zermelo–Fraenkel set theory; “Remainder Theorem” from Number theory; “The Quad­ratic Equation Proposition” and “The Subgroup Theorem” from Algebra; and “Dedekind Continuum Theorem” from Analysis, and thereby covers a sufficiently wide cross-section of modern mathematical sub-domains. Using these propositions, the book primarily has three objectives: to offer a deeper appreciation of these propositions and related concepts; to provide a better understanding of their relationship with other topics of Mathematics; and, above all, to throw light on the profound nature of the discipline that has developed and advanced over the millennia through a synergistic combination of imagination, inference, and insight.

The book meticulously dissects each of these chosen propositions in separate chapters while simultaneously probing their intricate interrelationships. This approach yields a heightened appreciation of their mathematical significance, bridging the divide be­tween educational levels. These propositions often appear poised between school-level mathematics and university-level rigour, and the book adeptly navigates this middle ground. Furthermore, it goes beyond mere logical inference, embracing the realms of imagination and insight. It offers a holistic, historical, and intellectual perspective, unravelling not just the necessity of each proposition but also its unique contributions to the fabric and evolution of Mathematics. In doing so, it sheds light on a constella­tion of interconnected mathematical concepts, enriching the reader's comprehension of this remarkable discipline.

Balakrishna Shetty, a notable diplomat and an accomplished mathematician, has served as a Guest Faculty at the Department of Mathematics in the Indraprastha Institute for Information Technology, New Delhi, from 2013 to 2015. Additionally, he holds the esteemed position of a Life Member within the Indian Society for History of Mathematics, which is based in the Department of Mathematics at Ramjas College, University of Delhi, India. He is an M.Sc. in Mathematics from IIT Kanpur, where he achieved a first-class ranking. He also holds a B.Sc. Honours in Mathematics from Presidency College, Kolkata, graduating with first-class honors in 1970. During his tenure at the School of Mathematics, Tata Institute of Fundamental Research, Mumbai, from 1972 to 1973, Shetty distinguished himself as a prominent researcher in the field of abstract harmonic analysis. His contributions have extended to the realm of literature as well, as evidenced by his authored book titled, What is Mathematics?, which was published by the National Book Trust India in 2013.

He has been Ambassador to several countries: the Kingdom of Sweden; the Kingdom of Bahrain; Latvia; Senegal; Cape Verde Islands; Guinea Bissau; Mali; Mauritania; and the High Commissioner to Gambia. He served as Minister (Economic), the Embassy of India in Paris, France, handling bilateral trade and investments with respect to France and relations with the the Organisation for the Economic Co-operation and Development (OECD); Joint Secretary at the Foreign Service Institute, the Ministry of External Affairs (MEA), New Delhi, India, in-charge of the Professional Course for Foreign Diplomats; Director and subsequently Joint Secretary (Technical Co-operation Division), the Ministry of External Affairs (MEA); Deputy High Commissioner, High Commission of India, Singapore, dealing with bilateral trade, investments, media and culture; First Secretary and subsequently Counsellor (Political), the Embassy of India inMoscow, Russia (June 1988–July 1991). He also held several other positions in India: Undersecretary (Economic Division); Undersecretary (State Trading and Overseas Indian Investments) in the Ministry of Commerce; and Deputy Director General (Administration), Indian Council for Cultural Relations, New Delhi. He also was posted to the Permanent Mission of India, Geneva; to High Commission of India, Dhaka, as Second Secretary (Media and Culture) and subsequently as First Secretary (Economic and Commerce).

Currently, he is involved with the following activities: President, Governing Body, Action for Food Production (AFPRO), New Delhi, a 50-year-old socio-technical institution declared as the Institution of National Importance by the Government of India, in the field of drinking water, sanitation, climate change and rural livelihood; Mentor, Salute the Soldier LLP, New Delhi, for assisting retired soldiers and their families; Advisor,IWAY, Pondicherry, for helping Lycee Francais de Pondichery and French citizens of Indian origin; Advisor, Edsix BrainLabs, IIT Madras Research Park, Chennai, in the field of cognition; Member, Governing Body, Jesus and Mary College, New Delhi, India; Board Advisor, Bank of Baroda eProcure Software Solutions, Bengaluru; and Resource Person for nation-wide sensitization programme on Mathematics for Teachers, Vigyan Prasar, Department of Science & Technology, Government of India (2013–2016). After retirement from the government services, he had been the Diplomatic Mentor, Indian Council for World Affairs, New Delhi (July 2011–December 2012).