Zero: The Biography of a Dangerous Idea: 8 key ideas
The core ideas of Zero: The Biography of a Dangerous Idea, each in under a minute, written in our own words. Want the full depth? Get the book.
- IDEA 1 OF 8
Zero was once a dangerous idea
Seife tells the history of zero, a number that many cultures feared or rejected.
He argues that zero and its twin, infinity, have challenged thinkers for thousands of years and shaped science and religion.
- IDEA 2 OF 8
Zero began as a placeholder
Seife explains that the Babylonians used a mark to show an empty place in their number system.
At first, though, it was not treated as a number in its own right.
- IDEA 3 OF 8
The Greeks rejected the void
Seife describes how Greek thinkers, following Aristotle, rejected the idea of nothingness and empty space.
This, in his view, held back their mathematics. For them, a void seemed to threaten the order of the world.
- IDEA 4 OF 8
India embraced zero
Seife explains that Indian mathematicians, such as Brahmagupta, treated zero as a true number and set rules for calculating with it.
Indian philosophy was comfortable with ideas of emptiness. This made calculation with it possible.
- IDEA 5 OF 8
Zero travelled to Europe
Seife describes how zero spread from India through the Arab world to Europe.
European thinkers at first resisted it before accepting the new numerals. Over time, merchants and scholars found the new system too useful to ignore.
- IDEA 6 OF 8
Zero and infinity are linked
Seife explains that dividing by zero leads towards infinity.
The two ideas, he argues, are closely tied together. A number divided by something that shrinks toward zero grows larger and larger without a limit, which is why the two seem joined.
- IDEA 7 OF 8
Calculus tamed the tiny
Seife describes how Newton and Leibniz used infinitely small quantities to invent calculus.
This required careful thinking about zero. Tiny quantities that shrink toward nothing could be handled with care, and this turned calculating change into a precise method.
- IDEA 8 OF 8
Zero troubles modern physics
Seife shows that zero and infinity still cause problems in physics, for example at the centre of black holes and the start of the universe.
In such places the numbers stop making sense, which suggests our theories are incomplete.
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