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For the last one month I was completely occupied with work . Weekdays and Weekends flew away before I realized that it has been quite sometime since I had read any book. This weekend , being a long weekend , decided to spend my time reading a book on ambiguity. I stumbled on to a reference to this book on some blog and was intending to read at some point in time. A nice holiday break and festive mood around was good enough to motivate me to read this book, which was touted as a mathematical novel.

There are 2 stories which are intertwined in this novel. One about Ravi Kapoor, who narrates his learnings from a class on Infinity at Stanford. The second story is about circumstances in the life of Ravi’s grandpa, Vijay Sahni who gets imprisoned for a brief period in his life. The narration of these two stories can be visualized by the following image:

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The upper box represents the story of Vijay Sahni. The lower box represents Ravi’s story in the novel.

The conversations between Vijay Sahni and Judge Taylor brings out Euclidean and Non Euclidean Geometry

The five postulates of Euclid based on which the entire “ELEMENTS” is built are :
Postulates :
1. It is possible to draw a straight line from any point to any point
2. It is possible to produce a finite straight line continuously in a straight line
3. It is possible to describe any circle with center and radius
4. All right angles equal one another
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

The fifth postulate controversial nature lead to the development of Non-Euclidean Geometry

The lower box is Ravi’s story where his stanford professor Nico, uses a perfect blend of examples and historical narrative and leads to the Continuum problem

Continuum Problem: Is there a set whose cardinality is greater than the cardinality of natural numbers, but less than the cardinality of the real
numbers?

What is the connection between the two stories ? Why does the book develop these themes in the first place ? What set theory and geometry have in common ? A reader would definitely be delighted from the way connections are made in the book using two stories.

Here is a snippet from one of the conversations between Vijay Sahni and the Judge
This freedom has me in awe. It is unbounded, and every single one of us possesses it. We are free to believe or not to believe; we may create mathematics or build homes or write poetry or do nothing at all; we can marry and raise a family or stay in bachelorhood; we can quest for new adventure or find comfort in the familiar; we can seek meaning or we can doubt that it is possible to find meaning. Every path is there to be taken or ignored, and none is ordained. We are given no certainties, yet we are given the capacity to feel certainty. There is no absolute meaning to latch onto, yet transcendence is within our grasp. We are free to chart our course, free to pursue our passions, and free to create the axioms of our lives. And it is in this glorious freedom that I find grace. This freedom, then, is my proof of His existence.

Here is a list of mathematicians who figure in the book as the stories progress

Image Zeno popularly known for his Paradox

Image Italian thinker Giordano Bruno
Image Galileo

Image Bhaskara (1114-1185)
Image Pythagoras (570-490 bc)

Image Cantor
Image Baruch (Benedict) Spinoza (1632-1677)
Image Euclid

Image David Hilbert (1862-1943),

Girolamo Saccheri (1667-1733):

Image Farkas (Wolfgang) Bolyai (1775-1856)
Image Farkas Bolyai’s son Janos (Johann) Bolyai

Image Nikolay Ivanovich Lobachevsky (1792-1856)

Image Johann Carl Friedrich Gauss (1777-1855)

Image Bernhard Riemann (1826-1866)

Overall this book reminds me of “The Lady tasting tea” which gives a good historical narrative of people contributing to the field of statistics.

I guess the take away from the book, besides getting a thrilling ride on the basis of mathematics is this gem of a statement:

It is true that absolute certainty may lie outside our reach, but we live for that magic moment of discovery when we are attuned to this sense of order and connectedness. And the existence of this order and connectedness is a leap of faith.

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