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Question in abstract algebra
In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Is every abelian group A with Ext1(A, Z) = 0 a free abelian
Whitehead_problem
British mathematician (1904–1960)
connection with algebraic K-theory. The Whitehead product is an operation in homotopy theory. The Whitehead problem on abelian groups was solved (as an independence
J._H._C._Whitehead
Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The
Whitehead's_algorithm
Yes-or-no question that cannot ever be solved by a computer
generalized by Rice's theorem. In 1973, Saharon Shelah showed the Whitehead problem in group theory is undecidable, in the first sense of the term, in
Undecidable_problem
Commutative group (mathematics)
the Whitehead problem: are all Whitehead groups of infinite order also free abelian groups? In the 1970s, Saharon Shelah proved that the Whitehead problem
Abelian_group
Limitative results in mathematical logic
hypothesis cannot be proved from ZFC. Shelah (1974) showed that the Whitehead problem in group theory is undecidable, in the first sense of the term, in
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
English mathematician and philosopher (1861–1947)
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as
Alfred_North_Whitehead
Topics referred to by the same term
Whitehead group in mathematics may mean: A group W with Ext(W, Z)=0; see Whitehead problem For a ring, the Whitehead group Wh(A) of a ring A, equal to
Whitehead_group
Combinatorial principle
Shelah showed that the diamond principle solves the Whitehead problem by implying that every Whitehead group is free. List of statements independent of ZFC
Diamond_principle
Anti-surface ship torpedo
rights to the Whitehead torpedo in 1869. By 1870 Whitehead's torpedoes were running at 17 knots (31 km/h; 20 mph). There was still the problem of course correction
Whitehead_torpedo
question of H. Friedman. In 1973, Saharon Shelah showed that the Whitehead problem ("is every abelian group A with Ext1(A, Z) = 0 a free abelian group
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Israeli mathematician
group for which every proper subgroup is countable. He showed that Whitehead's problem is independent of ZFC. He gave the first primitive recursive upper
Saharon_Shelah
Standard system of axiomatic set theory
statements independent of ZFC. These include the continuum hypothesis, the Whitehead problem, and the normal Moore space conjecture. Some of these conjectures
Zermelo–Fraenkel_set_theory
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Australian video game programmer
Christian Whitehead, also known as The Taxman, is an Australian video game programmer and designer. He is most recognized for his work creating updated
Christian_Whitehead
In mathematics, a module that has a basis
A famous example is the Whitehead problem, which asks whether a Whitehead group is free or not. As it turns out, the problem is independent of ZFC. Given
Free_module
Information which one can express but not use
effective problem-solving in realistic situations. The phenomenon of inert knowledge was first described in 1929 by Alfred North Whitehead: "[T]heoretical
Inert_knowledge
Philosophical problem
In philosophy of mind, the hard problem of consciousness (or simply the hard problem) is to explain how and why organisms have qualia, phenomenal consciousness
Hard_problem_of_consciousness
mathematics, the Kneser–Tits problem, introduced by Tits (1964) based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple
Kneser–Tits_conjecture
Problem in computer science
c2:HaltingProblem Alfred North Whitehead and Bertrand Russell, Principia Mathematica to *56, Cambridge at the University Press, 1962. Re: the problem of paradoxes
Halting_problem
American football player (born 1992)
Rodney Darnell "Lucky" Whitehead Jr. (born June 2, 1992) is an American former professional football player who was a wide receiver and kick returner
Lucky_Whitehead
View that mind is a ubiquitous feature of reality
and, more controversially, to Thales, Plato, Schopenhauer, Alfred North Whitehead, and Bertrand Russell. Views described as panpsychism were advocated by
