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guidance but also promoting his new way of calculation. The 16 sutras, he taught, were to be used as if they were mathematical formulae. While they might have sounded ambiguous, like chapter titles in an engineering book or numerological mantras, they in fact referred to specific rules. One of the most straightforward is the second, All from 9 and the last from 10. This is to be implemented whenever you are subtracting a number from a power of ten, such as 1000. If I want to calculate 1000 – 456, for example, then I subtract 4 from 9, 5 from 9 and 6 from 10. In other words, the first two numbers from 9 and the last from 10. The answer is 544. (The other sutras are applications for other situations, more of which I will introduce later.)

Tirthaji promoted Vedic Mathematics as a gift to the nation, arguing that maths that usually took schoolchildren 15 years to learn could, with the sutras, be learned in just eight months. He even went as far as claiming that the system could be expanded to cover not just arithmetic but algebra, geometry, calculus and astronomy. Due to Tirtharji’s moral authority and charisma as a public speaker, audiences loved him. The general public, he wrote, were ‘highly impressed, nay, thrilled, wonder-struck and flabbergasted!’ at Vedic Mathematics. To those who asked whether the method was maths or magic, he had a set reply: ‘It is both. It is magic until you understand it; and it is mathematics thereafter.’

In 1958, when he was 82 years old, Tirthaji visited the United States, which caused much controversy back home because Hindu spiritual leaders are forbidden from travelling abroad, and it was the first time that a Shankaracharya had ever left India. His trip provoked great curiosity in the US. The West Coast would later become a focus for flower power, gurus and meditation, but back then no one had seen anyone like him. When Tirthaji arrived in California the Los Angeles Times called him ‘one of the most important – and least-known – personages in the world’.

Tirthaji had a full schedule of talks and TV appearances. Though he spoke mostly about world peace, he devoted one lecture entirely to Vedic Mathematics. The venue was the California Institute of Technology, one of the most prestigious scientific institutions in the world. Tirthaji, who weighed not much more than seven stone and was wearing traditional robes, sat in a chair at the front of a wood-panelled classroom. In a quiet voice, but with a commanding presence, he told his audience: ‘I have been, from my childhood, equally fond of metaphysics on the one side and mathematics on the other. And I’ve found no difficulty at all.’

He went on to explain exactly how he had found the sutras, asserting that there was a wealth of hidden knowledge in the Vedic texts that came from the many double meanings of words and phrases. These mystical ‘puns’, he added, had been totally lost on Western Indologists. ‘The supposition is that mathematics was not part of the Vedic literature,’ he said, ‘but when I was able to find it, well, it was easy sailing.’

Tirthaji’s opening trick was to demonstrate how to multiply 9×8 without using a multiplication table. This uses the sutra All from 9 and the last from 10, although why it does so only becomes clear later.

First, he drew a 9 on the blackboard, followed by the difference of 9 from 10, which is –1. Underneath he drew 8 and next to it the difference of 8 from 10, which is –2.

9

–1

8

–2

The first number of the answer can be derived in four different ways. Either add the numbers in the first column and subtract ten (9 + 8 – 10 = 7). Or add the numbers in the second column and add ten (–1 – 2 + 10 = 7) or add either of the diagonals (9 – 2 = 7, and 8 – 1 = 7). The answer is always seven.

The second part of the answer is calculated by multiplying the two numbers in the second column (–1×–2 = 2). The complete answer is 72.

I find this trick immensely satisfying. Writing out a single-digit number next to its difference from ten is somehow like pulling it apart to reveal its inner