Jump to content

Timeline of algebra: Difference between revisions

From Wikipedia, the free encyclopedia
Content deleted Content added
m moved Algebra timeline to Timeline of algebra: This title makes this article a unique exception.
No edit summary
Line 83: Line 83:


[[Category:Algebra]]
[[Category:Algebra]]
[[Category:Mathematics timelines]]
[[Category:Mathematics timelines|Algebra]]

Revision as of 00:16, 22 September 2008

A timeline of key algebraic developments are as follows:

Year Event
Circa 1800 BC The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation.[citation needed]
Circa 1800 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script.[citation needed]
Circa 800 BC Indian mathematician Baudhayana, in his Baudhayana Sulba Sutra, discovers Pythagorean triples algebraically, finds geometric solutions of linear equations and quadratic equations of the forms ax2 = c and ax2 + bx = c, and finds two sets of positive integral solutions to a set of simultaneous Diophantine equations.[citation needed]
Circa 600 BC Indian mathematician Apastamba, in his Apastamba Sulba Sutra, solves the general linear equation and uses simultaneous Diophantine equations with up to five unknowns.[citation needed]
Circa 300 BC In Book II of his Elements, Euclid gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.[citation needed]
Circa 300 BC A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools.[citation needed]
Circa 100 BC Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.[citation needed]
Circa 150 AD Greek mathematician Hero of Alexandria, treats algebraic equations in three volumes of mathematics.[citation needed]
Circa 200 Hellenistic mathematician Diophantus lived in Alexandria and is often considered to be the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.[citation needed]
499 Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation, gives integral solutions of simultaneous indeterminate linear equations, and describes a differential equation.[citation needed]
Circa 625 Chinese mathematician Wang Xiaotong finds numerical solutions to certain cubic equations.[1]
628 Indian mathematician Brahmagupta, in his treatise Brahma Sputa Siddhanta, invents the chakravala method of solving indeterminate quadratic equations, including Pell's equation, and gives rules for solving linear and quadratic equations. He discovers that quadratic equations have two roots, including both negative as well as irrational roots.[citation needed]
Circa 7th century
Dates vary from the third to the twelfth centuries A.D.[2]
The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.[citation needed]
Circa 800 The Abbasid patrons of learning, al-Mansur, Haroun al-Raschid, and al-Mamun, had Greek, Babylonian, and Indian mathematical and scientific works translated into Arabic and began a cultural, scientific and mathematical awakening after a century devoid of mathematical achievements.[3]
820 The word algebra is derived from operations described in the treatise written by the Persian mathematician Muḥammad ibn Mūsā al-Ḵwārizmī titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered as the "father of algebra", much of whose works on reduction was included in the book and added to many methods we have in algebra now.[citation needed]
Circa 850 Persian mathematician al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.[citation needed]
Circa 850 Indian mathematician Mahavira solves various quadratic, cubic, quartic, quintic and higher-order equations, as well as indeterminate quadratic, cubic and higher-order equations.[citation needed]
Circa 990 Persian Abu Bakr al-Karaji, in his treatise al-Fakhri, further develops algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, ... and 1/x, 1/x2, 1/x3, ... and gives rules for the products of any two of these.[citation needed]
Circa 1050 Chinese mathematician Jia Xian finds numerical solutions of polynomial equations of arbitrary degree.[4]
1072 Persian mathematician Omar Khayyam gives a complete classification of cubic equations with positive roots and gives general geometric solutions to these equations found by means of intersecting conic sections.[5]
1114 Indian mathematician Bhaskara, in his Bijaganita (Algebra), recognizes that a positive number has both a positive and negative square root, and solves quadratic equations with more than one unknown, various cubic, quartic and higher-order polynomial equations, Pell's equation, the general indeterminate quadratic equation, as well as indeterminate cubic, quartic and higher-order equations.[citation needed]
1202 Algebra is introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci.[citation needed]
Circa 1300 Chinese mathematician Zhu Shijie deals with polynomial algebra, solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, quintic and higher-order polynomial equations.[citation needed]
Circa 1400 Indian mathematician Madhava of Sangamagramma finds the solution of transcendental equations by iteration, iterative methods for the solution of non-linear equations, and solutions of differential equations.[citation needed]
1412-1482 Arab mathematician Abū al-Hasan ibn Alī al-Qalasādī took "the first steps toward the introduction of algebraic symbolism." He used "short Arabic words, or just their initial letters, as mathematical symbols."[6]
1535 Nicolo Fontana Tartaglia and others mathematicians in Italy independently solved the general cubic equation.[7]
1545 Girolamo Cardano publishes Ars magna -The great art which gives Fontana's solution to the general quartic equation.[7]
1572 Rafael Bombelli recognizes the complex roots of the cubic and improves current notation.[citation needed]
1591 Francois Viete develops improved symbolic notation for various powers of an unknown and uses vowels for unknowns and consonants for constants in In artem analyticam isagoge.[citation needed]
1631 Thomas Harriot in a posthumus publication is the first to use symbols < and > to indicate "less than" and "greater than", respectively.[8]
1682 Gottfried Wilhelm Leibniz develops his notion of symbolic manipulation with formal rules which he calls characteristica generalis.[citation needed]
1683 Japanese mathematician Kowa Seki, in his Method of solving the dissimulated problems, discovers the determinant,[9] discriminant,[citation needed] and Bernoulli numbers.[9]
1685 Kowa Seki solves the general cubic equation, as well as some quartic and quintic equations.[citation needed]
1693 Leibniz solves systems of simultaneous linear equations using matrices and determinants.[citation needed]
1750 Gabriel Cramer, in his treatise Introduction to the analysis of algebraic curves, states Cramer's rule and studies algebraic curves, matrices and determinants.[10]
1824 Niels Henrik Abel proved that the general quintic equation is insoluble by radicals.[7]
1832 Galois theory is developed by Évariste Galois in his work on abstract algebra.[7]

