Mathematics is the most general science that deals with logics, sets, various classes of numbers and other constructions in the formal axiomatic way through the definitions, axioms, and theorems. With high level of abstraction, mathematics became the kernel of the scientific knowledge; it is widely used in other sciences and other kinds of human activity.
Historically, the primary branches of mathematics are arithmetics and geometry. Mathematics comes from the counting of similar objects, and from measurements. initially, mathematicians used to work with integer numbers and simple geometric (perhaps, bidimentional) figures. Then mathematics covered all areas, that allow the formalizable analysis.
Many areas of research were considered as independent research, but then became just branches of mathematics. The examples are
- Theory of probability
- Mathematical statistics
- Game theory
- Computational mathematics, Numerical simulations,
- Field theory
The mathematical knowledge is widely used in the computational algorithms. There exist special programming languages for simplification of mathematical deduction; the most popular are Mathematica and Maple.
Mathematics give the basis, the language used in all other sciences. Many authors believe, that the mathematical axioms are absolute true; such a believe may be considered as a kind of religion. In principle, the postulates of TORI allow the doubts in mathematical axioms. As an example, the negation of the axioms of arithmetics is considered in the article Mizugadro number. Practically, it is difficult (if at all) to formulate any scientific concept, negating the mathematical results. In this sense Mathematics if top of all other sciences.
http://www.ipod.org.uk/reality/reality_wigner.pdf Eugene Wigner. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960).
http://people.math.sfu.ca/~cbm/aands/ Abramowitz and Stegun: Handbook of Mathematical Functions.
http://www.nytimes.com/2016/02/28/opinion/sunday/the-wrong-way-to-teach-math.html ANDREW HACKER. The Wrong Way to Teach Math. FEB. 27, 2016. .. Most Americans have taken high school mathematics, including geometry and algebra, yet a national survey found that 82 percent of adults could not compute the cost of a carpet when told its dimensions and square-yard price. ..
2017.08.37. https://www.healio.com/news/psychiatry/20170830/math-tools-may-improve-prediction-in-psychiatry Quentin Huys. Math tools may improve prediction in psychiatry. August 31, 2017