Book review: To maths-haters, with love

Alex’s Adventures In Numberland: Dispatches From The Wonderful World Of Mathematics
Alex Bellos
Bloomsbury
448 pages
Rs922

Maths over the years has acquired a reputation of being both dry and difficult. Not surprisingly, most students these days find it the most difficult subject.

But as journalist and broadcaster Alex Bellos writes in his new book, Alex’s Adventures In Numberland: Dispatches From The Wonderful World Of Mathematics, “Maths can also be inspiring, accessible and, above all, creative…The thrill of maths is the moment of instant revelation…when suddenly everything makes sense. It is immensely satisfying, an almost physical pleasure.” Assuming Bellos is right, one can conclude that it is the way maths is taught that makes it boring.

Bellos in his book mixes maths with history, anecdotes, genius mathematicians, and even philosophy at times to give readers a sense that maths can be very exciting if presented the right way.
Take the case of the Pythagoras Theorem, one of the first theorems taught in school (for those who have forgotten, it states that the squares of two sides of a right-angled triangle are equal to the square of the hypotenuse). In 1940, Elisha Scott Loomis, published a book titled The Pythagorean Proposition which compiled 371 proofs of the theorem. It need not be said that the number of proofs must have only grown since then.

In fact, the Indian mathematician Bhaskara was so taken in by a pictorial proof of the Pythagoras theorem that “underneath a picture of it in his twelfth-century maths book Lilavati, he wrote no explanation, just the word ‘Behold!’ If only maths teachers at the middle school level kept such stories in mind and shared them with their students while teaching, the subject would be much more interesting.

Or take the case of the decimal number system. In India, we use lakh and crore as numbers instead of million and billion as is used worldwide. Lakh and crore are derived from the Hindi lakh and karod, which in turn come from the Sanskrit words laksh and koti. Of course, we all know this.

But that’s not where it ends. Bellos writes, “In ancient India, coining words for large numbers was a scientific and religious preoccupation. For example, in the Lalitavistara Sutra, a Sanskrit text that dates from the beginning of the fourth century at the latest, the Buddha is challenged to express numbers higher than a hundred koti (a crore). He replies: One hundred koti are called an ayuta, a hundred ayuta make niyuta, a hundred niyuta make a kankara...a hundred vibhutangama make a tallakshana….”

Tallakshana was a number which had 10 followed by 52 zeroes or 1,053 in mathematical terms. But this was just one counting system. There were other counting systems on top of this and the last number in the final system was equivalent to a number 10 followed by 420 zeroes.

Bellos writes beautifully about the history of mathematics, getting into intricate detail about how the number system evolved. He discusses questions such as: Why does the counting system have 10 numbers and not six or eight for that matter? How did the concept of zero evolve? Why did attempts to change the way we count time, from the current system where an hour has 60 minutes and a minute 60 seconds, to a decimal system where a day has 10 hours, each containing 100 minutes and 100 seconds, fail?

The impact maths has had on religion over the centuries is also dealt with in some detail. Bellos writes, “Mathematics plays more of a role in Islam than in any other major religion. More than a millennium before the invention of GPS (global positioning system) technology, the requirement to face Mecca relied on a complicated astronomical calculation — which is one reason why Islamic science was unequalled for almost 1,000 years.”

Apart from the history of maths, Bellos also delves into the contemporary maths scene. His account of the Sudoku success story is, in fact, one of the highlights of the book.

The name ‘Sudoku’ suggests that the game was invented in Japan. It wasn’t. In fact, the earliest version of the game was designed by Howard Gans, a retired architect and puzzle enthusiast from the state of Indiana in the United States. The game was called Numbers Place and made its first appearance in 1979.

Maki Kaji, a Japanese puzzle maker, came across this game and thought it would fit in perfectly in his new magazine. “He called his version Sudoku, the Japanese for ‘the number must appear only once’”. The magazine appeared in 1980 but the Sudoku got little attention.

It had to wait for nearly two decades before Wayne Gould, a New Zealander, while browsing at a book store in Tokyo came across a Sudoku book. He then spent the next six years writing a programme that generated Sudokus. Once the programme was ready, he approached the British national press. The Times of London decided to publish his Sudokus, and that’s how it got noticed and became a global phenomenon in no time.

Bellos writes for the lay reader but there are portions in the book, such as the last chapter on the concept of infinity, which is a bit heavy. However, despite these taxing portions, Bellos fills a huge gap as far as books on maths are concerned.

Very few authors can write about maths in a manner that is appealing as well as accessible. That’s largely because those who understand maths with all its beauty cannot write in simple English, and those who can write in simple English do not understand maths with all its beauty. Bellos does both.