Hello.
Mathematics was developed independently by countless ancient
societies, so it is not possible to identify just one ancient
civilization as having created it. However, it is possible to trace
the early history of mathematics on a civilization by civilization
basis, identify some of the reasons for its development, and trace the
multiple origins of some important mathematical concepts.
Perhaps the most important use for mathematics in an early
agricultural society was its application to astronomy, for the
creation and maintenance of a calendar to determine when is the best
time to plant and to harvest crops. At this level, mathematics can be
traced back very far indeed, to the beginnings of agriculture in
various places around the world. Indeed, very simple mathematics
(like counting) for practical use can reasonably be assumed to have
existed before agriculture. This type of mathematics existed nearly
everywhere.
Mathematics for practical use is one thing, but math for math's sake
is another. This also was developed independently in a number of
places, including:
Mesopotamia - In the Old Babylonian period, Mesopotamians introduced a
numeral system which introduced to the world the system of place value
(i.e. putting a string of numbers in a row to write a larger number).
The Mesopotamian numeral system was based upon the number 60, while
ours is based on the number 10. The Mesopotamians also developed a
placeholder which may have served the same function as our 0 by the
3rd century BCE but scholars still debate whether it was a true zero.
This useful practice was interestingly not taken up by the Greeks.
When "the West" readopted 0, it was through the Arabs, who had gotten
it from the Indians, who perhaps had adopted it from Southeast Asia.
The ancient Mesopotamians also solved linear and quadratic equations.
Egypt - More practical and less theoretical than Mesopotamian
mathematics, ancient Egypt had a system of mathematics sufficient for
a complex calendrical system and for the construction of massive
engineering projects such as the Pyramids. The Egyptians had a
numerical system similar to the Roman system which followed and
borrowed from it.
China - Most of what is known about early Chinese mathematics comes
from works compiled in the Western Han Dynasty (209 BCE - 8 CE), but
they include mathematical developments that were likely made in
earlier periods. The work Zhoubi Suanjing included an explication and
proof of the Pythagorean theorem. The Nine Chapters on the
Mathematical Art (Jiuzhang Suanshu) included many geometrical proofs
and an (admittedly rather bad) estimate of pi.
Greece/Rome - By far more is known in the Western academy about the
development of ancient Greek mathematics than those of other
civilizations, and information about that is easy to find, especially
if you check out the biographical links below, so I will not comment
very much on this history. There was very little increase in
mathematical knowledge during the Roman period, as the Romans
generally used Greek science and math as it was.
Further developments in mathematics were made in the early Islamic
empire and later in Europe and Japan (certain aspects of the calculus
were arrived at by mathematicians in Japan independently of Newton and
Leibnitz), but these cannot really be considered "ancient
mathematics."
Some sources/interesting links on ancient mathematics:
Biographies of mathematicians born before 500 AD (mostly Greek and
Indian mathematicians):
http://www-gap.dcs.st-and.ac.uk/~history/Indexes/_500_AD.html
Mesopotamian number system:
http://www.math.uvic.ca/courses/math415/Math415Web/meso/mnumber.html
History of Mathematics: China
http://aleph0.clarku.edu/~djoyce/mathhist/china.html
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surajambar-ga |
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