 concepts of zero and of negative numbers. He wrote in verse the Brahma-sphuta-siddhanta
..... Click the link for more information. (5th and 6th cent. A.D.). The Arabs were responsible for preserving the work of the Greeks, which they translated, commented upon, and augmented. In Baghdad, Al-KhowarizmiAl-Khowarizmi
, fl. 820, Arab mathematician of the court of Mamun in Baghdad. His treatises on Hindu arithmetic and on algebra made him famous. He is said to have given algebra its name, and the word algorithm is said to have been derived from his name.
..... Click the link for more information. (9th cent.) wrote an important work on algebra and introduced the Hindu numerals for the first time to the West, and Al-BattaniAl-Battani
, b. before 858, d. 929, Arab astronomer and mathematician. He is best known in astronomy for his improvements and corrections of the Ptolemaic tradition.
..... Click the link for more information. worked on trigonometry. In Egypt, Ibn al-HaythamIbn al-Haytham
, 965–c.1040, Arab mathematician. Ibn al-Haytham was born in Basra, but made his career in Cairo, where he supported himself copying scientific manuscripts.
..... Click the link for more information. was concerned with the solids of revolution and geometrical optics. The Persian poet Omar Khayyam wrote on algebra.
Western Developments from the Twelfth to Eighteenth Centuries
Word of the Chinese and Middle Eastern works began to reach the West in the 12th and 13th cent. One of the first important European mathematicians was Leonardo da Pisa (Leonardo FibonacciFibonacci, Leonardo
, b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation.
..... Click the link for more information. ), who wrote on arithmetic and algebra (Liber abaci, 1202) and on geometry (Practica geometriae, 1220). With the Renaissance came a great revival of interest in learning, and the invention of printing made many of the earlier books widely available. By the end of the 16th cent. advances had been made in algebra by Niccolò TartagliaTartaglia, Niccolò
, c.1500–1557, Italian engineer and mathematician. Largely self-educated, he taught mathematics at Verona, Brescia, and Venice. A pioneer in applying mathematics to artillery, he recorded his results in Della nova scientia (1537).
..... Click the link for more information. and Girolamo CardanoCardano, Girolamo or Geronimo
, 1501–76, Italian physician and mathematician. His works on arithmetic and algebra established his reputation.
..... Click the link for more information. , in trigonometry by François VièteViète or Vieta, François
, 1540–1603, French mathematician. As a founder of modern algebra, he introduced the use of letters as algebraic symbols and correlated algebra with geometry and trigonometry.
..... Click the link for more information. , and in such areas of applied mathematics as mapmaking by Mercator and others.
The 17th cent., however, saw the greatest revolution in mathematics, as the scientific revolution spread to all fields. Decimal fractions were invented by Simon StevinStevin, Simon
, 1548–1620, Dutch engineer and mathematician. His experiments in hydrostatics showed that the pressure exerted by a liquid is dependent only on its vertical height and not on the shape of the liquid's container, and demonstrated the principle of the
..... Click the link for more information. and logarithms by John NapierNapier, John
, 1550–1617, Scottish mathematician and theologian. He invented logarithms and wrote Mirifici logarithmorum canonis descriptio (1614), containing the first logarithmic table and the first use of the word logarithm.
..... Click the link for more information. and Henry BriggsBriggs, Henry,
1561–1630, English mathematician. He was the first professor of geometry at Gresham College, London (1596–1619), and Savilian professor of astronomy at Oxford (from 1619).
..... Click the link for more information. ; the beginnings of projective geome