Timeline of Mathematics - 1st Millennium BC

1st Millennium BC

• c. 1000 BC — Vulgar fractions used by the Egyptians. However, only unit fractions are used (i.e., those with 1 as the numerator) and interpolation tables are used to approximate the values of the other fractions.
• first half of 1st millennium BC — Vedic India — Yajnavalkya, in his Shatapatha Brahmana, describes the motions of the sun and the moon, and advances a 95-year cycle to synchronize the motions of the sun and the moon.
• c. 8th century BC — the Yajur Veda, one of the four Hindu Vedas, contains the earliest concept of infinity, and states that “if you remove a part from infinity or add a part to infinity, still what remains is infinity.”
• 800 BC — Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of two correctly to five decimal places.
• early 6th century BC — Thales of Miletus has various theorems attributed to him.
• c. 600 BC — the other Vedic “Sulba Sutras” (“rule of chords” in Sanskrit) use Pythagorean triples, contain of a number of geometrical proofs, and approximate π at 3.16.
• second half of 1st millennium BC — The Lo Shu Square, the unique normal magic square of order three, was discovered in China.
• 530 BC — Pythagoras studies propositional geometry and vibrating lyre strings; his group also discovers the irrationality of the square root of two.
• c. 500 BC — Indian grammarian Pānini writes the Astadhyayi, which contains the use of metarules, transformations and recursions, originally for the purpose of systematizing the grammar of Sanskrit.
• 5th century BC — Hippocrates of Chios utilizes lunes in an attempt to square the circle.
• 5th century BC — Apastamba, author of the Apastamba Sulba Sutra, another Vedic Sanskrit geometric text, makes an attempt at squaring the circle and also calculates the square root of 2 correct to five decimal places.
• c. 400 BC — Jaina mathematicians in India write the “Surya Prajinapti”, a mathematical text which classifies all numbers into three sets: enumerable, innumerable and infinite. It also recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
• 4th century BC — Indian texts use the Sanskrit word “Shunya” to refer to the concept of ‘void’ (zero).
• 370 BC — Eudoxus states the method of exhaustion for area determination.
• 350 BC — Aristotle discusses logical reasoning in Organon.
• 300 BC — Jain mathematicians in India write the “Bhagabati Sutra”, which contains the earliest information on combinations.
• 300 BC — Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics, and he proves the fundamental theorem of arithmetic.
• c. 300 BC — Brahmi numerals (ancestor of the common modern base 10 numeral system) are conceived in India.
• 300 BC — Mesopotamia, the Babylonians invent the earliest calculator, the abacus.
• c. 300 BC — Indian mathematician Pingala writes the “Chhandah-shastra”, which contains the first Indian use of zero as a digit (indicated by a dot) and also presents a description of a binary numeral system, along with the first use of Fibonacci numbers and Pascal's triangle.
• 260 BC — Archimedes proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He also gave a very accurate estimate of the value of the square root of 3.
• c. 250 BC — late Olmecs had already begun to use a true zero (a shell glyph) several centuries before Ptolemy in the New World. See 0 (number).
• 240 BC — Eratosthenes uses his sieve algorithm to quickly isolate prime numbers.
• 225 BC — Apollonius of Perga writes On Conic Sections and names the ellipse, parabola, and hyperbola.
• 150 BC — Jain mathematicians in India write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations.
• 140 BC — Hipparchus develops the bases of trigonometry.
• 50 BC — Indian numerals, a descendant of the Brahmi numerals (the first positional notation base-10 numeral system), begins development in India.
• final centuries BC — Indian astronomer Lagadha writes the “Vedanga Jyotisha”, a Vedic text on astronomy that describes rules for tracking the motions of the sun and the moon, and uses geometry and trigonometry for astronomy.