History of Math Chapter 5

Abu Kamil

"The Reckoner From Egypt." He was the second of the great Arabic writers on algebra. He wrote a commentary on Al-Khowarimi's work, but instead of 40 problems, he had 69.

Chang Ch'iu-chien

A Chinese mathematician from the sixth century. His most famous problem in indeterminate equations is called the "hundred fowls."

Pappus

A talented geometer, though not as skilled as Archimedes, Apollonius, or Euclid five centuries earlier. He wrote Mathematical Collection which contained eight books. It was intended to be a consolidation of the geometric knowledge of its time. He said that the three classical problems of antiquity were impossible to solve under the terms in which they had been formulated by the Greeks.

Omar Khayyam

Circa 1048-1123. He wrote Treatise on Demonstrations of Problems of al-Jabra and al-Muqabalah which considerably advanced the subject of algebra. He constructed solutions of all kinds of cubics using the intersecting conic sections. He adjusted the Persian calendar into the Jalalian calendar which is so accurate it requires only a days correction every 5000 years.

Ghiyath al-Din al-Kashi

Died 1429. He was a Persian mathematician who went to Samarkand to take charge of the observatory there. He made the observatory an institution of higher learning. He made sine and tangent tables for every minute of arc, along with calculations of the longitudinal motions of the sun and moon. He revised Ptolemy's star catalog, to give more precise positions for over 1000 stars. He had a value for pi correct to 16 decimal places.

Indian Mathematics

From 400 to 1200 AD, their mathematics was superior, save geometry, than the Greeks.

Diophantus

He brought fame back to the Museum. He lived in Alexandria in 250. He wrote Arithmetica which may be described as the earliest treatise devoted to algebra. Only 6 of the 13 books have been preserved. Arithmetica contains an assortment of individual problems (189 total). He went up to the sixth power. He did not accept negative numbers.

Abu Bakr al-Karaji

He is a mathematician from the end of the tenth century. He wrote al-Karaji which is the earliest detailed account of the algebra of polynomials.

Archimedes

He protected Syracuse from Roman invasion for years by his ingenious military machines.

Aurelius Cassiodorus

He was a younger friend of Boethius, and though he was not as great a scholar, his contribution to the preservation of the classical heritage was greater. He founded a large monastery with the conscious aim of making it a center of Christian learning and scholarship - the first education-oriented monastic house.

Nasir al-Din al-Tusi

He was an Arabic mathematician and astronomer circa 1201-1274. He was alive for Genghis Khan's death. Khan's grandson Hulagu Khan ruled the place that he lived, so he was loyal to Hulagu. Hulagu was interested in astrology so he built a magnificent observatory for him to use.

Aryabhata

He was an Indian mathematician who calculated the value of pi to be 3.1416. He studied the indeterminate equations.

Brahmagupta

He was an Indian mathematician who introduced negative numbers. He also gave the formula for the area of a cyclic quadrilateral. He studied the indeterminate equations. He was the first to obtain all possible integral solutions, doing so caused him to advance beyond Diophantus.

Thabit ibn Qurra

He was another Arabic mathematician circa 836-901. He knew many languages which allowed him to translate a lot of Greek mathematical works. He wrote Book on the Determination of Amicable Numbers which is usually regarded as the first completely original mathematics written in Arabic. Amicable numbers are number pairs which each number is equal to the sum of the proper divisors of the other. He gave a generalization of the Pythagorean theorem.

Bhaskara

He was the leading Indian mathematician of the twelfth century. He wrote Siddhanata Siromani that dealt with arithmetic and algebra.

Mohammed ibn Musa al-Khowarizmi

He was the most illustrious of the Arab mathematicians circa 780-850. He was court astronomer and was a scholar at the House of Wisdom. He had two books: one on arithmetic and one on algebra. His work introduced Europe to Hindu numerals and algebraic approach to mathematics. He uses zero in his books. Did not accept negative numbers. He, along with other Arabs, accepted irrational roots from quadratic equations.

Ptolemy VII

He was the victor in a power struggle in 146 BC. He banished from Egypt, so also from Alexandria, all scientists and scholars who had not demonstrated their loyalty to him. This causes Alexandria to lose the primacy that it had once held over leading Eastern centers of learning.

Liu Hui

He wrote a commentary on the Nine Chapters, which is the most important of all ancient work, studied by generation after generation for more than a thousand years. He had a value for pi of 3.14159.

Pell Equation

Mistakenly named after John Pell, though credit should really be given to Lord Brouncker for authoring the method of solution for The Cattle Problem of Archimedes.

Anicius Boethius

On of the few Roman mathematicians. He is characterized as "the last of the Romans and the first of the Scholastics." He held a number of political positions, the height of his power was in 522 when he became Master of the Offices (Prime Minister). He wrote The Consolation of Philosophy while he was in prison waiting execution. He copied Elements, and Intoductio Arithmeticae into De Institutione Arithmetica. It was his efforts that the Middle Ages came to know the principles of formal arithmetic. The last known edition was published in Paris in 1521.

Hypatia

She was the first prominent female mathematician. She lectured at the Museum on mathematics and philosophy, which were well attended. Though she was well liked by students - pagan or Christian - because of her pagan beliefs, she was waylaid by a mob of religious zealot. She was slashed by sharp oyster shells, and torn limb from limb, her remains set on fire. Her death marked the end of the long and glorious history of Greek mathematicians.

Roman Mathematics

They had a decline of mathematical activity and originality. Their chief concern was the application of arithmetic and geometry to impressive engineering projects: viaducts, bridges, roads, public buildings, and land surveys.

Nine Chapters on the Mathematical Art

This marks the beginning of the mathematical tradition in China. The date and origin is unknown, but it represents the collective effort of many mathematical minds over several centuries.

Christianity

This religious group was the scapegoat of the Roman empire for many years until, in the fourth century, a Roman emperor, Constantine the Great (312 AD), was Christian. It was in 392 when Emperor Theodosius closed all pagan temples and forbid any pagan practices that the empire was officially Christian. Greek learning was identified with paganism, and Christians looted libraries and pagan temples, including the Museum.

House of Wisdom

This was set up by Caliph al-Ma'mun. It was comaparble to the Museum. An intense effort was made to acquire Greek manuscripts in order to translate them into Arabic.

Cattle of the Sun Problem

This wasn't solved until 1965 using a computer, though the problem was proposed by Archimedes. It has 206,545 digits.

Ancient Chinese Mathematics

We do not have a lot of information about this, apart from practical problems connected with everyday life. However we do know that they had the Pythagorean theorem long before the Pythagoreans did.