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Mathematical theorem
The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain
Mountain_pass_theorem
Italian mathematician (1944–2020)
calculus of variations cannot be applied. In particular, the so-called mountain pass theorem he established with Paul Rabinowitz is nowadays a classical tool
Antonio_Ambrosetti
bifurcation theorem and the mountain pass theorem, the latter done jointly with Antonio Ambrosetti. However also the linking and saddle point theorems, results
Paul_Rabinowitz
simple boundedness is needed. See, for example, the proof of the mountain pass theorem in section 8.5 of Evans. A continuously Fréchet differentiable functional
Palais–Smale compactness condition
Palais–Smale_compactness_condition
(game theory) Mountain pass theorem (calculus of variations) Noether's second theorem (calculus of variations, physics) Parthasarathy's theorem (game theory)
List_of_theorems
Critical point on a surface graph which is not a local extremum
Hyperbolic equilibrium point Hyperbolic geometry Minimax theorem Max–min inequality Mountain pass theorem Howard Anton, Irl Bivens, Stephen Davis (2002): Calculus
Saddle_point
Canadian-American mathematician (1925–2020)
solutions of wave equations.[BCN80] They were able to apply the mountain pass theorem to their new functional, thereby establishing the existence of periodic
Louis_Nirenberg
Concept in physics and mathematics
systems[clarification needed] are an example of this. Calculus of variations Mountain pass theorem Principle of least action Variational principle Gradient descent
Path_of_least_resistance
Analyzes the topology of a manifold by studying differentiable functions on that manifold
of algebraic topology Morse–Smale system Mountain pass theorem – Mathematical theorem Sard's lemma – Theorem in mathematical analysisPages displaying
Morse_theory
Function related to statistics and probability theory
while informally appealing to a mountain pass property. Mascarenhas restates their proof using the mountain pass theorem. In the proofs of consistency and
Likelihood_function
Differential calculus on function spaces
Nehari manifold Hu–Washizu principle Luke's variational principle Mountain pass theorem Category:Variational analysts Measures of central tendency as solutions
Calculus_of_variations
French mathematician (born 1956)
Lions showed that one could apply standard methods such as the mountain pass theorem, together with some technical work of Walter Strauss, in order to
Pierre-Louis_Lions
Antonio Ambrosetti, 75, Italian mathematician, discoverer of the mountain pass theorem. Patricia Beatty, 84, Canadian choreographer and dancer. Jorge Horacio
Deaths_in_November_2020
Theorem in topology
In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a
Jordan_curve_theorem
English mathematician
frames". His collaboration with Norbert Wiener included the Paley–Wiener theorem in harmonic analysis. Paley was originally selected as the 1934 American
Raymond_Paley
Every graph has evenly many odd vertices
combinatorial structures. For example, in the proofs of Sperner's lemma and the mountain climbing problem the geometric properties of the formula commonly arise
Handshaking_lemma
Topics referred to by the same term
Columbia) Burke Brook, part of the Don River in Toronto, Ontario Burkes Pass, a mountain pass and town in South Canterbury, New Zealand Burke, Idaho, a ghost
Burke_(disambiguation)
Map of most or all of the surface of the Earth
network – navigational aid drawn on maps Theorema Egregium – a geometric theorem Time zone American Cartographic Association's Committee on Map Projections
World_map
Evolutionary algorithm designed for maximizing manufacturing yield
x ) N ( x − m ) d x {\displaystyle P(m)=\int s(x)N(x-m)\,dx} Then the theorem of GA states: For any s(x) and for any value of P < q, there always exist
Gaussian_adaptation
Challenger Ray Lampkin Passes Sprint Car Hall Of Famer Casey Luna, 95 Remembering Mildred Pitts Walter Radio Remembers Rocky Allen Mountain Bike Pioneer Charlie
2026 deaths in the United States
2026_deaths_in_the_United_States
Problem of constructing equal-area shapes
proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number
Squaring_the_circle
Void between celestial bodies
Tadokoro, M. (1968), "A Study of the Local Group by Use of the Virial Theorem", Publications of the Astronomical Society of Japan, 20 (3): 230, Bibcode:1968PASJ
Outer_space
German mathematician (1882–1935)
contributions to abstract algebra. She also proved Noether's first and second theorems, which are fundamental in mathematical physics. Noether was described by
Emmy_Noether
Overuse of a shared resource
