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Michael Freedman
Michael Hartley Freedman (born April 21, 1951) is an American mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists. Life and career Freedman was born in Los Angeles, California, in the United States. His father, Benedict Freedman, was an American Jewish aeronautical engineer, musician, writer, and mathematician. His mother, Nancy Mars Freedman, performed as an actress and also trained as an artist. His parents cowrote a series of novels together.. He entered the University of California, Berkeley, but dropped out after two semesters. In the same year he wrote a letter to Ralph Fox, a Princeton University professor at the time, and was admitted to the university's graduate school, where in 1968 he continued his studies and received a Ph.D. in 1973 for ... [...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] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles Times
The ''Los Angeles Times'' is an American Newspaper#Daily, daily newspaper that began publishing in Los Angeles, California, in 1881. Based in the Greater Los Angeles city of El Segundo, California, El Segundo since 2018, it is the List of newspapers in the United States, sixth-largest newspaper in the U.S. and the largest in the Western United States with a print circulation of 118,760. It has 500,000 online subscribers, the fifth-largest among U.S. newspapers. Owned by Patrick Soon-Shiong and published by California Times, the paper has won over 40 Pulitzer Prizes since its founding. In the 19th century, the paper developed a reputation for civic boosterism and opposition to Trade union, labor unions, the latter of which led to the Los Angeles Times bombing, bombing of its headquarters in 1910. The paper's profile grew substantially in the 1960s under publisher Otis Chandler, who adopted a more national focus. As with other regional newspapers in California and the United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nancy Freedman
Nancy Mars Freedman (July 4, 1920, in Evanston, Illinois – August 10, 2010, in Greenbrae, California) was an American feminist novelist, the co-author of '' Mrs. Mike''.. Life Upbringing Freedman (née Nancy Mars) was a professional child actress for touring stage plays, and she met her husband Benedict Freedman in 1940 in Hollywood, where he was working as a writer and she was trying to break into movies. They married in 1940 despite her poor health, which began with a bout of rheumatic fever at age three and lasted her entire life. Writing career She began writing novels with her husband in 1947 with ''Mrs. Mike'', the fictionalized story of their friend Katherine Mary Flannigan who married a Mountie and moved from Boston to the Canadian wilderness. It became a bestseller and inspired a 1950 film adaptation. The two Freedmans wrote nine more novels together, and Freedman wrote several more by herself. Her later works, including ''Mary, Mary Quite Contrary'' (1968) and ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benedict Freedman
Benedict Freedman (December 19, 1919 – February 24, 2012) was an American novelist and mathematician, the co-author of '' Mrs. Mike'' and a professor of mathematics at Occidental College in Los Angeles.. Life Upbringing Freedman was born to a Jewish family in New York City. His father, David, emigrated to America from Romania. He studied at Columbia University from ages 13 to 16, but dropped out without graduating after the death of his father. He took up his father's profession as a radio writer, and moved to the west coast where he worked for MGM Studios. Career Writing Freedman met his wife Nancy Freedman in 1940, when she was trying to break into acting. They married in 1941 despite her poor health; during the war Freedman continued to write, but also worked as an aeronautical engineer for Hughes Aircraft. The couple wrote their 1947 novel, '' Mrs. Mike'', based on the real-life adventures of their friend Katherine Mary Flannigan who married a Mountie and moved from Boston ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the semi-exclave of Alaska in the northwest and the archipelago of Hawaii in the Pacific Ocean. The United States asserts sovereignty over five Territories of the United States, major island territories and United States Minor Outlying Islands, various uninhabited islands in Oceania and the Caribbean. It is a megadiverse country, with the world's List of countries and dependencies by area, third-largest land area and List of countries and dependencies by population, third-largest population, exceeding 340 million. Its three Metropolitan statistical areas by population, largest metropolitan areas are New York metropolitan area, New York, Greater Los Angeles, Los Angel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California