Panpsychism
English actor (born 1939)
Geoffrey Whitehead (born 1 October 1939) is an English actor. He has appeared in a range of television, film and radio roles. Whitehead was born on 1 October
Geoffrey_Whitehead
19/20th-century German-American aviator
Gustave Albin Whitehead (born Gustav Albin Weisskopf; 1 January 1874 – 10 October 1927) was a German–American aviation pioneer. Between 1897 and 1915
Gustave_Whitehead
Homological algebra is the study of homological functors
cohomology Galois cohomology Lie algebra cohomology Sheaf cohomology Whitehead problem Homological conjectures in commutative algebra This list page primarily
List of homological algebra topics
List_of_homological_algebra_topics
Axiom in the mathematical field of set theory
MA + ¬CH implies that there exists a Whitehead group that is not free; Shelah used this to show that the Whitehead problem is independent of ZFC. Martin's
Martin's_axiom
finite simple groups Herzog–Schönheim conjecture Subset sum problem Whitehead problem Word problem for groups Amenable group Capable group Commensurability
List_of_group_theory_topics
English footballer
Dean Whitehead (born 12 January 1982) is an English football coach and former professional footballer who is Darrell Clarke's assistant manager at EFL
Dean_Whitehead
3-volume treatise on mathematics, 1910–1913
of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–1927
Principia_Mathematica
Open question in philosophy of how abstract minds interact with physical bodies
The mind–body problem is a philosophical problem concerning the relationship between thought and consciousness in the human mind and body. It addresses
Mind–body_problem
Overview of claims to the first powered airplane flight
adopted a bill naming Gustave Whitehead as the first to fly, a claim he made in 1901, later challenged by profound problems of documentation and contradictory
Claims to the first airplane flight
Claims_to_the_first_airplane_flight
Impossible task in computing
p. 3ff. Whitehead, Alfred North; Russell, Bertrand, Principia Mathematica to *56, Cambridge at the University Press, 1962. Re: the problem of paradoxes
Entscheidungsproblem
Unanswered question in the study of consciousness
binding problem is the problem of how objects, background, and abstract or emotional features are combined into a single experience. The binding problem refers
Binding_problem
American basketball player (born 1984)
in basketball. His combination of speed and size often created matchup problems for opposing teams because James was capable of charging past larger defenders
LeBron_James
American poet
Ron Whitehead is an American poet, author and activist. Whitehead was born on a farm in Kentucky, but traveled to the University of Louisville and Oxford
Ron_Whitehead
English explorer and naturalist (1860–1899)
John Whitehead (30 June 1860 – 2 June 1899) was an English explorer, naturalist and professional collector of natural history specimens in Southeast Asia
John_Whitehead_(explorer)
Species of bird endemic to New Zealand
The whitehead (Mohoua albicilla; Māori: pōpokotea) is a species of small (15 cm in length, 18.5/14.5 g.) passerine bird endemic to New Zealand. It is
Whitehead_(bird)
Family of mathematical knots
loop and then linking the ends together. (That is, a twist knot is any Whitehead double of an unknot.) The twist knots are an infinite family of knots
Twist_knot
treatment of the problem of evil written from the perspective of 'process' philosophical and theological thought." Griffin builds on Whitehead's view that God
Religious responses to the problem of evil
Religious_responses_to_the_problem_of_evil
Rhodesian politician (1905–1971)
Sir Edgar Cuthbert Fremantle Whitehead, KCMG OBE (8 February 1905 – 22 September 1971) was a Rhodesian politician and statesman who served as Prime Minister
Edgar_Whitehead
Homotopy invariant of maps between n-spheres
contains 2 Z {\displaystyle 2\mathbb {Z} } . Moreover, the image of the Whitehead product of identity maps equals 2, i. e. h ( [ i n , i n ] ) = 2 {\displaystyle
Hopf_invariant
Branch of philosophy
mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the hard problem of consciousness
