Mathematics
Mathematics is the science and study of quantity, structure, space, and change. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions" Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects Mathematics continued to develop, Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.
The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time and nothing much more advanced until around 3000BC onwards when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, building and construction and astronomy
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today.
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Natural numbers |
Integers |
Rational numbers |
Real numbers |
Complex numbers |
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Geometry |
Trigonometry |
Differential geometry |
Topology |
Fractal geometry |
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Calculus |
Vector calculus |
Differential equations |
Dynamical systems |
Chaos theory |
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Number theory |
Abstract algebra |
Group theory |
Order theory |
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