Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers by Amir D. Aczel
My rating: 4 of 5 stars

Everything Is Not Everything

One of the enduring but fruitless debates in the philosophy of mathematics is whether or not numbers exist apart from human thought about them. This little book provides a pleasing alternative to these abstruse arguments by suggesting that numbers and the mathematics which use numbers as its raw material are a remarkable genre of religious poetry devoted to the concept of the ‘void’. The oldest form of this poetry seems to arise in the Buddhist cultures of Southeast Asia, at the latest in about the sixth century CE, and in any case well before equivalent discoveries in Europe.

The critical insight of these religious meditations is the necessity of the (at least metaphorical) existence of the Shunyata, nothingness - what modern mathematicians would come to call the empty set, or more colloquially: zero. The form of logic that led to the discovery of zero is not only fascinating in itself, but it also remains relevant for addressing one of the most persistent of modern mathematical problems: the so-called Russell Paradox. According to set theory, the set of all sets both does and does not contain itself. Clearly there is a fly deep in the mathematical ointment. But there does seem to be a solution - in the wonderfully laconic explanation by a Buddhist monk: “Everything is not everything.” Zero might just be “the womb of all the other numbers.” It just doesn’t get more poetic than that.*

Aczel tells a personal tale of historical research, philosophical exploration, and at times somewhat trying travel in an enjoyable, unpretentious, and wonderfully informative style. His asides alone - from the linguistic remnants of the old French system of base 20 counting, to the ‘topos’ of Alexander Grothendieck, a leading mathematician of the 20th century - are worth the price of admission. But his central point “that the number system we use today developed in the East because of religious, spiritual, philosophical, and mystical reasons—not for the practical concerns of trade and industry as in the West,” is a remarkable and enlightening observation... and suitably poetic.

* Interestingly the great Leibniz seems to have a similar but independent conception. According to Laplace, as quoted by Dantzig: “Leibnitz saw in his binary arithmetic the image of Creation ... He imagined that Unity represented God, and Zero the void; that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in his system of numeration.“ See: https://www.goodreads.com/review/show...

Postscript: for a remarkably similar source of scientific insight in religious poetry see: https://www.goodreads.com/review/show...

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