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The scribes who made such discoveries must have believed mathematics to be worthy of study in its own right, not just as a practical tool.

The older Sumerian system of numerals followed an additive decimal (base-10) principle similar to that of the Egyptians.

Unlike the Egyptians, the mathematicians of the Old Babylonian period went far beyond the immediate challenges of their official accounting duties.

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 .

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.

It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter.

India’s contributions to the development of contemporary mathematics were made through the considerable influence of Indian achievements on Islamic mathematics during its formative years.

A separate article, It is important to be aware of the character of the sources for the study of the history of mathematics.

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, ) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms.

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