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Григорий Яковлевич Перельман
Grigori Yakovlevich Perelman (, ; born 13June 1966) is a Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg and has declined requests for interviews since 2006. In the 1990s, partly in collaboration with Yuri Burago, Mikhael Gromov, and Anton Petrunin, he made contributions to the study of Alexandrov spaces. In 1994, he proved the soul conjecture in Riemannian geometry, which had been an open problem for the previous 20 years. In 2002 and 2003, he developed new techniques in the analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leningrad
Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601,911 residents as of 2021, with more than 6.4 million people living in the Saint Petersburg metropolitan area, metropolitan area. Saint Petersburg is the List of European cities by population within city limits, fourth-most populous city in Europe, the List of cities and towns around the Baltic Sea, most populous city on the Baltic Sea, and the world's List of northernmost items#Cities and settlements, northernmost city of more than 1 million residents. As the former capital of the Russian Empire, and a Ports of the Baltic Sea, historically strategic port, it is governed as a Federal cities of Russia, federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard S
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic language">Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include " Richie", " Dick", " Dickon", " Dickie", " Rich", " Rick", "Rico (name), Rico", " Ricky", and more. Richard is a common English (the name was introduced into England by the Normans), German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Portuguese and Spanish "Ricardo" and the Italian "Riccardo" (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Ander ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Breakthrough Of The Year
The Breakthrough of the Year is an annual award for the most significant development in scientific research made by the American Association for the Advancement of Science, AAAS journal ''Science (journal), Science,'' an academic journal covering all branches of science. Originating in 1989 as the ''Molecule of the Year'', and inspired by ''Time (magazine), Time'' Time Magazine Person of the Year, Person of the Year, it was renamed the Breakthrough of the Year in 1996. Molecule of the Year * 1989 Polymerase chain reaction, PCR and DNA polymerase * 1990 the manufacture of synthetic diamonds * 1991 buckminsterfullerene * 1992 nitric oxide * 1993 p53 * 1994 DNA repair enzyme Breakthrough of the Year * 1996: Understanding HIV * 1997: Dolly (sheep), Dolly the sheep, the first mammal to be Clone (genetics), cloned from adult cells * 1998: Accelerating expansion of the universe, Accelerating universe * 1999: Prospective stem-cell therapy, stem-cell therapies * 2000: Full genome sequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'' is the peer review, peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' cover the full range of List of academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BBC News
BBC News is an operational business division of the British Broadcasting Corporation (BBC) responsible for the gathering and broadcasting of news and current affairs in the UK and around the world. The department is the world's largest broadcast news organisation and generates about 120 hours of radio and television output each day, as well as online news coverage. The service has over 5,500 journalists working across its output including in 50 foreign news bureaus where more than 250 foreign correspondents are stationed. Deborah Turness has been the CEO of news and current affairs since September 2022. In 2019, it was reported in an Ofcom report that the BBC spent £136m on news during the period April 2018 to March 2019. BBC News' domestic, global and online news divisions are housed within the largest live newsroom in Europe, in Broadcasting House in central London. Parliamentary coverage is produced and broadcast from studios in London. Through BBC English Regions, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Problem
In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known). In the history of science, some of these supposed open problems were "solved" by means of showing that they were not well-defined. In mathematics, many open problems are concerned with the question of whether a certain definition is or is not consistent. Two notable examples in mathematics that have been solved and ''closed'' by researchers in the late twentieth century are Fermat's Last Theorem and the four-color theorem.K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", ''Illinois J. Math'' 21: 429–490. K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", ''Illinois J. Math'' 21: 491–567. An important open mathematics problem solved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricci Flow
In differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due to formal similarities in the mathematical structure of the equation. However, it is nonlinear and exhibits many phenomena not present in the study of the heat equation. The Ricci flow, so named for the presence of the Ricci tensor in its definition, was introduced by Richard Hamilton, who used it through the 1980s to prove striking new results in Riemannian geometry. Later extensions of Hamilton's methods by various authors resulted in new applications to geometry, including the resolution of the differentiable sphere conjecture by Simon Brendle and Richard Schoen. Following the possibility that the singularities of solutions of the Ricci flow could identify the topological data predicted by William ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soul Theorem
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related soul conjecture, formulated by Cheeger and Gromoll at that time, was proved twenty years later by Grigori Perelman. Soul theorem Cheeger and Gromoll's soul theorem states: :If is a complete connected Riemannian manifold with nonnegative sectional curvature, then there exists a closed totally convex, totally geodesic embedded submanifold whose normal bundle is diffeomorphic to . Such a submanifold is called a soul of . By the Gauss equation and total geodesicity, the induced Riemannian metric on the soul automatically has nonnegative sectional curvature. Gromoll and Meyer had earlier studied the case of positive sectional curvature, where they showed that a sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexandrov Space
In geometry, Alexandrov spaces with curvature ≥ ''k'' form a generalization of Riemannian manifolds with sectional curvature ≥ ''k'', where ''k'' is some real number. By definition, these spaces are locally compact complete length spaces where the lower curvature bound is defined via comparison of geodesic triangles in the space to geodesic triangles in standard constant-curvature Riemannian surfaces. One can show that the Hausdorff dimension of an Alexandrov space with curvature ≥ ''k'' is either a non-negative integer or infinite. One can define a notion of "angle" (see Comparison triangle#Alexandrov angles) and "tangent cone" in these spaces. Alexandrov spaces with curvature ≥ ''k'' are important as they form the limits (in the Gromov–Hausdorff metric) of sequences of Riemannian manifolds with sectional curvature ≥ ''k'', as described by Gromov's compactness theorem. Alexandrov spaces with curvature ≥ ''k'' were introduced by the Russian mathematician Aleks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Leonidovich Gromov
Mikhael Leonidovich Gromov (also Mikhail Gromov, Michael Gromov or Misha Gromov; ; born 23 December 1943) is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of Institut des Hautes Études Scientifiques in France and a professor of mathematics at New York University. Gromov has won several prizes, including the Abel Prize in 2009 "for his revolutionary contributions to geometry". Early years, education and career Mikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His father Leonid Gromov was Russian-Slavic and his mother Lea was of Jewish heritage. Both were pathologists. His mother was the cousin of World Chess Champion Mikhail Botvinnik, as well as of the mathematician Isaak Moiseevich Rabinovich. Gromov was born during World War II, and his mother, who worked as a medical doctor in the Soviet Army, had to leave the front line in order to give birth to him. When Gromov was nine years ol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steklov Institute Of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Saint Petersburg, Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the ''St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences'' or PDMI RAS, located in Saint Petersburg, Russia. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
