Start here · Essential guide
How Humans Counted Before Written Numbers
A careful look at the evidence for early counting, from notched bones to clay tokens and body-based systems, and at what such finds can and cannot prove.
Counting, Numerals and Mathematics
Counting Systems and Bases
Tally marks, knotted cords, abaci and the different bases people counted in.
Base 12 and the Duodecimal Tradition
How counting in dozens works, the finger-joint method for reaching sixty on two hands, and the measures and societies that have favoured twelve over ten.
Base 20 Counting in Basque, Georgian and Yoruba
How Basque, Georgian and Yoruba build their number words around twenty, and how the score and fourscore survive in older English, French and Danish.
Body Counting Systems of Papua New Guinea
How the Oksapmin and some neighbouring peoples of Papua New Guinea count by naming points on the arm, shoulder and face, and what happens when money arrives.
Finger Reckoning in Medieval Europe and Bede
How the monk Bede described a system of hand positions for signalling numbers up to a million, why medieval Europe needed it, and how it lasted into print.
Leibniz, the I Ching and Binary Notation
How Leibniz, who had devised base-two arithmetic, recognised it in the I Ching hexagrams sent to him by a Jesuit in China, and what historians make of it.
Quipu and the Knotted Cord Records of the Inca
How Inca khipu cords recorded numbers with knots in decimal positions, and which questions about names, stories and other non-numerical content remain open.
The Abacus from Suanpan to Soroban
How the counting frame developed from Mediterranean counting tables and pebbles into the Chinese suanpan and the Japanese soroban, and how each layout works.
The Ishango Bone and Early Tally Marks
What the notched Ishango bone from the Congo is, its groups of marks, and why archaeologists disagree on whether it shows arithmetic, a calendar or neither.
Related topics
More in counting, numerals and mathematics
Numeral Systems Through History How Egyptians, Greeks, Romans, Babylonians and Indian scholars wrote numbers. Number Words and Language Where number names come from and how languages shape counting. Mathematical Curiosities in History Famous sequences, ratios and puzzles that gave numbers a reputation.