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Timothy Trudgian
Timothy Trudgian is an Australian mathematician specializing in number theory and related fields. He is known for his work on Riemann zeta function, analytic number theory, and distribution of primes. He currently is a Professor at the University of New South Wales (Canberra). Education and Career Trudgian completed his BSc (Hons) at the Australian National University in December 2005, then his Ph.D. from the University of Oxford in June 2010 under the supervision of Roger Heath-Brown. His dissertation was titled ''Further results on Gram's Law''. Research Trudgian has made significant contributions to the field of (analytic) number theory. His research includes work on Riemann zeta function, distribution of primes, and primitive root modulo n. One of his notable achievements is proving that the Riemann hypothesis is true up to 3 trillion. In 2024, together with Terence Tao and Andrew Yang, Trudgian published an ''on-going'' database of known theorems for various exponen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brisbane
Brisbane ( ; ) is the List of Australian capital cities, capital and largest city of the States and territories of Australia, state of Queensland and the list of cities in Australia by population, third-most populous city in Australia, with a population of approximately 2.8 million. Brisbane lies at the centre of South East Queensland, an urban agglomeration with a population of over 4 million. The Brisbane central business district, central business district is situated within a peninsula of the Brisbane River about from its mouth at Moreton Bay. Brisbane's metropolitan area sprawls over the hilly floodplain of the Brisbane River Valley between Moreton Bay and the Taylor Range, Taylor and D'Aguilar Range, D'Aguilar mountain ranges, encompassing several local government in Australia, local government areas, most centrally the City of Brisbane. The demonym of Brisbane is ''Brisbanite''. The Moreton Bay penal settlement was founded in 1824 at Redcliffe, Queensland, Redcliff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution Of Primes
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is , where is the prime-counting function (the number of primes less than or equal to ''N'') and is the natural logarithm of . This means that for large enough , the probability that a random integer not greater than is prime is very close to . Consequently, a random integer with at most digits (for large enough ) is about half as likely to be prime as a random integer with at most digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theorists
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry). Questions in number theory can often be understood through the study of analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is that it deals wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Australian Mathematicians
Australian(s) may refer to: Australia * Australia, a country * Australians, citizens of the Commonwealth of Australia ** European Australians ** Anglo-Celtic Australians, Australians descended principally from British colonists ** Aboriginal Australians, indigenous peoples of Australia as identified and defined within Australian law * Australia (continent) ** Indigenous Australians * Australian English, the dialect of the English language spoken in Australia * Australian Aboriginal languages * ''The Australian'', a newspaper * Australiana, things of Australian origins Other uses * Australian (horse), a racehorse * Australian, British Columbia, an unincorporated community in Canada See also * The Australian (other) * Australia (other) * * * Austrian (other) Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen * Austrian German dialect * Something associated with the count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Australian Mathematical Society
The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the society's listed purposes is to promote the cause of mathematics in the community by representing the interests of the profession to government. The society also publishes three mathematical journals. Professor Jessica Purcell is the current president of the society. Society awards * The Australian Mathematical Society Medal * The George Szekeres Medal * The Gavin Brown Prize * The Mahler Lectureship * The B.H. Neumann Prize Society journals The society publishes three journals through Cambridge University Press: * ''Journal of the Australian Mathematical Society'' * ''ANZIAM Journal'' (formerly ''Series B, Applied Mathematics'') * ''Bulletin of the Australian Mathematical Society'' ANZIAM ANZIAM (Australia and New Zealand Industrial and Applied Mathematics) is a division of The Australian Mathematical Society (AustMS). Members ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lean (proof Assistant)
Lean is a proof assistant and a functional programming language. It is based on the calculus of constructions with inductive types. It is an open-source project hosted on GitHub. Development is currently supported by the non-profit Lean Focused Research Organization (FRO). History Lean was developed primarily by Leonardo de Moura while employed by Microsoft Research and now Amazon Web Services, and has had significant contributions from other coauthors and collaborators during its history. It was launched by Leonardo de Moura at Microsoft Research in 2013. The initial versions of the language, later known as Lean 1 and 2, were experimental and contained features such as support for homotopy type theory – based foundations that were later dropped. Lean 3 (first released Jan 20, 2017) was the first moderately stable version of Lean. It was implemented primarily in C++ with some features written in Lean itself. After version 3.4.2 Lean 3 was officially end-of-lifed while devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Tao
Terence Chi-Shen Tao (; 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. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014, and is a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers, and is widely regarded as one of the greatest living mathematicians. Life and career Family Tao's parents are first generation immigrants from Hong Kong to Australia.'' Wen Wei Po'', Page A4, 24 August ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Hypothesis
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by , after whom it is named. The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Millennium Prize Problems of the Clay Mathematics Institute, which offers US$1 million for a solution to any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields. The Riemann zeta function ''ζ''(''s'') is a function whose argument ''s'' may be any complex numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Root Modulo N
In modular arithmetic, a number is a primitive root modulo if every number coprime to is congruent to a power of modulo . That is, is a ''primitive root modulo'' if for every integer coprime to , there is some integer for which ≡ (mod ). Such a value is called the index or discrete logarithm of to the base modulo . So is a ''primitive root modulo'' if and only if is a generator of the multiplicative group of integers modulo . Gauss defined primitive roots in Article 57 of the '' Disquisitiones Arithmeticae'' (1801), where he credited Euler with coining the term. In Article 56 he stated that Lambert and Euler knew of them, but he was the first to rigorously demonstrate that primitive roots exist for a prime . In fact, the ''Disquisitiones'' contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive. A primitive root exists if and only if ''n'' is 1, 2, 4, ''p''''k'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a 'person who professes'. Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word ''professor'' is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well, and often to instructors or lecturers. Professors often conduct original research and commonly teach undergraduate, Postgraduate educa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
