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Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may ...
Mutual fund separation theorem (financial mathematics) Müntz–Szász theorem (functional analysis) Mycielski's theorem (graph theory) Myers theorem (differential geometry) Myhill–Nerode theorem (formal languages)
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. [2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. [4]
Sergey Mergelyan was born on 19 May 1928 in Simferopol in an Armenian family. [4] His father Nikita (Mkrtich) Ivanovich Mergelov, a former private entrepreneur (Nepman), his mother Lyudmila Ivanovna Vyrodova, the daughter of the manager of the Azov-Black Sea bank, who was shot in 1918.
The book has four chapters, [2] covering the solutions to 21 continuous pursuit–evasion problems, [3] with an additional 10 "challenge problems" left for readers to solve, with solutions given in an appendix. [3] [4] The problems are presented as entertaining stories [5] that "breathe life into the mathematics and invite wider engagement", [6 ...
Today, mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory ...
Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative, and the ...