1792. Third U.S. president Thomas Jefferson in 1792 (when he was Secretary of State): "Comparing them by their faculties of memory, reason, and imagination, it appears to me that in memory [the Negro] are equal to the whites; in reason much inferior, as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid; and that in imagination they are dull, tasteless, and anomalous." Present day AND ancient achievements contradict such statments. In response, these web page have been created to exhibit accomplishments of the peoples of Africa and the African Diaspora within the Mathematical Sciences.
1908. Mathematics Historian W. Rouse Ball:
The history of mathematics cannot with certainty be traced back
to any school or period before that of the ... Greeks.
1953. Mathematician Morris Kline: [The Egyptians] barely recognized mathematics as a distinct discipline ... [Mathematics] finally secured a new grip on life in the highly congenial soil of Greece and waxed strongly for a short period . . . With the decline of Greek civilization the plant remained dormant for a thousand years . . . when he plant was transported to Europe proper and once more imbedded in fertile soil. [Also see Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972)]
All three statements above are samples of eurocentric egoism in the history of mathematics. Though Jefferson apparently changed is attitutude, somewhat, after contact with Benjamin Banneker (see his twelve page letter). Rouse simply ignored, or was ingnorant of, the Sulbasutras (~800 BC), already known to European mathematicians of his time. Kline, on the other hand, certainly ignored or dismissed research outside of mathematic's historians of his time - research presenting evidence of mathematics coming from China, Egypt, India, Mesopotamia - even from pre-Columbus Mayans in Central America.
A supposed key to the Egyptian's inferior mathematics is that they had no concept of zero. This is absolutely false. The concept was even more than just a "blank space" to indicate a zero.
Another commonly expressed eurocentric view is that before the Greeks, there was no mathematics in the sense of the characteristic intellectual activity which goes under the name today. The argument goes: pre-Greek mathematics had neither a well-defined idea of proof nor any perception of the need for a proof. Where the Egyptians were involved in these activities which could be described as "mathematics," these activities were purely utilitarian, such as the construction of calendars, parcelling out lands, administration of harvests, organization of pubblic works (e.g., irrigation or flood control), or collection of taxes. Empirical rules were devised to help undertake these activities, but there remains no evidence of any overt concern with abstraction and proofs which form the core of mathematics. We contend something different.
Purely Eurocentric origins of mathematics can no longer be upheld. The oldest (35,000 BC) mathematical object was found in Swaziland. The oldest example of arithmetic (6000 BC) was found in Zaire.The 4000 year old, so-called Moscow papyrus, contains geometry, from the Middle Kingdom of Egypt, the consequence of the formula for the volume of a truncated square pyramid. From Herodotus (~450 BC) to Proclus (~400 BC) to Aristotle (~350 BC), Egypt was the cradle of mathematics (astronomy and surveying too). From the earliest, the great Greek mathematicians, including Pythagoras (~500 BC), Thales (~530 BC), and Exodus (the teacher of Aristotle) all learned much of their mathematics from Egypt (Mesopotamia, and possibily India) - even the concept of zero.
It is true that a zero placeholder was not used (or needed) in the Egyptian hieroglyphic or hieratic numerals because these numerals did not have positional value. But the zero concept has many other applications.
Generalizations about the area of a circle or the volume of a truncated square pyramid are most evident in Egyptian mathematics. Checking the correctness of a division by a subsequent multiplication or verifying the solutions of different types of equation by the method of substitution are found from a time before the Greeks "existed." A method, in common use in Europe until the 19th century, for solving linear equations is generally known as the method of false position. This method was in common use to solve practical practical problems such as finding the potency of beer or optimal feed mixtures for cattle and poultry in Egyptian mathematics.
A century before U.S. slavery was ended, slaves and even ordinary African slave traders demonstrated mathematical abilities more sophisticated than the European buyers.
Some 250 years prior to Newton and Liebnitz, a 15th century
Indian mathematician, Madhava
of Kerala, derived infinite series for
and for
some trigonometric functions. Here we limit
to Africa our discussions of ancient
mathematics, and will not discuss the extremely significant
results due to Indian, Chinese, Babylonian, South American and
other non-European groups.
Debate on the Relationship between Egyptian and Greek mathematics
the method of false position: to solve x - x/3 = 14, one could guess x=3 (especially since 3 divides 3). But this obviously yields 3 - 3/3 = 2 = 14/7. So try 7*3 or x = 21.
Mathematicians of the African Diaspora
visitors since opening 5/25/97
These web pages are brought to
you by
The
Mathematics Department of
The State University of New York at Buffalo.
These web pages are created
and maintained by
Dr. Scott W. Williams
Professor of Mathematics
http://www.math.buffalo.edu/mad/myths_lies.html
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