California () is a U.S. state, state in the Western United States that lies on the West Coast of the United States, Pacific Coast. It borders Oregon to the north, Nevada and Arizona to the east, and shares Mexico–United States border, an international border with the Mexico, Mexican state of Baja California to the south. With almost 40million residents across an area of , it is the List of states and territories of the United States by population, largest state by population and List of U.S. states and territories by area, third-largest by area. Prior to European colonization of the Americas, European colonization, California was one of the most culturally and linguistically diverse areas in pre-Columbian North America. European exploration in the 16th and 17th centuries led to the colonization by the Spanish Empire. The area became a part of Mexico in 1821, following Mexican War of Independence, its successful war for independence, but Mexican Cession, was ceded to the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles
Los Angeles, often referred to by its initials L.A., is the List of municipalities in California, most populous city in the U.S. state of California, and the commercial, Financial District, Los Angeles, financial, and Culture of Los Angeles, cultural center of Southern California. With an estimated 3,878,704 residents within the city limits , it is the List of United States cities by population, second-most populous in the United States, behind only New York City. Los Angeles has an Ethnic groups in Los Angeles, ethnically and culturally diverse population, and is the principal city of a Metropolitan statistical areas, metropolitan area of 12.9 million people (2024). Greater Los Angeles, a combined statistical area that includes the Los Angeles and Riverside–San Bernardino metropolitan areas, is a sprawling metropolis of over 18.5 million residents. The majority of the city proper lies in Los Angeles Basin, a basin in Southern California adjacent to the Pacific Ocean in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exotic R4
In mathematics, an exotic \R^4 is a differentiable manifold that is homeomorphic (i.e. shape preserving) but not diffeomorphic (i.e. non smooth) to the Euclidean space \R^4. The first examples were found in 1982 by Michael Freedman and others, by using the contrast between Freedman's theorems about topological 4-manifolds, and Simon Donaldson's theorems about smooth 4-manifolds. There is a continuum of non-diffeomorphic differentiable structures \R^4, as was shown first by Clifford Taubes. Prior to this construction, non-diffeomorphic smooth structures on spheres exotic sphereswere already known to exist, although the question of the existence of such structures for the particular case of the 4-sphere remained open (and remains open as of 2024). For any positive integer ''n'' other than 4, there are no exotic smooth structures \R^n; in other words, if ''n'' ≠ 4 then any smooth manifold homeomorphic to \R^n is diffeomorphic to \R^n. Small exotic R4s An exotic \R^4 is cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robion Kirby
Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant for classifying the piecewise linear structures on a topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links. Along with his significant mathematical contributions, he has over 50 doctoral students and is the editor of an influential problem list. Career He received his Ph.D. from the University of Chicago in 1965, with thesis "Smoothing Locally Flat Imbeddings" written under the direction of . He soon became an assistant professor at UCLA. While there he developed his " torus trick" which enabled him to solve, in dimensions greater than four (with additional joint work with Siebenmann), four of John Milnor's seven ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Poincaré Conjecture
In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold that is a homotopy sphere a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differentiable (Diff). Then the statement is :Every homotopy sphere (a closed ''n''-manifold which is homotopy equivalent to the ''n''-sphere) in the chosen category (i.e. topological manifolds, PL manifolds, or smooth manifolds) is isomorphic in the chosen category (i.e. homeomorphic, PL-isomorphic, or diffeomorphic) to the standard ''n''-sphere. The name derives from the Poincaré conjecture, which was made for (topological or PL) manifolds of dimension 3, where being a homotopy sphere is equivalent to being simply connected and closed. The generalized Poincaré conjecture is known to be true or false in a number of instances, due to the work of many distinguished topologists, including the Fields medal awardees John Milnor, Steve Smale, Mic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Santa Barbara
The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an independent teachers college, UCSB joined the University of California system in 1944. It is the third-oldest undergraduate campus in the system, after University of California, Berkeley, UC Berkeley and University of California, Los Angeles, UCLA. UCSB's campus sits on the oceanfront site of a converted WWII-era United States Marine Corps, Marine Corps air station. UCSB is organized into three undergraduate colleges (UCSB College of Letters and Science, Letters and Science, UCSB College of Engineering, Engineering, College of Creative Studies, Creative Studies) and two graduate schools (Gevirtz Graduate School of Education, Education and Bren School of Environmental Science & Management, Environmental Science & Management), offering more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
