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Mathematics
Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, 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 from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. 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. 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.
 Philosophy of mathematics
 Lists of mathematics topics
 Mathematics and art
 Mathematics education
 Relationship between mathematics and physics
 Science, Technology, Engineering, and Mathematics
 Mathematics at Encyclopædia Britannica
 Mathematics on In Our Time at the BBC. (listen now)
 Free Mathematics books Free Mathematics books collection.
 Encyclopaedia of Mathematics online encyclopaedia from Springer, Graduatelevel reference work with over 8,000 entries, illuminating nearly 50,000 notions in mathematics.
 HyperMath site at Georgia State University
 FreeScience Library The mathematics section of FreeScience library
 Rusin, Dave: The Mathematical Atlas. A guided tour through the various branches of modern mathematics. (Can also be found at NIU.edu.)
 Cain, George: Online Mathematics Textbooks available free online.
 Mathematical Structures, list information about classes of mathematical structures.
 Mathematician Biographies. The MacTutor History of Mathematics archive Extensive history and quotes from all famous mathematicians.
 Metamath. A site and a language, that formalize mathematics from its foundations.
 Nrich, a prizewinning site for students from age five from Cambridge University
 Open Problem Garden, a of open problems in mathematics
 Some mathematics applets, at MIT
 Weisstein, Eric et al.: Wolfram MathWorld: World of Mathematics. An online encyclopedia of mathematics.
 Patrick Jones' Video Tutorials on Mathematics
 Citizendium: Theory (mathematics).
 du Sautoy, Marcus, A Brief History of Mathematics, BBC Radio 4 (2010).
 Maths.SE A Q&A site for mathematics
 MathOverflow A Q&A site for researchlevel mathematics
 National Museum of Mathematics, located in New York City

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Mathematics