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Herman Te Riele
Hermanus Johannes Joseph te Riele (born 5 January 1947) is a Dutch mathematician at CWI in Amsterdam with a specialization in computational number theory. He is known for proving the correctness of the Riemann hypothesis for the first 1.5 billion non-trivial zeros of the Riemann zeta function with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture with Andrew Odlyzko, and for factoring large numbers of world record size. In 1987, he found a new upper bound for π(''x'') − Li(''x''). In 1970, Te Riele received an engineer's degree in mathematical engineering from Delft University of Technology and, in 1976, a PhD degree in mathematics and physics from University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ... (1976). References * * ...
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Centrum Wiskunde & Informatica
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Council (NWO) and is located at the Amsterdam Science Park. This institute is famous as the creation site of the programming language Python. It was a founding member of the European Research Consortium for Informatics and Mathematics (ERCIM). Early history The institute was founded in 1946 by Johannes van der Corput, David van Dantzig, Jurjen Koksma, Hendrik Anthony Kramers, Marcel Minnaert and Jan Arnoldus Schouten. It was originally called ''Mathematical Centre'' (in Dutch: ''Mathematisch Centrum''). One early mission was to develop mathematical prediction models to assist large Dutch engineering projects, such as the Delta Works. During this early period, the Mathematics Institute also helped with designing the wings of the Fokker ...
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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 ...
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Mertens Conjecture
In mathematics, the Mertens conjecture is the statement that the Mertens function M(n) is bounded by \pm\sqrt. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in ), and again in print by , and disproved by . It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor. Definition In number theory, the Mertens function is defined as : M(n) = \sum_ \mu(k), where μ(k) is the Möbius function; the Mertens conjecture is that for all ''n'' > 1, : , M(n), < \sqrt.


Disproof of the conjecture

Stieltjes claimed in 1885 to have proven a weaker result, namely that m(n) := M(n)/\sqrt was
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Andrew Odlyzko
Andrew Michael Odlyzko (Andrzej Odłyżko) (born 23 July 1949) is a Polish- American mathematician and a former head of the University of Minnesota's Digital Technology Center and of the Minnesota Supercomputing Institute. He began his career in 1975 at Bell Telephone Laboratories, where he stayed for 26 years before joining the University of Minnesota in 2001. Work in mathematics Odlyzko received his B.S. and M.S. in mathematics from the California Institute of Technology and his Ph.D. from the Massachusetts Institute of Technology in 1975. In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity, combinatorics, probability, and error-correcting codes. In the early 1970s, he was a co-author (with D. Kahaner and Gian-Carlo Rota) of one of the founding papers of the modern umbral calculus. In 1985 he and Herman te Riele disproved the Mertens conjecture. In mat ...
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Engineer's Degree
An engineer's degree is an advanced academic degree in engineering which is conferred in Europe, some countries of Asia and Latin America, North Africa and a few institutions in the United States. The degree may require a thesis but always requires a non-abstract project. The duration of study typically ranges from 4 to 5 years, depending on the country and university. Additionally, there may be further requirements for certifications or licenses to practice engineering after graduation. North America United States In the United States, the engineer's degree requires a year of study beyond a master's degree or two years from a bachelor's degree and often includes a requirement for a research thesis. At the U.S. Naval Postgraduate School the thesis is required to be "more extensive and complete in problem scope and solution than a master's thesis", although "not necessarily meeting the test of original research and contribution to fundamental knowledge that is applied to PhD ...
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Delft University Of Technology
The Delft University of Technology (TU Delft; ) is the oldest and largest Dutch public university, public Institute of technology, technical university, located in Delft, Netherlands. It specializes in engineering, technology, computing, design, and natural sciences. It is considered one of the leading technical universities in Europe and is consistently ranked as one of the best schools for architecture and engineering in the world. According to the QS World University Rankings it ranked 3rd worldwide for architecture and 13th for Engineering, Engineering & Technology in 2024. It also ranked 3rd best worldwide for Mechanical engineering, mechanical and aerospace engineering, 3rd for Civil engineering, civil and structural engineering, 11th for chemical engineering, and 12th for design. With eight Faculty (division), faculties and multiple research institutes, TU Delft educates around 27,000 students (undergraduate and postgraduate), and employs more than 3,500 doctoral candidates ...
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University Of Amsterdam
The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlands still in operation. The UvA is one of two large, publicly funded research universities in the city, the other being the Vrije Universiteit Amsterdam (VU). It is also part of the largest research universities in Europe with 31,186 students, 4,794 staff, 1,340 PhD students and an annual budget of €600 million. It is the List of universities in the Netherlands, largest university in the Netherlands by enrollment. The main campus is located in Amsterdam-Centrum, central Amsterdam, with a few faculties located in adjacent Government of Amsterdam, boroughs. The university is organised into seven faculties: Humanities, Social science, Social and Psychology, Behavioural Sciences, Economics and Business, Science, Law, Medicine, Dentistry. Clo ...
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21st-century Dutch Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men (Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican revolt ...
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1947 Births
It was the first year of the Cold War, which would last until 1991, ending with the dissolution of the Soviet Union. Events January * January–February – Winter of 1946–47 in the United Kingdom: The worst snowfall in the country in the 20th century causes extensive disruption of travel. Given the low ratio of private vehicle ownership at the time, it is mainly remembered in terms of its effects on the railway network. * January 1 – The ''Canadian Citizenship Act, 1946, Canadian Citizenship Act'' comes into effect, providing a Canadian citizenship separate from British law. * January 4 – First issue of weekly magazine ''Der Spiegel'' published in Hanover, Germany, edited by Rudolf Augstein. * January 10 – The United Nations adopts a resolution to take control of the free city of Trieste. * January 15 – Elizabeth Short, an aspiring actress nicknamed the "Black Dahlia", is found brutally murdered in a vacant lot in Los Angeles; the mysterious case is never solv ...
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Delft University Of Technology Alumni
Delft () is a city and municipality in the province of South Holland, Netherlands. It is located between Rotterdam, to the southeast, and The Hague, to the northwest. Together with them, it is a part of both the Rotterdam–The Hague metropolitan area and the Randstad. Delft is a popular tourist destination in the Netherlands, famous for its historical connections with the reigning House of Orange-Nassau, for its blue pottery, for being home to the painter Jan Vermeer, and for hosting Delft University of Technology (TU Delft). Historically, Delft played a highly influential role in the Dutch Golden Age. In terms of science and technology, thanks to the pioneering contributions of Antonie van Leeuwenhoek and Martinus Beijerinck, Delft can be considered to be the birthplace of microbiology. History Early history The city of Delft came into being beside a canal, the 'Delf', which comes from the word ''delven'', meaning to delve or dig, and this led to the name Delft. A ...
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Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ...
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