“Inspiration requires marketing, and marketing requires stirring communication,” they continue, in the ‘mathematical novel’.

The human capacity to be able to play with infinity and to begin to make sense of it represents one of the greatest achievements of our species, the authors say, through Nico, a key character in the novel.

“In one of the most momentous events in human history the Greeks found that there is indeed room for an entirely new class of numbers,” Nico tells an attentive class.

What did the Greeks find? That there are quantities that do not correspond to the ratio of two whole numbers. “Previous to this discovery they believed that this was impossible — that every quantity in the universe was either a whole number or a ratio of two whole numbers (fractions).”

Demonstrable existence of a different type of quantity was a shock to the system, akin perhaps to what the discovery of extraterrestrial life would be today, continues the teacher.

“The Pythagoreans encountered square-root 2 as the hypotenuse of a right-angled triangle that has both sides equal to 1,” explains Nico, tracing the history of ‘the first intellectual crisis in mathematics’… that resulted in the ‘irrational’ exuberance.

The session was over, but Nico continued. “Rational numbers and irrational numbers are together called real numbers,” he’d say. “Any decimal expansion, whether or not it terminates or repeats, is a real number.”

He would cite Cantor for the ‘extraordinary claim that the set of natural numbers is the same size as the set of rational numbers, but that the set of real numbers is larger than the set of rationals.’ Another of Cantor’s daring suggestions was that there were different kinds of infinity, and that one infinity could be larger than another.

“Je le vois, mais je ne le crois pas! I see it but I don’t believe it!” reads one of Cantor’s quotes from an 1877 letter, about how he was surprised at his own discovery! Yet, “the essence of mathematics lies in its freedom,” as he said, at a different time.

“Many thought he was mad to believe this, but in the end his ideas have prevailed,” says Nico. “Infinity does indeed come in different sizes. That, ladies and gentlemen, is one of the gemstones of this course.”

A book for the math-avid, both current and aspiring.

D. MURALI

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