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Szpiro Conjecture
In number theory, Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known ''abc'' conjecture. It is named for Lucien Szpiro, who formulated it in the 1980s. Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld, in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. Original statement The conjecture states that: given ε > 0, there exists a constant ''C''(ε) such that for any elliptic curve ''E'' defined over Q with minimal discriminant Δ and conductor ''f'', we have : \vert\Delta\vert \leq C(\varepsilon ) \cdot f^. Modified Szpiro conjecture The modified Szpiro conjecture states that: given ε > 0, there exists a constant ''C''(ε) su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of 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 are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arakelov Theory
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions. Background The main motivation behind Arakelov geometry is the fact there is a correspondence between prime ideals \mathfrak \in \text(\mathbb) and finite places v_p : \mathbb^* \to \mathbb, but there also exists a place at infinity v_\infty, given by the Archimedean valuation, which doesn't have a corresponding prime ideal. Arakelov geometry gives a technique for compactifying \text(\mathbb) into a complete space \overline which has a prime lying at infinity. Arakelov's original construction studies one such theory, where a definition of divisors is constructor for a scheme \mathfrak of relative dimension 1 over \text(\mathcal_K) such that it extends to a Riemann surface X_\infty = \mathfrak(\mathbb) for every valuation at infinity. In addition, he equips these Riemann surfaces with Hermitian me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condescension or oversimplification." The articles in the magazine are freely available to read online. ''Scientific American'', ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like ''Spektrum der Wissensch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Stix
Jakob M. Stix (born in 1974) is a German mathematician. He specializes in arithmetic algebraic geometry (étale fundamental group, anabelian geometry and other topics). Stix studied mathematics in Freiburg and Bonn and received his doctorate in 2002 from Florian Pop at the University of Bonn (''Projective Anabelian Curves in Positive Characteristic and Descent Theory for Log-Etale Covers''). His dissertation was awarded the best doctoral thesis of the year 2002 by the Mathematical Institute of the University of Bonn. He was a post-doctoral student at the Institute for Advanced Study. In 2008, he became junior research group leader at the Mathematics Center of the University of Heidelberg, where he habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ... in 2011 (''Evidence for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Scholze
Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He has been called one of the leading mathematicians in the world. He won the Fields Medal in 2018, which is regarded as the highest professional honor in mathematics. Early life and education Scholze was born in Dresden and grew up in Berlin. His father is a physicist, his mother a computer scientist, and his sister studied chemistry. He attended the in Berlin-Friedrichshain, a gymnasium devoted to mathematics and science. As a student, Scholze participated in the International Mathematical Olympiad, winning three gold medals and one silver medal. He studied at the University of Bonn and completed his bachelor's degree in three semesters and his master's degree in two further semesters. He obtained his Ph.D. in 2012 under the supervisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publishes a monthly Dutch-language edition. First published on 22 November 1956, ''New Scientist'' has been available in online form since 1996. Sold in retail outlets (paper edition) and on subscription (paper and/or online), the magazine covers news, features, reviews and commentary on science, technology and their implications. ''New Scientist'' also publishes speculative articles, ranging from the technical to the philosophical. ''New Scientist'' was acquired by Daily Mail and General Trust (DMGT) in March 2021. History Ownership The magazine was founded in 1956 by Tom Margerison, Max Raison and Nicholas Harrison as ''The New Scientist'', with Issue 1 on 22 November 1956, priced at one shilling (a twentieth of a pound in pre-decimal UK cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inter-universal Teichmüller Theory
Inter-universal Teichmüller theory (abbreviated as IUT or IUTT) is the name given by mathematician Shinichi Mochizuki to a theory he developed in the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints posted in 2012 to his website. The most striking claimed application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the ''abc'' conjecture. Mochizuki and a few other mathematicians claim that the theory indeed yields such a proof but this has so far not been accepted by the mathematical community. History The theory was developed entirely by Mochizuki up to 2012, and the last parts were written up in a series of four preprints. Mochizuki made his work public in August 2012 with none of the fanfare that typically accompanies major advan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shinichi Mochizuki
is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. Mochizuki has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted attention from non-mathematicians due to claims it provides a resolution of the ''abc'' conjecture. Biography Early life Shinichi Mochizuki was born to parents Kiichi and Anne Mochizuki. When he was five years old, Shinichi Mochizuki and his family left Japan to live in the United States. His father was Fellow of the Center for International Affairs and Center for Middle Eastern Studies at Harvard University (1974–76). Mochizuki attended Phillips Exeter Academy and graduated in 1985. Mochizuki entered Princeton University as an undergraduate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Masser
David William Masser (born 8 November 1948) is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated the abc conjecture, which has been called "the most important unsolved problem in Diophantine analysis".. Early life and education Masser was born on 8 November 1948 in London, England. He graduated from Trinity College, Cambridge with a B.A. (Hons) in 1970. In 1974, he obtained his M.A. and Ph.D. at the University of Cambridge, with a doctoral thesis under the supervision of Alan Baker titled ''Elliptic Functions and Transcendence''. Career Masser was a Lecturer at the University of Nottingham from 1973 to 1975, before spending the 1975-1976 year as a Research Fellow of Trinity College at the University of Cambridge. He returned to the University of Nottingham to serve as a L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Oesterlé
Joseph Oesterlé (born 1954) is a French mathematician who, along with David Masser, formulated the ''abc'' conjecture which has been called "the most important unsolved problem in diophantine analysis In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...". He is a member of Bourbaki. References External links *The ABC conjecture 1954 births Living people < ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