information. Skills acquisition and training, when all parties involved pass the buck on implementing it. The effects of climate change have been given
Tragedy_of_the_commons
American AI researcher and writer (born 1979)
Marcello (2014). "Program Equilibrium in the Prisoner's Dilemma via Löb's Theorem". Multiagent Interaction without Prior Coordination: Papers from the AAAI-14
Eliezer_Yudkowsky
Triangle with at least two sides congruent
{b^{2}}{4}}}}.} This formula can also be derived from the Pythagorean theorem using the fact that the altitude bisects the base and partitions the isosceles
Isosceles_triangle
Reduced pressure caused by a flow restriction in a tube or pipe
archaeologists from the British Museum confirmed the finding. In windy mountain passes, resulting in erroneous pressure altimeter readings The mistral wind
Venturi_effect
Missing Russian-American mathematician
Science Talent Search for a paper dealing with a variant of Fermat's Last Theorem, mentored by Leonid Vaserstein, a math professor at Penn State University
Aleksandr_Khazanov
Topics referred to by the same term
audio broadcast Eureka Streams, an open source software project Eureka theorem, a result of Gauss that every natural number is the sum of three triangular
Eureka
fundamentals of geography; digested into various definitions, problems, theorems, and paradoxes: with a transient survey of the surface of the earthly ball
Timeline of the name Palestine
Timeline_of_the_name_Palestine
2018 film by Terry Gilliam
under new colours." In November 2013 during the promotion of The Zero Theorem at the Venice Film Festival, Gilliam told Variety "I'm going to try to
The Man Who Killed Don Quixote
The_Man_Who_Killed_Don_Quixote
Indian mathematician and astronomer (1114–1185)
was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satamala mountain ranges of Western Ghats, believed to be the town of Patana in Chalisgaon
Bhāskara_II
Diplomatic policy of concessions
Sudetenland, Czechoslovakia lost 800,000 citizens, much of its industry and its mountain defences in the west. The rest of Czechoslovakia was left weak and powerless
Appeasement
two valleys via a mountain pass). Kusner's half-way models are saddle points for Willmore energy, arising (according to a theorem of Bryant) from certain
Minimax_eversion
Energy Transfer to simplify structure through merger". 2 August 2018. "Linde passes important 50 percent threshold in Praxair tender". reuters.com. 20 October
List of largest mergers and acquisitions
List_of_largest_mergers_and_acquisitions
Country in South Asia
BCE) contain the earliest extant verbal expression of the Pythagorean theorem (although very likely it had been known to the Old Babylonians.) All mathematical
India
French mathematician, physicist and engineer (1854–1912)
long passed — he was also unusually strong. Bell notes the terrible eyesight of Poincaré, he almost completely remembered formulas and theorems by ear
Henri_Poincaré
Angle to the horizontal plane
simply, one can calculate the horizontal run by using the Pythagorean theorem, after which it is trivial to calculate the (standard math) slope or the
Grade_(slope)
Chinese astronomer (1768–1797)
examples of her work are: “Transiting Tong Pass” So important is the doorway, occupying the throat of the mountain Looking down from the heaven, The sun sees
Wang_Zhenyi_(astronomer)
2023 film by Christopher Nolan
Urbaniak as Kurt Gödel, an Austrian logician and mathematician known for his theorems that revolutionized mathematics and had far-reaching implications for philosophy
Oppenheimer_(film)
Local and global geometry of the universe
example of a negatively curved surface would be the shape of a saddle or mountain pass. A triangle drawn on a saddle surface will have the sum of the angles
Shape_of_the_universe
theoretical physicist (Yang–Mills theory, Wu–Yang dictionary, Lee–Yang theorem), Nobel Prize laureate (1957). István Ágh, 87, Hungarian poet. Trevor Bentham
Deaths_in_October_2025
Census-designated place in New Mexico, United States
administrative assistant to Oppenheimer and philosopher known for the Hawkins–Simon theorem. Louis Hempelmann, physician who was the director of the Manhattan Project
Los_Alamos,_New_Mexico
Model of conflict for two players in game theory
of them swerves from the white line before the other, the other, as they pass, shouts 'Chicken!', and the one who has swerved becomes an object of contempt
Chicken_(game)
French general and emperor (1769–1821)
name, there does not appear to be a connection between him and Napoleon's theorem. This is depicted in Bonaparte Crossing the Alps by Hippolyte Delaroche
Napoleon
Numerological practice of reading a word or phrase as a number
English mathematician John Dee, who makes reference to the Agrippa code in Theorem XVI of his 1564 book, Monas Hieroglyphica. Although Aleister Crowley, as
