Zero
From an empty column to the engine of computing — how nothing became the most useful number.
Each star is a thinker or work; solid lines draw the constellation of a school, dashed threads the passage of ideas between eras.
Select any point on the timeline to read about it.
All entries by era
Zero 2000 BCE – 2030 CE
From an empty column to the engine of computing — how nothing became the most useful number.
- 1800 BCE
Babylonian mathematics. Babylonian scribes writing in base 60 leave a gap where a digit is missing, later marking it with a pair of slanted wedges. It is a placeholder, not yet a number — a way to tell sixty from six, but never a value in its own right.
- 36 BCE
Maya Long Count. Mesoamerican scribes independently invent a shell glyph for zero within their vigesimal Long Count calendar, one of the earliest firmly dated uses anywhere. It shows that the placeholder idea can arise wherever positional notation does — yet, isolated, it never enters wider mathematics.
- 628 CE
Brahmagupta, Brahmasphutasiddhanta. In India, Brahmagupta gives the first known arithmetic of zero: a number minus itself is zero, and he states rules for adding, subtracting and multiplying with it. His attempt to divide by zero fails, but for the first time nothing is treated as a quantity to be calculated with.
- 830 CE
al-Khwarizmi, on Indian numerals. In Baghdad, al-Khwarizmi expounds the Indian decimal system, zero included, and his name gives us 'algorithm'. Translated into Latin, the Arabic word for zero, ṣifr, becomes both 'cipher' and 'zero', carrying the idea into Europe.
- 876 CE
Gwalior inscription, India. A temple inscription at Gwalior recording a garden's dimensions contains a small circle for zero in the number 270 — long regarded as the oldest firmly dated Indian zero in the modern circular form. Nothing finally has a settled, everyday shape.
- 1202 CE
Fibonacci, Liber Abaci. Fibonacci's Liber Abaci teaches European merchants the Hindu-Arabic numerals, showing how zero makes bookkeeping and calculation far easier than Roman numerals allow. Suspicious authorities in cities like Florence even banned the new figures as too easy to forge, but commerce won.
- 1637 CE
Descartes, La Géométrie. With coordinate geometry, Descartes places zero at the origin where the axes cross, making it the anchor of the entire number line and plane. Zero is no longer merely a digit but the fixed point from which position and magnitude are measured.
- 1703 CE
Leibniz, on binary arithmetic. Leibniz publishes a system in which every number is written with only 0 and 1, and reads a near-theological meaning into it: all things arising from unity and nothing. Two and a half centuries later this binary code becomes the native language of the computer.
- 1821 CE
Cauchy, on limits. Cauchy's rigorous theory of limits shows how quantities can tend to zero without ever reaching it, finally putting the calculus of vanishing differences on firm ground. Division by zero is banished as undefined, but the limit toward zero becomes the beating heart of analysis.
- 1937 CE
Turing & Shannon, digital logic. Shannon shows that electrical switches can carry Boolean logic, and Turing defines the universal machine that reads and writes symbols on a tape. Zero and one, off and on, become the atoms of computation on which the entire digital age is built.
The milestones
c. 1800 BCE
Babylonian mathematics
An empty space in the count
Babylonian scribes writing in base 60 leave a gap where a digit is missing, later marking it with a pair of slanted wedges. It is a placeholder, not yet a number — a way to tell sixty from six, but never a value in its own right.
36 BCE
Maya Long Count
Zero in the New World
Mesoamerican scribes independently invent a shell glyph for zero within their vigesimal Long Count calendar, one of the earliest firmly dated uses anywhere. It shows that the placeholder idea can arise wherever positional notation does — yet, isolated, it never enters wider mathematics.
628 CE
Brahmagupta, Brahmasphutasiddhanta
Zero becomes a number
In India, Brahmagupta gives the first known arithmetic of zero: a number minus itself is zero, and he states rules for adding, subtracting and multiplying with it. His attempt to divide by zero fails, but for the first time nothing is treated as a quantity to be calculated with.
c. 830
al-Khwarizmi, on Indian numerals
The cipher travels west
In Baghdad, al-Khwarizmi expounds the Indian decimal system, zero included, and his name gives us 'algorithm'. Translated into Latin, the Arabic word for zero, ṣifr, becomes both 'cipher' and 'zero', carrying the idea into Europe.
876 CE
Gwalior inscription, India
The oldest dated written zero
A temple inscription at Gwalior recording a garden's dimensions contains a small circle for zero in the number 270 — long regarded as the oldest firmly dated Indian zero in the modern circular form. Nothing finally has a settled, everyday shape.
1202
Fibonacci, Liber Abaci
Zero enters European commerce
Fibonacci's Liber Abaci teaches European merchants the Hindu-Arabic numerals, showing how zero makes bookkeeping and calculation far easier than Roman numerals allow. Suspicious authorities in cities like Florence even banned the new figures as too easy to forge, but commerce won.
1637
Descartes, La Géométrie
Zero as the origin
With coordinate geometry, Descartes places zero at the origin where the axes cross, making it the anchor of the entire number line and plane. Zero is no longer merely a digit but the fixed point from which position and magnitude are measured.
1703
Leibniz, on binary arithmetic
Everything from 0 and 1
Leibniz publishes a system in which every number is written with only 0 and 1, and reads a near-theological meaning into it: all things arising from unity and nothing. Two and a half centuries later this binary code becomes the native language of the computer.
1821
Cauchy, on limits
Approaching zero rigorously
Cauchy's rigorous theory of limits shows how quantities can tend to zero without ever reaching it, finally putting the calculus of vanishing differences on firm ground. Division by zero is banished as undefined, but the limit toward zero becomes the beating heart of analysis.
1937
Turing & Shannon, digital logic
Zero as a bit
Shannon shows that electrical switches can carry Boolean logic, and Turing defines the universal machine that reads and writes symbols on a tape. Zero and one, off and on, become the atoms of computation on which the entire digital age is built.