Philosophy_of_mind
American novelist (1882-1932)
Henry St. Clair Whitehead (March 5, 1882 – November 23, 1932) was an American Episcopal minister and author of horror, some non fiction and fantasy fiction
Henry_S._Whitehead
Determining whether a knot is the unknot
Unsolved problem in mathematics Can unknots be recognized in polynomial time? More unsolved problems in mathematics In mathematics, the unknotting problem is
Unknotting_problem
American escapologist and stuntman (1874–1926)
22, 1926, speculated that Houdini's death was caused by Jocelyn Gordon Whitehead, who repeatedly struck Houdini's abdomen. The accounts of the witnesses
Harry_Houdini
Self-propelled underwater weapon
Fulton's use of the term to describe his stationary mines, and later Robert Whitehead's naming of the first self-propelled torpedo. Surface-skimming incendiary
Torpedo
American chef and politician (born 1988)
data center moratorium". Wisconsin Examiner. Retrieved August 2, 2026. Whitehead, Sandra (February 17, 2026). "Wisconsin lawmakers propose repeal of Walker-era
Francesca_Hong
Ancient Greek philosopher (c. 428-347 BC)
Christian, Jewish and Islamic philosophy. In modern times, Alfred North Whitehead said: "the safest general characterization of the European philosophical
Plato
Two interlinked loops with five structural crossings
In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings
Whitehead_link
Tyrie Remain 42.7% South East England 49.4% 50.6% Southampton Test Alan Whitehead Remain 8.7% South East England 49.4% 50.6% South Antrim Danny Kinahan
Results of the 2016 United Kingdom European Union membership referendum by constituency
Results_of_the_2016_United_Kingdom_European_Union_membership_referendum_by_constituency
Whitehead conjecture (also known as the Whitehead asphericity conjecture) is a claim in algebraic topology. It was formulated by J. H. C. Whitehead in
Whitehead_conjecture
German mathematician (1862–1943)
mathematics. His approach differed from the later "foundationalist" Russell–Whitehead or "encyclopedist" Nicolas Bourbaki, and from his contemporary Giuseppe
David_Hilbert
Intersection of Set Theory and General Topology
¬CH implies that there exists a Whitehead group that is not free; Shelah used this to show that the Whitehead problem is independent of ZFC. Forcing is
Set-theoretic_topology
Mathematical concept
isomorphism problem. It is notable that this means that the isomorphism problem, orbit problems (in particular the conjugacy problem) and Whitehead's problem are
Hyperbolic_group
Slovenian cyclist (born 1998)
multiple Monuments. During the 2025 Tour de France, The Athletic's Jacob Whitehead called Pogačar "a possible equal of Eddy Merckx—or more" in light of his
Tadej_Pogačar
President of the United States (2017–2021; since 2025)
at Debate". The New York Times. Retrieved September 25, 2024. Perry, Whitehead & Grubbs 2021, p. 229, Christian nationalist ideology was among the strongest
Donald_Trump
HTTP extension for collaborative editing
began in 1996 when Jim Whitehead worked with the World Wide Web Consortium (W3C) to host two meetings to discuss the problem of distributed authoring
WebDAV
Polynomials arising in knot theory
knot (11n34) Kinoshita–Terasaka knot (11n42) (−2,3,7) pretzel (12n242) Whitehead (52 1) Borromean rings (63 2) L10a140 Satellite Composite knots Granny
HOMFLY_polynomial
American black metal solo project
Leviathan is an American black metal solo project that started in 1998 by Jef Whitehead under the pseudonym Wrest. On all Leviathan albums, Wrest records all
Leviathan_(musical_project)
American documentary filmmaker (born 1949)
Martin Smith (born January 28, 1949) is an American producer, writer, director and correspondent. Smith has produced dozens of nationally broadcast documentaries
Martin_Smith_(documentarian)
Lecturer in the History of Maths at the Open University Vicky Neale, Whitehead Lecturer at the Mathematical Institute and Balliol College, Oxford 2 October
List of In Our Time programmes
List_of_In_Our_Time_programmes
Film by Christopher Nolan
the land, sea, and air. It features an ensemble cast including Fionn Whitehead, Tom Glynn-Carney, Jack Lowden, Harry Styles in his feature film debut
