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20,000 BCE
The Ishango Bone
The Ishango Bone is one of the oldest mathematical artifacts. It was discovered in 1950 in Central Africa. The bone contains a series of notches. These notches could have been used for counting or even for understanding prime numbers. Counting was done by tallying, which is still known and used today. -
3500 BCE
Earliest Known Use of Mathematics
The Ancient Egyptians used complex mathematics such as algebra, arithmetic and geometry as far back as 3500 BC. The Egyptian mathematics was already fairly-well developed in their hieroglyphic writing; they had improved on the tallying system. For example, they used a stroke for 1, a heel bone for 10, a coiled rope for 100, and a lotus flower for 1000. Much of the content is very similar to what we learn about calculation and geometry in school today. -
2000 BCE
Babylonian Number System
The Babylonians used a system in their computations that was based on two wedge-shaped symbols. These symbols could easily be formed in clay tablets. This system is known as a sexagesimal system, just as ours is a decimal system. A sexagesimal system is based on increasing powers of sixty. -
800 BCE
Roman Numeration System
They originated in ancient Rome and were used for counting. Roman numerals are based on the Roman alphabet; I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. The Roman numeration is additive. Roman numerals are still known and used today. -
400 BCE
Maya Civilization Numeration System
The Maya civilization numeration system consisted of two symbols: a dot for the number 1 and a bar for the number 5. They were arranged vertically and evaluated by adding the place-value amounts for each group. For example, the lower group represented single units, the second group was multiplied by 20, the third group was multiplied by 18 x 20, and the fourth group was multiplied by 18 x 20 squared, and the value of the fifth group was multiplied by 18 x 20 cubed. -
300 BCE
Euclid Proves the Fundamental Theorem of Arithmetic
Euclid, a Greek mathematician who is known as the "Father of Geometry," proves the fundamental theorem of arithmetic, which states that all natural numbers (1, 2, 3, ...) can be expressed as a product of one or more prime numbers. Euclid also proves that there are infinitely many prime numbers by contradiction and identifies prime numbers as building blocks for all numbers. This lead to the discovery of unique factorization. -
240 BCE
Sieve of Eratosthenes
The Sieve of Eratosthenes was invented by the Greek mathematician, geographer, astronomer, historian, and poet, Eratosthenes of Cyrene. The Sieve of Eratosthenes is used to find all prime numbers. Sieve of Eratosthenes Video -
600
Hindu-Arabic Numeration System
The Hindu-Arabic numeration system was invented in India. It was picked up by the Arabs in the 7th and 8th centuries. The Europeans, then, learned from the Arabs. It uses place-value and is based on powers of ten. Its symbols are 0, 1, 2, 3, 4, 5 ,6 ,7 ,8 , and 9 and they are known as digits. -
620
Negative Numbers
Negative numbers can be traced back to the Chinese. However, two important mathematicians, Brahmagupta and Bhaskara, were among the first to recognize and work with negative numbers. Brahmagupta realized that there could be such a thing as a negative number and presented rules for them. For example, a negative times a negative is positive. -
628
The Number Zero
The Babylonians treated zero as a placeholder, and the Greeks and Romans treated zero as a symbol for lack of quantity. Brahmagupta treated zero as a number. He established the basic rules for zero. For example, 1 + 0 = 1, 1 - 0 = 1, and 1 x 0 = 0. -
Mersenne Primes
Marin Mersenne discovers the Mersenne Primes 8,191 and 131,071. Mersenne Primes are numbers that can be expressed in the form: 2p − 1, where p is a prime number. However, not all numbers of the form 2p − 1 are prime, but those which are prime are known as Mersenne Primes, named after French mathematician, Marin Mersenne. -
Leonhard Euler Discovers the 31st Mersenne Prime
Leonhard Euler discovers the 31st Mersenne Prime (M31) using trial division.
