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Lists Of Unsolved Problems
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine * Unsolved problems in astronomy * Unsolved problems in biology * Unsolved problems in chemistry * Unsolved problems in geoscience * Unsolved problems in medicine * Unsolved problems in neuroscience * Unsolved problems in physics Mathematics, statistics and information sciences * Unsolved problems in mathematics * Unsolved problems in statistics * Unsolved problems in computer science * Unsolved problems in information theory Social sciences and humanities * Problems in philosophy * Unsolved problems in economics * Unsolved problems in fair division See also * Cold case (unsolved crimes) * List of ciphertexts * List of hypothetical technologies * List of NP-complete problems * List of paradoxes * List of PSPACE-complete problems * List of undecidable problems * List of unsolved deaths This list of unsolved death ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Conjectures
This is a list of notable mathematical conjectures. Open problems The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a Google Scholar search for the term, in double quotes . Conjectures now proved (theorems) The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names. * Deligne's conjecture on 1-motives * Goldbach's weak conjecture (proved in 2013) * Sensitivity conjecture (proved in 2019) Disproved (no longer conjectures) The conjectures in following list were not necessarily generally accepted as true before being disproved. * Atiyah conjecture (not a conjecture to start with) * Borsuk's conjecture * Chinese hypothesis (not a conjecture to start with) * Doomsday conjecture * Euler's sum of powers conjecture * Ganea conjecture * Generalized Smith conjecture * Hauptvermutung * Hedetniemi's conjecture, counterexample announced 2019 * Hirsch conject ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Unsolved Problems In Fair Division
This page lists notable open problems related to fair division - a field in the intersection of mathematics, computer science, political science and economics. Open problems in fair cake-cutting Query complexity of envy-free cake-cutting In the problem of envy-free cake-cutting, there is a cake modeled as an interval, and ''n'' agents with different value measures over the cake. The value measures are accessible only via queries of the form "evaluate a given piece of cake" or "mark a piece of cake with a given value". With ''n=2'' agents, an envy-free division can be found using two queries, via divide and choose. With ''n>2'' agents, there are several open problems regarding the number of required queries. 1. First, assume that the entire cake must be allocated (i.e., there is ''no disposal''), and pieces may be disconnected. ''How many queries are required?'' * Lower bound: \Omega(n^2); * Upper bound: O\left(n^\right). 2. Next, assume that some cake may be left unal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Problems
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] |
Lists Of Unsolved Problems
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine * Unsolved problems in astronomy * Unsolved problems in biology * Unsolved problems in chemistry * Unsolved problems in geoscience * Unsolved problems in medicine * Unsolved problems in neuroscience * Unsolved problems in physics Mathematics, statistics and information sciences * Unsolved problems in mathematics * Unsolved problems in statistics * Unsolved problems in computer science * Unsolved problems in information theory Social sciences and humanities * Problems in philosophy * Unsolved problems in economics * Unsolved problems in fair division See also * Cold case (unsolved crimes) * List of ciphertexts * List of hypothetical technologies * List of NP-complete problems * List of paradoxes * List of PSPACE-complete problems * List of undecidable problems * List of unsolved deaths This list of unsolved death ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unknowability
In philosophy, unknowability is the possibility of inherently unaccessible knowledge. It addresses the epistemology of that which cannot be known. Some related concepts include the limits of knowledge, ''ignorabimus'', unknown unknowns, the halting problem, and chaos theory. Nicholas Rescher provides the most recent focused scholarship for this area in ''Unknowability: An Inquiry into the Limits of Knowledge'', where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability. Background Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular, Baruch Spinoza's Theory of Attributes argues that a human's finite mind cannot understand infinite substance; accordingly, infinite substance, as it is in itself, is in-principle unknowable to the finite mind. Immanuel Kant brought focus to unknowability theory in his use of the noumenon con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lists Of Problems
The following articles contain lists of problems: * List of philosophical problems *List of undecidable problems *Lists of unsolved problems *List of NP-complete problems *List of PSPACE-complete problems Here are some of the more commonly known problems that are PSPACE-complete when expressed as decision problems. This list is in no way comprehensive. Games and puzzles Generalized game, Generalized versions of: * Amazons (game), Amazons * At ... {{DEFAULTSORT:Problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Unsolved Deaths
This list of unsolved deaths includes notable cases where: * The cause of death could not be officially determined following an investigation * The person's identity could not be established after they were found dead * The cause is known, but the manner of death (homicide, suicide, accident) could not be determined following an investigation * Different official investigations have come to different conclusions Cases where there are unofficial alternative theories about deaths – the most common theory being that the death was a homicide – can be found under: :Death conspiracy theories, Death conspiracy theories. Unsolved murders Unsolved deaths Ancient * The Younger Lady (25–35) is the informal name given to the mummy of a woman who lived during the Eighteenth Dynasty of Egypt (c. 1549 to 1292 BCE), and was discovered in the Egyptian Valley of the Kings in tomb KV35 by archaeologist Victor Loret in 1898. The cause of her death is unknown. Through recent DNA tests, this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Undecidable Problems
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC. Problems about abstract machines * The halting problem (determining whether a Turing machine halts on a given input) and the morta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of PSPACE-complete Problems
Here are some of the more commonly known problems that are PSPACE-complete when expressed as decision problems. This list is in no way comprehensive. Games and puzzles Generalized game, Generalized versions of: * Amazons (game), Amazons * Atomix (computer game), Atomix * Checkers if a draw is forced after a polynomial number of non-jump moves * Dyson Telescope Game * TipOver, Cross Purposes * Generalized geography, Geography * Two-player game version of Instant Insanity * Ko rule, Ko-free Go (game), Go * Ladder (Go), Ladder capturing in GoGo ladders are PSPACE-complete * m,n,k-game, Gomoku * Hex (board game), Hex * Konane * Lemmings (video game), Lemmings * Node Kayles * Poset Game * Reversi * River Cro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Paradoxes
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article in this encyclopedia. These paradoxes may be due to fallacious reasoning (falsidical), or an unintuitive solution (Veridical paradox, veridical). The term ''paradox'' is often used to describe a counter-intuitive result. However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called ''antinomy,'' point out genuine problems in our understanding of the ideas of truth and Definite description, description. Logic * : The supposition that, "if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved" leads to paradoxical conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of NP-complete Problems
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in no way comprehensive. Many problems of this type can be found in . Graphs and hypergraphs Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). * 1-planarity * 3-dimensional matching * Bandwidth problem * Bipartite dimension * Capacitated minimum spanning tree *Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. * Clique cover problem * Clique problem * Complete coloring, a.k.a. achromatic number * Cycle rank * Degree-constrained spanning tre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
