# 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":

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 ...
Mathematics As Science
... Gauss referred to mathematics as "the Queen of the Sciences" ... Of course, mathematics is in this sense a field of knowledge ... empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics ...
Athanasius Kircher - Life
... At Heiligenstadt, he taught mathematics, Hebrew and Syriac, and produced a show of fireworks and moving scenery for the visiting Elector Archbishop of ... priesthood in 1628 and became professor of ethics and mathematics at the University of Würzburg, where he also taught Hebrew and Syriac ... based himself in the city for the rest of his life, and from 1638, he taught mathematics, physics and oriental languages at the Collegio Romano for several years ...
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 University of Ljubljana ... He taught and solved problems from many fields the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics ...
Foundations Of Mathematics - Foundational Crisis - Philosophical Views - Logicism
... 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 ...

### 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)

Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
Simone Weil (1909–1943)

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)