Algebra Timeline Project

*Moscow Papyrus was the oldest mathematical text from ancient Egypt.
*Egyptians introduced the earliest fully-developed base 10 numeration system
* As early as about 6000 BCE, the Pharaoh’s surveyors used measurements based on body parts to measure land and buildings very early in Egyptian history, and a decimal numeric system was developed based on our ten fingers.
*The Rhind Papyrus, dating from around 1650 BCE, is a kind of instruction manual in arithmetic and geometry.

*Sumerians and Babylonians created mathematics that was based on a sexegesimal, or base 60, numeric system, which could be counted using the twelve knuckles on one hand the five fingers on the other hand.
* Babylonian tablets dating from about 1800 to 1600 BCE cover topics like fractions, algebra, methods for solving linear, quadratic and even some cubic equations, and the calculation of regular reciprocal pairs.

*Ancient Chinese numbering system dates back to at least the 2nd millennium BCE, used small bamboo rods arranged to represent the numbers 1 to 9, which were then places in columns representing units, tens, hundreds, thousands, etc. which was their decimal place value system.
*Among the greatest mathematicians of ancient China was Liu Hui, who produced a detailed commentary on the “Nine Chapters” in 263 CE.

*Indian mathematics provided evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes, and roots.
* Brahmagupta established the basic mathematical rules for dealing with zero and negative numbers.
*The Indians were responsible for the earliest recorded usage of a circle character for the number zero is usually attributed to a 9th Century engraving in a temple in Gwalior in central India.

*Classic Period stretches from about 250 CE to 900 CE.
*The Mayan and Mesoamerican used a vigesimal number system based on base 20, the numerals consisted of three symbols: zero, a shell shape; one, a dot; and five, a bar. Addition and subtraction was adding up dots and bars.
*Astronomy and calendar calculations in Mayan society required mathematics, and constructed a number system.
*Pre-classic Maya and their neighbors developed the concept of zero by at least as early as 36 BCE

*During the late 4th and early 3rd Century BCE Euclid was the great chronicler of mathematics and who virtually invented classical (Euclidean) geometry.
*Eratosthenes of Alexandria was a mathematician, astronomer and geographer who devised the first system of latitude and longitude, and calculated the circumference of the earth to a remarkable degree of accuracy. His greatest legacy is the “Sieve of Eratosthenes” algorithm for identifying prime numbers.

*Both originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, al-Khwarizmi and al-Kindi, about the 12th century.
*A set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system.
*Al-Khwarizmi and al-Kindi,represented a profound break with previous methods of counting, such as the abacus, and paved the way for the development of algebra.

*abstract algebra in the early 20th century was distinguished in the area of study from the other parts of algebra.
*through the end of the nineteenth century many of these problems were in some way related to the theory of algebraic equations like systems of linear equations,formulas for solutions of general,polynomial equations.

*The Islamic Empire established across Persia, the Middle East, Central Asia, North Africa, Iberia and parts of India from the 8th Century.
*The Persian mathematician Muhammad Al-Khwarizmi in the 9th Century introduced fundamental algebraic methods of “reduction” and “balancing” and provided an exhaustive account of solving polynomial equations up to the second degree.
* A Golden Age of Islamic science and mathematics flourished throughout the medieval period from the 9th to 15th Centuries.

*The Renaissance began in Italy and spread across most of Europe.
*German Albrecht Dürer included an order-4 magic square in his engraving "Melencolia I" in 1514. The so-called "supermagic square" has many more lines of addition symmetry than a regular 4 x 4 magic square.
*Italian Franciscan, Luca Pacioli, published a book on arithmetic, geometry, and book-keeping that introduced symbols for plus and minus for the first time. These symbols became standard notation.

*Europe’s first great medieval mathematician was the Italian Leonardo of Pisa, better known as Fibonacci.
*Although best known for the so-called Fibonacci Sequence of numbers and spreading the use of the Hindu-Arabic numeral system throughout Europe early in the 13th Century,
*Of the 14th Century, Frenchman Nicole Oresme developed,the first time-speed-distance graph.
*The German scholar Regiomontatus of the 15th century helped separate trigonometry from astronomy

*John Napier invented the logarithm which, arises from the multiplication of two or more numbers is equivalent to adding their logarithms, contributed to science, astronomy, and mathematics by making difficult calculations easy.
* The 1st published work on probability theory and to outline the concept of mathematical expectation was Dutchman Christiaan Huygens in 1657.
* Italian Bonaventura Cavalieri developed a geometrical approach to calculus, Cavalieri's principle, in the early 1630's.

*Jacob and Johann Bernoulli of Basel, Switzerland were responsible for further developing calculus through the generalization and extension known as the "calculus of variation".
*Adrien-Marie Legendre made contributions of abstract algebra and mathematical analysis in the late 18th and early 19th Centuries.
*Johann Lambert, Swiss mathematician, provided proof in 1761 that π is irrational and can not be expressed as a simple fraction using integers only or as a terminating or repeating decimal.

*France and Germany in the age of revolution in the 18th century treated mathematics quite differently.
*In 1806, Jean-Robert Argand published his paper on how complex numbers could be represented on geometric diagrams and using trigonometry and vectors.
*A Frenchman Galois' worked the groundwork for further developments to beginnings of the field of abstract algebra, including areas like algebraic geometry, group theory, rings, fields, modules, vector spaces, and non-commutative algebra.

G.H. Hardy and his young Indian protégé Srinivasa Ramanujan, were great mathematicians of the early 20th Century who applied themselves to solving problems of the previous century. *In the 1970s and 1980s, Mandelbrot set iterations of complex quadratic polynomial equations in algebra. *Mathematics community of Germany and Austria by the anti-Jewish Nazi regime in the 1930 and 1940s, the focus of world mathematics moved to America,of the old European universities in rural New Jersey.