Start here · Essential guide
Famous Number Sequences and Their Histories
A guided tour of the best-known number sequences, from primes and figurate numbers to Fibonacci, Pascal's triangle and Collatz, and where each idea began.
Counting, Numerals and Mathematics
Mathematical Curiosities in History
Famous sequences, ratios and puzzles that gave numbers a reputation.
Approximations of Pi Through the Ages
How Babylonian, Egyptian, Greek, Indian and Chinese mathematicians estimated the ratio of a circle's circumference to its diameter, and how close each came.
Fibonacci Numbers Before Fibonacci
The sequence 1, 2, 3, 5, 8, 13 appeared in Indian studies of poetic metre centuries before Leonardo of Pisa used it in his 1202 rabbit problem.
Irrational Numbers and the Legend of Hippasus
What we can and cannot say about Hippasus, the Pythagorean said to have been drowned for revealing incommensurable lengths, and how late the sources are.
Magic Squares from the Lo Shu to Durer
Follow the magic square from a Chinese river legend and the 3 by 3 Lo Shu through medieval Islamic scholars to the 4 by 4 square in Durer's 1514 engraving.
Negative Numbers in Chinese and Indian Mathematics
How Chinese counting rods and Brahmagupta's rules for fortunes and debts treated negative numbers, and why European mathematicians resisted them for centuries.
Perfect and Amicable Numbers in Greek Mathematics
How Euclid and Nicomachus treated perfect numbers, and how the pair 220 and 284 became the classic example of amicable numbers in the Pythagorean tradition.
Prime Numbers and Euclid
How Greek mathematicians defined primes, how Euclid showed there are infinitely many, and how the sieve of Eratosthenes lists them by crossing out multiples.
The Golden Ratio from Euclid to Pacioli
What Euclid actually wrote about the extreme and mean ratio, how Pacioli named it the divine proportion, and why claims about art and nature need caution.
Triangular and Square Numbers as Figurate Numbers
How Greek thinkers arranged pebbles into triangles, squares and other shapes to study number, and what simple patterns the arrangements revealed.
Related topics
More in counting, numerals and mathematics
Numeral Systems Through History How Egyptians, Greeks, Romans, Babylonians and Indian scholars wrote numbers. Counting Systems and Bases Tally marks, knotted cords, abaci and the different bases people counted in. Number Words and Language Where number names come from and how languages shape counting.