Gematria
British mathematician (1854–1929)
symmetric functions and enumeration of plane partitions; see MacMahon Master theorem. His two volume Combinatory analysis, published in 1915/16, is the first
Percy_Alexander_MacMahon
Indian mathematician and astronomer (598–668)
Brahmagupta dedicated a substantial portion of his work to geometry. One theorem gives the lengths of the two segments a triangle's base is divided into
Brahmagupta
Romance ethnic group
infinitesimals and exhaustion to rigorously derive and prove the range of geometric theorems, and invented the innovative Archimedean screw, compound pulleys, and defensive
Sicilians
Osterwalder, 83, Swiss mathematician and physicist (Osterwalder–Schrader theorem). Darrell Pritchett, 78, American special effects artist (The Walking Dead
Deaths_in_December_2025
Indian-American mathematician and statistician (Cramér–Rao bound, Rao–Blackwell theorem). Herlander Ribeiro, 80, Portuguese Olympic freestyle swimmer (1960, 1964)
Deaths_in_August_2023
that the ancient Mesopotamians might have been aware of the Pythagorean theorem over a millennium before Pythagoras. Mathematical achievements from Mesopotamia
History_of_science
Obsolete theories in natural history and natural philosophy
superseded by the Bering Strait (discovered 1728) Mountains of Kong and Mountains of the Moon - mythical mountain ranges in Central Africa, based on the accounts
List of superseded scientific theories
List_of_superseded_scientific_theories
Captain Larry Taylor of Signal Mountain passes away at age 81 Luis Tejada cause of death: Panama's top scorer passes away League Mourns Loss of LWVUS
Deaths_in_January_2024
Prefecture and commune in France
(1607–1665), who spent his life in Toulouse, where he wrote Fermat's Last Theorem and was a lawyer in the city's parlement; Paul Sabatier (1854–1941), 1912
Toulouse
1996 video game
a tower-like rock formation going by the names Sword Cape and Triangle Mountain, at the foot of which stand two rocks dated as 8000 years old with unknown
Yu-no
Greek island in the eastern Aegean Sea
Greek philosopher and mathematician Pythagoras, after whom the Pythagorean theorem is named, the philosophers Melissus of Samos and Epicurus, and the astronomer
Samos
German philosopher (1788–1860)
Rudolstadt, hoping that no army would pass through the small town. He spent his time in solitude, hiking in the mountains and the Thuringian Forest and writing
Arthur_Schopenhauer
In economics, an imposed cost or benefit
economic decision-making Club good – Type of economic goods Coase theorem – Theorem in economics Externalities of automobiles – Impacts of car usePages
Externality
Country in Southeastern Europe
test), mathematician Constantin Carathéodory (known for the Carathéodory theorems and Carathéodory conjecture), astronomer E. M. Antoniadi, archaeologists
Greece
1887 investigation of the speed of light
interferometer rest frame to the aether rest frame. Therefore, the Pythagorean theorem gives the actual beam travel distance of L 2 + ( v T 3 ) 2 {\textstyle
Michelson–Morley_experiment
Swiss astronomer (1898–1974)
the Coma galaxy cluster in 1933, Zwicky was the first to use the virial theorem to discover the existence of a gravitational anomaly. Using the number
Fritz_Zwicky
German-born theoretical physicist (1879–1955)
rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said that only
Albert_Einstein
Chinese-American physicist (Lee–Yang theory, Kinoshita–Lee–Nauenberg theorem, Lee–Yang theorem), Nobel Prize laureate (1957). Juan Ramón Martínez, 76, Salvadoran
Deaths_in_August_2024
French polymath (1596–1650)
mathematics with Jacobus Golius, who confronted him with Pappus's hexagon theorem, and astronomy with Martin Hortensius. In October 1630, he had a falling-out
René_Descartes
binary outcome Naive Bayes – probabilistic classifier based on Bayes' theorem Ordinary least squares – estimation method for parameters in linear regression
List_of_data_science_software
Form of political manipulation
(November 2007). "Flagrant Gerrymandering: Help from the Isoperimetric Theorem?". SIAM News. 40 (9). Archived from the original on 29 October 2021. Retrieved
Gerrymandering
Indian computer scientist (1962–2009)
(BASES). He was a winner of the Gödel Prize in 2001 for his work on the PCP theorem and its applications to hardness of approximation. Motwani was found dead
Rajeev_Motwani
Development of mathematics in South Asia
Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians
Indian_mathematics
American domestic terrorist (1942–2023)
Wedderburn's Theorem". American Mathematical Monthly. 71 (6): 652–653. doi:10.2307/2312328. JSTOR 2312328. A proof of Wedderburn's little theorem in abstract
