mathematics: Development of Mathematics

The earliest records of mathematics show it arising in response to practical needs in agriculture, business, and industry. In Egypt and Mesopotamia, where evidence dates from the 2d and 3d millennia b.c., it was used for surveying and mensuration; estimates of the value of π (pi) are found in both locations. There is some evidence of similar developments in India and China during this same period, but few records have survived. This early mathematics is generally empirical, arrived at by trial and error as the best available means for obtaining results, with no proofs given. However, it is now known that the Babylonians were aware of the necessity of proofs prior to the Greeks, who had been presumed the originators of this important step.

Sections in this article:

• Introduction
• In the Twentieth Century
• In the Nineteenth Century
• Western Developments from the Twelfth to Eighteenth Centuries
• Chinese and Middle Eastern Advances
• Greek Contributions
• Development of Mathematics
• Applied Mathematics
• Geometry
• Analysis
• Algebra
• Foundations
• Bibliography

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