According to Wikipedia...1) The oldest known mathematical object is the
Lebombo bone, discovered in the Lebombo mountains of
Swaziland and dated to approximately 35,000 BC.
[10] It consists of 29 distinct notches deliberately cut into a baboon's fibula.
[11] There is evidence that women used counting to keep track of their
menstrual cycles; 28 to 30 scratches on bone or stone, followed by a distinctive marker.
[12]2) The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of
regular reciprocal pairs (see
Plimpton 322).
[20] The tablets also include multiplication tables and methods for solving
linear and
quadratic equations. The Babylonian tablet YBC 7289 gives an approximation to √2 accurate to five decimal places.
3) The Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the
decimal system. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context.
4) The oldest mathematical text discovered so far is the
Moscow papyrus, which is an
Egyptian Middle Kingdom papyrus dated c. 2000–1800 BC.[
citation needed] Like many ancient mathematical texts, it consists of what are today called word problems or story problems, which were apparently intended as entertainment.
5) In
China, the Emperor
Qin Shi Huang (Shi Huang-ti) commanded in 212 BC that all books in Qin Empire other than officially sanctioned ones should be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics. From the
Western Zhou Dynasty (from 1046 BC), the oldest mathematical work to survive the
book burning is the
I Ching, which uses the 8 binary 3-
tuples (trigrams) and 64 binary 6-
tuples (hexagrams) for philosophical, mathematical, and mystical purposes. The binary tuples are composed of broken and solid lines, called yin (female) and yang (male), respectively (see
King Wen sequence).
6) The earliest civilization on the Indian subcontinent is the
Indus Valley Civilization that flourished between 2600 and 1900 BC in the
Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.
[27]7) The
Surya Siddhanta (c. 400) introduced the
trigonometric functions of
sine,
cosine, and inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky. The cosmological time cycles explained in the text, which was copied from an earlier work, correspond to an average
sidereal year of 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into to Arabic and Latin during the Middle Ages.
8) In the 12th century,
Bhaskara first conceived
differential calculus, along with the concepts of the
derivative,
differential coefficient, and differentiation. He also stated
Rolle's theorem (a special case of the
mean value theorem), studied
Pell's equation, and investigated the derivative of the sine function. From the 14th century, Madhava and other
Kerala School mathematicians further developed his ideas. They developed the concepts of
mathematical analysis and
floating point numbers, and concepts fundamental to the overall development of
calculus, including the mean value theorem, term by term
integration, the relationship of an area under a curve and its antiderivative or integral, the
integral test for convergence,
iterative methods for solutions to
non-linear equations, and a number of
infinite series,
power series,
Taylor series, and trigonometric series. In the 16th century,
Jyeshtadeva consolidated many of the Kerala School's developments and theorems in the Yuktibhasa, the world's first differential calculus text, which also introduced concepts of
integral calculus.