Ted_Kaczynski
Field of mathematics and science based on non-linear systems and initial conditions
whose orbit passes through V. This implies that it is impossible to decompose the system into two open sets. An important related theorem is the Birkhoff
Chaos_theory
Sound Test: Gus Visser and His Singing Duck (1925) Theodore Rex (1995) Theorem (1968) The Theory of Everything: (2006 TV & 2014) The Theory of Flight
List_of_films:_T
List of notable people who belong to the Brahmin caste
Indian mathematician, known for his proof of the Narasimhan–Seshadri theorem. Kannan Soundararajan, Indian-American mathematician, professor at Stanford
List_of_Brahmins
1979 science fiction novel by Arthur C. Clarke
course of Clarke's final novel (co-written with Frederik Pohl), The Last Theorem. Winner, Hugo Award for Best Novel - 1980 Winner, Nebula Award for Best
The_Fountains_of_Paradise
Measured time difference as explained by relativity theory
{\displaystyle \Delta t'} . Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity: The total time
Time_dilation
The Seattle Times. Retrieved 2019-09-09. "Bill McKinney, Deliverance's Mountain Man and Eastwood Sidekick, Dead at 80". E! Online. Retrieved 2011-12-02
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Zero Point (2014) Zero se Restart (2024) Zero to Sixty (1978) The Zero Theorem (2013) Zero Tolerance: (1994, 1999 & 2015) Zero Woman series: Zero Woman:
List_of_films:_numbers
Mechanism for regulating the speed of clocks
Clairaut created the first hydrostatic model of the Earth, Clairaut's theorem, which allowed the ellipticity of the Earth to be calculated from gravity
Pendulum
Infinitely detailed mathematical structure
growth Mathematics portal Systems science portal Banach fixed point theorem – Theorem about metric spacesPages displaying short descriptions of redirect
Fractal
School in Auckland, New Zealand
[note b][note c] The school was constructed on the corner of Khyber Pass Road and Mountain Road, a site which had been given to the church for educational
St_Peter's_College,_Auckland
Greek mathematician and physicist (c. 287 – 212 BC)
the method of exhaustion to derive and rigorously prove many geometrical theorems, including the area of a circle, the surface area and volume of a sphere
Archimedes
Decade of the Gregorian calendar (1990–1999)
Positioning System (GPS) becomes fully operational. Proof of Fermat's Last Theorem is discovered by Andrew Wiles. Construction started in 1998 on the International
1990s
Poetic form, traditionally fourteen specifically rhymed lines
Religion, French Catholic jurist and poet Jean de La Ceppède published the Theorems, a sequence of 515 sonnets with non-traditional rhyme schemes, about the
Sonnet
Fourth standardized moment in statistics
may be a lot of values either all below or above the mean. Applying band-pass filters to digital images, kurtosis values tend to be uniform, independent
Kurtosis
Indian inventions
number. Kosambi–Karhunen–Loève theorem (also known as the Karhunen–Loève theorem) The Kosambi-Karhunen-Loève theorem is a representation of a stochastic
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Extreme points Glaciers Highest point by states Islands Lakes Mountains Mountain passes Plains Indo-Gangetic Eastern coastal Western coastal Rivers Valleys
Timeline_of_Indian_history
Computational model used in machine learning
universal function approximator, as proven by the universal approximation theorem. However, the proof does not specify the number of neurons required, the
Neural network (machine learning)
Neural_network_(machine_learning)
American annual event
Spacelings & Baseheads Space Time Continuum Stacey Pullen Theo Parrish Theorem Tikiman Urban Tribe Clark Warner Alan Ester Lacksidaisycal & Montana RX-7
Detroit Electronic Music Festival
Detroit_Electronic_Music_Festival
2011 French TV series or program
hacking the physics department's computers and revising most of the accepted theorems they were working from – while they threw him out of school, they also
XIII:_The_Series
American theoretical physicist (1918–1988)
to have it published. Its main result is known as the Hellmann–Feynman theorem. In 1939, Feynman received a bachelor's degree and was named a Putnam Fellow
Richard_Feynman
symbols pave the entrance, and one interior canopy displays the geometrical theorem known to some of us as Pascal's Mystic Hexagram." The mathematical symbols
List of works by Rafael Viñoly
List_of_works_by_Rafael_Viñoly
Island in the North Atlantic Ocean
term electron in 1891. John Stewart Bell was the originator of Bell's Theorem and a paper concerning the discovery of the Bell-Jackiw-Adler anomaly and
Ireland
Ethical theory based on maximizing well-being
