Indian mathematician who set out rules for calculating with zero in 628 CE
Muhammad ibn Musa al-Khwarizmi
Baghdad scholar whose arithmetic text carried the system into the Islamic world and later Europe
Plate 027
c. 3rd–7th century CE
India
No photograph is shown for this exhibition. The museum displays an image only where it can show the object honestly.
About this date
A dot used as a placeholder appears in the Bakhshali manuscript, whose earliest layers some radiocarbon studies place in the 3rd–4th century CE, but dating is contested. Brahmagupta gave rules for arithmetic with zero in 628 CE.
About credit
Place-value counting with a symbol for zero developed over centuries among Indian mathematicians. Earlier cultures, including the Babylonians and the Maya, used placeholders independently.
Chapter II
The world before
Life before Zero and the Decimal Number System
Roman numerals and counting boards made large calculations slow and error-prone. Several cultures had no symbol for an empty place.
II
The human achievement
How it came about
Indian mathematicians combined ten symbols with place value and treated zero as a number in its own right, as Brahmagupta’s text does. Al-Khwarizmi’s book on Indian numerals (c. 825) spread the system, and Fibonacci’s Liber Abaci (1202) introduced it to merchants in Europe.
III
Understanding the invention
How it works
Zero and the Decimal Number System, explained in two steps.
01
Step 01 of 02
Position carries value
The same digit means different things in different places: in 305 the 3 stands for hundreds.
Position carries value
Zero holds the place
IV
The transformation
What changed for humanity
Commerce
Merchants could compute interest, exchange rates and profit with written methods.
Mathematics
Negative numbers, algebra and calculus rely on zero as a number.
Written arithmetic became fast and accurate for ordinary people. Algebra, accounting, science and, eventually, computing depend on it.
V
Before and after
Life before and after Zero and the Decimal Number System
Before
Counting boards and Roman numerals.
After
A few lines of written working.
On larger screens, drag the divider (or use the arrow keys) to give more room to the world before or after.
Binary computing uses place value with two digits.
VII
Human stories
The people and the moments
A merchant’s son in Pisa
Fibonacci said he learned the numerals from Arab teachers while his father worked as a customs official in North Africa. He wrote his book to teach the system to Italian traders.
Where accounts differ, this museum follows the documented record and says so.