Dunkirk_(2017_film)
Fictional character from Sherlock Holmes stories
Moriarty first appears in the short story "The Adventure of the Final Problem", first published in The Strand Magazine in December 1893. He also plays
Professor_Moriarty
Fictional detective created by Agatha Christie
Roger Ackroyd was made by The Wireless Theatre Company and started Ben Whitehead as the voice of Hercule. In 2021 L.A. Theatre Works produced an adaptation
Hercule_Poirot
Video game and media franchise
iOS and Android devices. After Australian programmer Christian "Taxman" Whitehead developed a version of Sonic CD for modern consoles in 2011, he collaborated
Sonic_the_Hedgehog
Subfield of automated reasoning and mathematical logic
and Whitehead in their influential Principia Mathematica, first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought
Automated_theorem_proving
Rage comic character and internet meme
Internet culture at its finest". The Next Web. Retrieved June 13, 2020. Whitehead, Thomas (March 4, 2015). "Copyright Owner of 'Trollface' Image Explains
Trollface
1969 film by Alan Rafkin
Henry Jones, Edgar Buchanan, and Gary Collins. The Reverend Samuel D. Whitehead, former Marine, bricklayer, and recent seminary graduate, is ecstatic
Angel_in_My_Pocket
Olesons' spoiled daughter, Nellie. Then Laura encounters an even greater problem, when all the children have to write an essay for Parents' Day, but she
List of Little House on the Prairie episodes
List_of_Little_House_on_the_Prairie_episodes
Type of mathematical knot
The class of satellite knots include composite knots, cable knots, and Whitehead doubles. A satellite link is one that orbits a companion knot K in the
Satellite_knot
British racing driver (1914–1958)
Peter Nield Whitehead (12 November 1914 – 21 September 1958) was a British racing driver. He was born in Menston, Yorkshire and was killed in an accident
Peter Whitehead (racing driver)
Peter_Whitehead_(racing_driver)
Theorem in geometric topology
way he believed his question would be answered. In the 1930s, J. H. C. Whitehead claimed a proof but then retracted it. In the process, he discovered some
Poincaré_conjecture
2018 short story collection by Nana Kwame Adjei-Brenyah
Adjei-Brenyah among their "5 Under 35 Authors" for 2018, chosen by author Colson Whitehead. The book was included on the long list for the Andrew Carnegie Medals
Friday_Black
Web-based publication of MIT course content
chronological reading lists and discussion topics, a majority provided homework problems and exams (often with solutions) and lecture notes. Some courses also included
MIT_OpenCourseWare
Problem in game theory
Paise Restaurant Problem for extending it from binary choice (go to the bar or stay home) to multiple options for each player. Whitehead, Duncan (2008-09-17)
El_Farol_Bar_problem
Largest species of toothed whale
ISBN 978-0-7006-1772-2. Zbl 0945.14001. Whitehead 2003, p. 343. Whitehead 2003, p. 122. Whitehead 2003, p. 123. Whitehead 2003, p. 185. Mammals in the Seas
Sperm_whale
Retirement for Age February 15, 1939 2227 8050 Exemption of Robert F. Whitehead from Compulsory Retirement for Age February 15, 1939 2228 8051 Limiting
List of executive actions by Franklin D. Roosevelt
List_of_executive_actions_by_Franklin_D._Roosevelt
prices: 'We had to apply market rates'". City AM. Retrieved May 7, 2026. Whitehead, Jacob; Harpur, Charlotte (June 16, 2026). "Which World Cup matches had
List of 2026 FIFA World Cup controversies
List_of_2026_FIFA_World_Cup_controversies
Group whose operation is a composition of braids
braid groups. The word problem is also efficiently solved via the Lawrence–Krammer representation. In addition to the word problem, there are several known
Braid_group
English philosopher and logician (1872–1970)
Principia Mathematica (with Alfred North Whitehead). 3 vols. Cambridge: Cambridge University Press 1912. The Problems of Philosophy. London: Williams and Norgate
Bertrand_Russell
News. June 15, 2023. Ritman, Alex; Barnes, Mike (June 19, 2023). "Paxton Whitehead, Stage Veteran and 'Back to School' Actor, Dies at 85". The Hollywood
2023_in_American_television
