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Abigailk.com History of mathematics Mathematical beauty Mathematical notation Fields of Mathematics Mathematics lists Mathematics is a science Common misconceptions

History of mathematics

The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g., addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry.

Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse.

From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations on taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change.
Mathematics since has been much extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both.

Mathematical discoveries

Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proof."
The word "mathematics" comes from the Greek μάθημα (máthema) which means "science, knowledge, or learning"; μαθηματικός (mathematikós) means "fond of learning". Today, the term refers to a specific body of knowledge -- the rigorous, deductive study of quantity, structure, space and change.

While almost all cultures use basic mathematics1 (counting and measuring), new mathematical discoveries have been reported in relatively few cultures and ages. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical discoveries come to light only in a few locales. The most ancient mathematical texts come from ancient Egypt in the Middle Kingdom period circa 2000-1800 BC (Berlin 6619), Mesopotamia circa 1900-1700 BC (Plimpton 322), and ancient India circa 800-600 BC (Sulba Sutras). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical discovery after basic arithmetic and geometry. Ancient Greece and the Hellenistic cultures of Egypt, Mesopotamia and the city of Syracuse increased mathematical knowledge immensely. Jaina mathematicians contributed from the 4th century BC to the 2nd century AD, while the Han Dynasty in ancient China contributed the Sea Island Manual and The Nine Chapters on the Mathematical Art from the 2nd century BC to the 2nd century AD. Hindu mathematicians from the 5th century and Islamic mathematicians from the 9th century made major contributions to mathematics.

One striking feature about the history of ancient and medieval mathematics is that bursts of mathematical discovery tended to be followed by centuries of non-discovery. Beginning in Renaissance Italy in the 16th century, new mathematical discoveries, interacting with new scientific discoveries, were made at an ever increasing pace, and this continues to the present day. People throughout the world have contributed to modern mathematics.

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Abigailk.com History of mathematics Mathematical beauty Mathematical notation Fields of Mathematics Mathematics lists Mathematics is a science Common misconceptions