निश्चय (niścaya)

Kurt Godel was the first to prove that mathematics is not certain. According to him, there will be statements about numbers which are true but cannot be proved. These statements can be either true or false. In the novel “A Certain Ambiguity”, mathematics had entered a different dimension in the lives of the two main fictional characters: Ravi Kapoor and Vijay Sanhi. Mathematics had caused an exciting twist in their lives which you will find out after reading the content of the book that was written by two Indian mathematicians Gaurav Suri and Hartosh Singh Bal.

Ravi is the grandson of Vijay. When Ravi was just a child, his mathematician grandfather showed him a certain problem in a calculator. Vijay wanted to give his grandson a mystical insight towards mathematics. He wanted to know what approach the child would do to give the problem a solution. Unfortunately, the next day became the end of Vijay’s life, but at least he started the mathematical career of his grandson. He was the one who gave Ravi the exciting   feeling for mathematics and without him, the whole story of Ravi’s life would be boring. The next stage of Ravi’s life happened when he got admitted to Stanford.

Ravi had difficulty in choosing his major but his father pursued him to have economics for it will attract many corporate recruiters. He did not know that it is in Stanford where he could find a shocking truth about his grandfather. Nico Aliprantis is a 62-year-old math teacher who became friends with Ravi. He was the teacher of the class “Thinking About Infinity” which Ravi had entered because of curiosity. Obviously, the topic of the course is infinity and through this, Ravi was exposed to notions concerning Zeno’s paradox, convergence of infinite sums, Cantor’s theory of transfinite cardinals, Zermelo-Fraenkel axioms of set theory and especially the Continuum Hypothesis. It was a coincidence having Nico’s subject of dissertation to be Vijay’s specialization, the algebraic number theory. Nico showed Ravi a book and turned to the page where his grandfather’s name was. Ravi had read a footnote saying that the key ideas contained in the paper were formulated by his grandfather while he was serving a prison sentence in Morisette, New Jersey, in 1919.

Vijay was imprisoned due to a blasphemy law. A sheriff complained over his anti-Christian speech in an event. But despite this accusation, Vijay offered no resistance. He and the judge had a conversation in jail which was mainly focused on the axiomatic method of mathematics, first with the Eucledian Geometry then later with the non-Eucledian geometry. There became a conflict between the judge’s Christianity and Vijay’s view of mathematics as a mathematician. Despite the fact that he’s in jail, Vijay was never afraid to reveal his ideas which he got from Euclid’s “Elements”. He believed that like Euclid, we must use the method of incorporating all known geometrical ideas into a self-consistent system based on a handful of axioms.

The mathematical concepts contained in the book began from Zeno’s paradoxes and infinitude of primes down to Godel’s Incompleteness and Paul Cohen’s Consistency theorems. Ravi and his grandfather both faced dilemmas while understanding the certainty of mathematics. They were stuck in the abyss of beliefs and choices while measuring the real scope of their mortal knowledge.

To react with what I read, I appreciate the main purpose of the novel which is to make mathematics beautiful in the eyes of its users. To really love a thing, you must first have a deep connection to it. Through a fictional (story) approach, the authors were able to connect with its readers. The book was able to give entertainment and at the same time knowledge. It encouraged the readers to discover something and enjoy the feeling of discovering it.  Math is all about discoveries and applications, after all. As a mere student who is still in a long-term brain processing, I accepted the book with gladness, but to those grown-ups whom we call now experts, they might have a very different insight. Everyone will surely have their own opinion with regard to this novel but I’m also pretty sure that after reading the book, you will be able to build another perception towards mathematics aside from misery.