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List Of Unsolved Problems In Graph Theory
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more than one discipline and are studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative, and the problems listed here vary widely in both difficulty and importance. Lists of unsolved problems in mathematics Various mathematicians and organiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problems
A mathematical problem is a problem that can be Representation (mathematics), represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the Orbit#Planetary orbits, orbits of the planets in the Solar System, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the Foundations of mathematics, nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problem (mathematics education), word problems, they are used in mathematics education to teach students to connect real-world situations to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995), where he currently is Professor Emeritus, with research interests in algorithms, numerical analysis and global analysis. Education and career Smale was born in Flint, Michigan and entered the University of Michigan in 1948. Initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself A's. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. Smale obtained his Bachelor of Science degree in 1952. Despite his grades, with some luck, Smale was accepted as a graduate student at the University of Michigan's mathematics department. Yet again, Smale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smale's Problems
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999. Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of Hilbert's problems that had been published at the beginning of the 20th century. Table of problems In later versions, Smale also listed three additional problems, "that don't seem important enough to merit a place on our main list, but it would still be nice to solve them:" # Mean value problem #Is the three-sphere a minimal set ( Gottschalk's conjecture)? #Is an Anosov diffeomorphism of a compact manifold topologically the same as the Lie group model of John Franks? See also * Millennium Prize Problems * Simon problems * Taniyama's problems * Hilbert's problems Hilbert's problems are 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Thurston
William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurston was a professor of mathematics at Princeton University, University of California, Davis, and Cornell University. He was also a director of the Mathematical Sciences Research Institute. Early life and education William Thurston was born in Washington, D.C., to Margaret Thurston (), a seamstress, and Paul Thurston, an aeronautical engineer. William Thurston suffered from congenital strabismus as a child, causing issues with depth perception. His mother worked with him as a toddler to reconstruct three-dimensional images from two-dimensional ones. He received his bachelor's degree from New College in 1967 as part of its inaugural class. For his undergraduate thesis, he developed an intuitionist foundation for topology. Following th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thurston's 24 Questions
Thurston's 24 questions are a set of mathematical problems in differential geometry posed by American mathematician William Thurston in his influential 1982 paper ''Three-dimensional manifolds, Kleinian groups and hyperbolic geometry'' published in the ''Bulletin of the American Mathematical Society''. These questions significantly influenced the development of geometric topology and related fields over the following decades. History The questions appeared following Thurston's announcement of the geometrization conjecture, which proposed that all compact 3-manifolds could be decomposed into geometric pieces. This conjecture, later proven by Grigori Perelman in 2003, represented a complete classification of 3-manifolds and included the famous Poincaré conjecture as a special case. By 2012, 22 of Thurston's 24 questions had been resolved. Table of problems Thurston's 24 questions are: See also * Geometrization conjecture * Hilbert's problems * Taniyama's problems * List ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yutaka Taniyama
was a Japanese mathematician known for the Taniyama–Shimura conjecture. Life Taniyama was born on 22 November 1927 in Kisai, a town in Saitama. He was the sixth of eight children born to a doctor's family. He studied at Urawa High School (present-day Saitama University) after graduating from Fudouoka Middle School. He suspended his college for two years due to his medical condition, but finally graduated in 1950. During Taniyama's college years, he aspired to be a mathematician after reading Teiji Takagi's work. In 1958, Taniyama worked as an Associate Professor after years of assistant at the University of Tokyo. He also obtained his doctorate from the University in May. In October, Taniyama was engaged to be married to , while the Institute for Advanced Study in Princeton, New Jersey offered him a position. On 17 November 1958, Taniyama committed suicide by poisoning himself with gas. He left a note explaining how far he had progressed with his teaching duties, and apolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taniyama's Problems
Taniyama's problems are a set of 36 mathematical problems posed by Japanese mathematician Yutaka Taniyama in 1955. The problems primarily focused on algebraic geometry, number theory, and the connections between modular forms and elliptic curves. History In the 1950s post-World War II period of mathematics, there was renewed interest in the theory of modular curves due to the work of Taniyama and Goro Shimura. During the 1955 international symposium on algebraic number theory at Tokyo and Nikkō—the first symposium of its kind to be held in Japan that was attended by international mathematicians including Jean-Pierre Serre, Emil Artin, Andre Weil, Richard Brauer, K. G. Ramanathan, and Daniel Zelinsky—Taniyama compiled his 36 problems in a document titled ''"Problems of Number Theory"'' and distributed mimeographs of his collection to the symposium's participants. These problems would become well known in mathematical folklore. Serre later brought attention to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Biography Edmund Landau was born to a Jewish family in Berlin. His father was Leopold Landau, a gynecologist, and his mother was Johanna Jacoby. Landau studied mathematics at the University of Berlin, receiving his doctorate in 1899 and his habilitation (the post-doctoral qualification required to teach in German universities) in 1901. His doctoral thesis was 14 pages long. In 1895, his paper on scoring chess tournaments is the earliest use of eigenvector centrality. Landau taught at the University of Berlin from 1899 to 1909, after which he held a chair at the University of Göttingen. He married Marianne Ehrlich, the daughter of the Nobel Prize-winning biologist Paul Ehrlich, in 1905. At the 1912 International Congress of Mathematicians Landau listed four problems in number theory about primes that he said were pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau's Problems
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. They are as follows: # Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? # Twin prime conjecture: Are there infinitely many primes ''p'' such that ''p'' + 2 is prime? # Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares? # Are there infinitely many primes ''p'' such that ''p'' − 1 is a perfect square? In other words: Are there infinitely many primes of the form ''n''2 + 1? , all four problems are unresolved. Progress toward solutions Goldbach's conjecture Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Gold ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Mathematical Society
The Canadian Mathematical Society (CMS; French: ''Société mathématique du Canada'') is an association of professional mathematicians dedicated to advancing mathematical research, outreach, scholarship and education in Canada. The Society serves the national and international communities through the publication of high-quality academic journals and community bulletins, as well as by organizing a variety of mathematical competitions and enrichment programs. These include the Canadian Open Mathematics Challenge (COMC), the Canadian Mathematical Olympiad (CMO), and the selection and training of Canada's team for the International Mathematical Olympiad (IMO) and the European Girls’ Mathematical Olympiad (EGMO). The CMS was originally conceived in June 1945 as the Canadian Mathematical Congress. A name change was debated for many years; ultimately, a new name was adopted in 1979, upon the Society’s incorporation as a non-profit charitable organization. The Society is affi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