References

  1. ^ O'Connor, John J.; Robertson, Edmund F., "Wang Xiaotong", MacTutor History of Mathematics Archive, University of St Andrews
  2. ^ (Hayashi 2005, p. 371) Quote:"The dates so far proposed for the Bakhshali work vary from the third to the twelfth centuries AD, but a recently made comparative study has shown many similarities, particularly in the style of exposition and terminology, between Bakhshalī work and Bhāskara I's commentary on the Āryabhatīya. This seems to indicate that both works belong to nearly the same period, although this does not deny the possibility that some of the rules and examples in the Bakhshālī work date from anterior periods."
  3. ^ Boyer (1991). "The Arabic Hegemony". p. 227. The first century of the Muslim empire had been devoid of scientific achievement. This period (from about 650 to 750) had been, in fact, perhaps the nadir in the development of mathematics, for the Arabs had not yet achieved intellectual drive, and concern for learning in other parts of the world had faded. Had it not been for the sudden cultural awakening in Islam during the second half of the eighth century, considerably more of ancient science and mathematics would have been lost. To Baghdad at that time were called scholars from Syria, Iran, and Mesopotamia, including Jews and Nestorian Christians; under three great Abbasid patrons of learning - al Mansur, Haroun al-Raschid, and al-Mamun - The city became a new Alexandria. It was during the caliphate of al-Mamun (809-833), however, that the Arabs fully indulged their passion for translation. The caliph is said to have had a dream in which Aristotle appeared, and as a consequence al-Mamun determined to have Arabic versions made of all the Greek works that he could lay his hands on, including Ptolemy's Almagest and a complete version of Euclid's Elements. From the Byzantine Empire, with which the Arabs maintained an uneasy peace, Greek manuscripts were obtained through peace treaties. Al-Mamun established at Baghdad a "House of Wisdom" (Bait al-hikma) comparable to the ancient Museum at Alexandria. {{cite book}}: Missing or empty |title= (help)
  4. ^ O'Connor, John J.; Robertson, Edmund F., "Jia Xian", MacTutor History of Mathematics Archive, University of St Andrews
  5. ^ Boyer (1991). "The Arabic Hegemony". pp. 241–242. Omar Khayyam (ca. 1050-1123), the "tent-maker," wrote an Algebra that went beyond that of al-Khwarizmi to include equations of third degree. Like his Arab predecessors, Omar Khayyam provided for quadratic equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the sixteenth century later showed), arithmetic solutions were impossible; hence he gave only geometric solutions. The scheme of using intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the method to cover all third-degree equations (having positive roots). {{cite book}}: Missing or empty |title= (help)
  6. ^ O'Connor, John J.; Robertson, Edmund F., "Abu'l Hasan ibn Ali al Qalasadi", MacTutor History of Mathematics Archive, University of St Andrews
  7. ^ a b c d Stewart, Ian (2004). Galois Theory (Third Edition ed.). Chapman & Hall/CRC Mathematics. {{cite book}}: |edition= has extra text (help)
  8. ^ Boyer, Carl B. (1991). "Prelude to Modern Mathematics". A History of Mathematics (Second Edition ed.). John Wiley & Sons, Inc. p. 306. ISBN 0471543977. Harriot knew of relationships between roots and coefficients and between roots and factors, but like Viete he was hampered by failure to take note of negative and imaginary roots. In notation, however, he advanced the use of symbolism, being responsible for the signs > and < for "greater than" and "less than." {{cite book}}: |edition= has extra text (help)
  9. ^ a b O'Connor, John J.; Robertson, Edmund F., "Takakazu Shinsuke Seki", MacTutor History of Mathematics Archive, University of St Andrews
  10. ^ O'Connor, John J.; Robertson, Edmund F., "Gabriel Cramer", MacTutor History of Mathematics Archive, University of St Andrews