often justified by reference to Harsanyi's utilitarian theorem or the Von Neumann–Morgenstern theorem. According to the utilitarian, justice is the maximization
Utilitarianism
Term for accelerations felt as weight in multiples of standard gravity
typical person can handle about 5 g0 (49 m/s2) (meaning some people might pass out when riding a higher-g roller coaster, which in some cases exceeds this
G-force
Italian-American physicist (1901–1954)
behaves as if it were a Euclidean space. Fermi submitted his thesis, "A theorem on probability and some of its applications" (Un teorema di calcolo delle
Enrico_Fermi
Italian Renaissance polymath (1501–1576)
probability; he introduced the binomial coefficients and the binomial theorem in the Western world. He wrote more than 200 works on science. Cardano
Gerolamo_Cardano
Japanese actor (born 1954)
Landa) Carnage (Alan Cowan) Django Unchained (Dr. King Schultz) The Zero Theorem (Qohen Leth) Spectre (Ernst Stavro Blofeld) The Legend of Tarzan (Captain
Kazuhiro_Yamaji
Town in Eastern Cape, South Africa
roads by the Royal Engineers. He built eight mountain passes including Michell's Pass and Bain's Kloof Pass. He can rightly be called the father of South
Graaff-Reinet
Geometrical concept
the object do not subtract away, as would be required by the Divergence Theorem applied to the constant vector field r ^ {\displaystyle \mathbf {\hat {r}}
Cross_section_(geometry)
French polymath (1623–1662)
mathematics — to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic), then
Blaise_Pascal
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
Biblical
cloud; mass of darkness; fountain; eye
Surname or Lastname
English
English : from Old French bas(se) ‘low’, ‘short’ (Latin bassus ‘thickset’; see Basso), either a descriptive nickname for a short person or a status name meaning ‘of humble origin’, not necessarily with derogatory connotations.English : in some instances, from Middle English bace ‘bass’ (the fish), hence a nickname for a person supposedly resembling this fish, or a metonymic occupational name for a fish seller or fisherman.Scottish : habitational name from a place in Aberdeenshire, of uncertain origin.Jewish (Ashkenazic) : metonymic occupational name for a maker or player of bass viols, from Polish, Ukrainian, and Yiddish bas ‘bass viol’.German : see Basse.
Surname or Lastname
English
English : topographic name for someone who lived near a spring or well, from Old French fontane, Middle English fontayne ‘fountain’; in some cases the name may have arisen from French habitational names (Fontaine, Fonteyne, Lafontaine) of the same derivation.
Boy/Male
French
Mountain.
Surname or Lastname
English
English : from a pet form of the medieval personal name Pascal, which was brought to England from France.German : topographic name from Pass ‘pass’, ‘passage’ (from Middle Low German pas ‘pace’, ‘passage way’, ‘water gauge’).Jewish (Ashkenazic) : metonymic occupational name or nickname from Yiddish and Polish pas ‘belt’, ‘girdle’.
Boy/Male
Indian
Famous pass
Female
English
English short form of Latin Cassandra, CASS means "she who entangles men."Â
Girl/Female
Biblical
Mass, heap. An hour, eye, fountain.
Girl/Female
Indian, Punjabi, Sikh
Pass through
Surname or Lastname
English
English : status name denoting a serf, Middle English, Old French vass(e), from Late Latin vassus, of Celtic origin. Compare Welsh gwas ‘boy’, Gaelic foss ‘servant’.English : variant of Vause.Swedish : variant of Wass.South German : variant of Fass.Hungarian : from vas ‘iron’, hence a metonymic occupational name for a blacksmith, or a nickname for a resilient, tough man.
Boy/Male
Muslim
Famous pass
Male
Finnish
Pet form of Finnish Paavo, PASI means "small."Â
Surname or Lastname
English
English : variant of Pask, from the byform pasche, Latin pascha.Americanized spelling of German Pasch.
Surname or Lastname
English
English : from the medieval female personal name Cass, a short form of Cassandra. This was the name (of uncertain, possibly non-Greek, origin) of an ill-fated Trojan prophetess of classical legend, condemned to foretell the future but never be believed; her story was well known and widely popular in medieval England.
Surname or Lastname
English
English : topographic name from Old French montagne ‘mountain’ (see Montagne).Irish : either of Norman origin, as 1, or an Anglicized form of Gaelic Ó Manntáin (see Manton 2).
Girl/Female
Indian, Punjabi, Sikh
Pass through
Surname or Lastname
English
English : variant spelling of Fountain.
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
Boy/Male
Indian, Sanskrit
Like Amountain; A Powerful Mountain
Girl/Female
Biblical
Cloud, mass of darkness, fountain, eye.
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM
MOUNTAIN PASS-THEOREM