# Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the abstract study of topics encompassing quantity, structure, space, change, and other properties; it has no generally accepted definition.

Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences." Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions." David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." Albert Einstein (1879–1955) 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."

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.

### Other articles related to "mathematics":

Mathematics As Science
... Gauss referred to mathematics as "the Queen of the Sciences" ... Of course, mathematics is in this sense a field of knowledge ... course, the role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics ...
Egon Zakrajšek
... He graduated from technical mathematics at the Department of mathematics and physics of then Faculty for natural sciences and technology (FNT) of the ... solved problems from many fields the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics, discrete mathematics, graph and network ...
Foundations Of Mathematics - Foundational Crisis - Philosophical Views - Logicism
... is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic ...
Otto Toeplitz - Life and Work
... Toeplitz's father and grandfather were mathematics teachers ... Toeplitz studied mathematics in the University of Breslau and was awarded a doctorate in algebraic geometry in 1905 ... Mathematics faculty included David Hilbert, Felix Klein, and Hermann Minkowski ...

### Famous quotes containing the word mathematics:

... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.
Amelia E. Barr (1831–1919)

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.
George Bernard Shaw (1856–1950)

Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.
Walter Reisch (1903–1963)