History of mathematics
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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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