Most populous city in the United States
York City (4th ed.). New York: Crown Publishers. ISBN 978-0-8129-3107-5. Whitehead, Colson (2003). The Colossus of New York: A City in 13 Parts. Doubleday
New_York_City
1960 article by Eugene Wigner
in describing nature. Albert Einstein and the philosopher Alfred North Whitehead had previously thought that the success of abstract mathematics in physical
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
2010 video game
games of the seventh generation of video game consoles. Eurogamer's Dan Whitehead hoped the eighth generation of consoles would offer "similarly powerful
Red_Dead_Redemption
1996 film by Arlene Sanford
led to the disappearance of Dr. Whitehead's son Gilligan and Carol's first husband, a professor. In Dr. Whitehead's words, "The Minnow is lost", and
A_Very_Brady_Sequel
American political party
white evangelical Protestant affiliation, and higher church attendance. Whitehead, Andrew L.; Perry, Samuel L. (2020). Taking America Back for God. doi:10
Republican Party (United States)
Republican_Party_(United_States)
Mathematical logician and philosopher
thinking in the 20th century (at a time when Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the
Kurt_Gödel
American actor (born 1955)
1984 Riptide Taxi Driver Episode: "The Hardcase" Falcon Crest "Buzz" Whitehead Episode: "Strangers" 1985 V Isaac Henley Episode: "Breakout" 1986 The
Xander_Berkeley
Austrian–British philosopher of science (1902–1994)
of problem solving. Popper presents falsifiability as both an ideal and as an important principle in a practical method of effective human problem solving;
Karl_Popper
Basic distinction in philosophy
subjectivity and objectivity with a gray area in-between, or that the problem of other minds is best viewed through the concept of intersubjectivity
Subjectivity and objectivity (philosophy)
Subjectivity_and_objectivity_(philosophy)
American criminal and cult leader (1934–2017)
Archived from the original on August 13, 2020. Retrieved August 18, 2020. Whitehead, John W. (August 3, 2010). "Helter Skelter: Racism and Murder". HuffPost
Charles_Manson
Conjecture in knot theory relating quantum invariants and hyperbolic geometry
and links with volume zero (Roland van der Veen), Twisted Whitehead links (Hao Zheng), Whitehead doubles of nontrivial torus knots T ( p , q ) {\displaystyle
Volume_conjecture
Residential school in Canada
Whitehead, Margaret (1981). The Cariboo Mission: A History of the Oblates. Victoria, British Columbia, Canada: Sono Nis Press. pp. 11–17. Whitehead,
Saint Joseph's Mission (Williams Lake)
Saint_Joseph's_Mission_(Williams_Lake)
1986 American comedy film by Alan Metter
Young, Terry Farrell, William Zabka, Ned Beatty, Sam Kinison, Paxton Whitehead, Robert Downey Jr., M. Emmet Walsh, and Adrienne Barbeau. It was directed
Back_to_School
Millennium Prize Problems Painlevé conjecture Mathematical fallacy Superseded theories in science List of incomplete proofs List of unsolved problems in mathematics
List_of_conjectures
Use of mathematics as a philosophical framework
7–78. doi:10.1017/CBO9780511805042.004. ISBN 978-0-521-24594-4. Whitehead, Whitehead, Alfred North and Bertrand Russell (1963). Principia Mathematica
Mathematicism
Severe outbreak of cholera that occurred in London in 1854
manage". By talking to local residents (with the help of Reverend Henry Whitehead), Snow identified the outbreak's source as the public water pump on Broad
1854 Broad Street cholera outbreak
1854_Broad_Street_cholera_outbreak
American author (born 1963)
'The Dutch House' And Her Problem with Villains". Time. Retrieved 2020-04-28. Maher, John (May 4, 2020). "Moser, Whitehead, McDaniel, Grandin, Boyer,
Ann_Patchett
British mathematician (born 1987)
he was awarded the SASTRA Ramanujan Prize. In 2015, he was awarded a Whitehead Prize and in 2016 an EMS Prize. In 2016, he showed that, for any given
James_Maynard_(mathematician)
2007 novel by Mark Peter Hughes
They gradually open up to one another about their problems: Stella thinks she's stupid and has problems with her parents, Wen's father will be marrying
Lemonade_Mouth
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