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Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences.
Tau functions are an important ingredient in the modern mathematical theory of integrable systems, and have numerous applications in a variety of other domains.They were originally introduced by Ryogo Hirota [1] in his direct method approach to soliton equations, based on expressing them in an equivalent bilinear form.
The Erdős–Rankin conjecture on prime gaps, proved by Ford, Green, Konyagin, and Tao in 2014. [17] The Erdős discrepancy problem on partial sums of ±1-sequences. Terence Tao announced a solution in September 2015; it was published in 2016. [18]
This approach departs from the classical logic used in conventional mathematics by denying the law of the excluded middle, e.g., NOT (a ≠ b) does not imply a = b.In particular, in a theory of smooth infinitesimal analysis one can prove for all infinitesimals ε, NOT (ε ≠ 0); yet it is provably false that all infinitesimals are equal to zero. [2]
Although additive combinatorics is a fairly new branch of combinatorics (the term additive combinatorics was coined by Terence Tao and Van H. Vu in their 2006 book of the same name), a much older problem, the Cauchy–Davenport theorem, is one of the most fundamental results in this field.
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense.
Tao Group was a software company with headquarters in Reading, Berkshire, UK. It developed the Intent software platform, which enabled content portability by delivering services in a platform-independent format called Virtual Processor (VP).
Sullivan showed that students following the nonstandard analysis course were better able to interpret the sense of the mathematical formalism of calculus than a control group following a standard syllabus. This was also noted by Artigue (1994), page 172; Chihara (2007); and Dauben (1988). [citation needed]