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This growth has been greatest in societies complex enough to sustain these activities and to provide leisure for contemplation and the opportunity to build on the achievements of earlier mathematicians.All mathematical systems (for example, Euclidean geometry) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms.For example, they introduced a versatile numeral system, which, like the modern system, exploited the notion of place value, and they developed computational methods that took advantage of this means of expressing numbers; they solved linear and quadratic problems by methods much like those now used in algebra; their success with the study of what are now called Pythagorean number triples was a remarkable feat in number theory.

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However, the exponential growth of mathematics means that, for the period from the 19th century on, historians are able to treat only the major figures in any detail.

In addition, there is, as the period gets nearer the present, the problem of perspective.

The tablets indicate that the Mesopotamians had a great deal of remarkable mathematical knowledge, although they offer no evidence that this knowledge was organized into a deductive system.

Future research may reveal more about the early development of mathematics in Mesopotamia or about its influence on Greek mathematics, but it seems likely that this picture of Mesopotamian mathematics will stand.

The article East Asian mathematics covers the mostly independent development of mathematics in China, Japan, Korea, and Vietnam.

The substantive branches of mathematics are treated in several articles.

Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

In many cultures—under the stimulus of the needs of practical pursuits, such as commerce and agriculture—mathematics has developed far beyond basic counting.

It is important to be aware of the character of the sources for the study of the history of mathematics.

The history of Mesopotamian and Egyptian mathematics is based on the extant original documents written by scribes.

From the period before Alexander the Great, no Greek mathematical documents have been preserved except for fragmentary paraphrases, and, even for the subsequent period, it is well to remember that the oldest copies of Euclid’s .

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