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We do not know when, how, or why operations like addition or multiplication were invented, but they appeared several thousand years ago, apparently independently, in China, India, Mesopotamia, and Egypt. The oldest clay tablets with mathematics on it were found in Mesopotamia (nowadays Iraq) dating about 4000 years ago. The oldest written texts in mathematics - papyruses - come from Egypt, where civilization was already about 2000 years old when those papyruses were written. In ancient Sulba Sutras that come from India and are about 3500 years old one can find rules for building altars.
Among other things there is a famous theorem of Pythagoras about the sides of a right triangle. It is believed that Pythagoras was the first to prove this theorem - which means to answer the question of why this theorem is correct. That is why this fact is known as the Pythagoras theorem. This was happening in ancient Greece about 2500 years ago. From this time on there is a tradition in mathematics to always answer the question of why your result is true.
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