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specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would
Four_exponentials_conjecture
Major unsolved problem in transcendental number theory
theorem above. The currently unproven four exponentials conjecture would also follow from Schanuel's conjecture: If z 1 , z 2 {\displaystyle z_{1},z_{2}}
Schanuel's_conjecture
Condition on transcendence of numbers
of the five exponentials theorem as well, although it as yet unproven so is known as the sharp five exponentials conjecture. This conjecture implies both
Six_exponentials_theorem
tree Exponential type Exponentially equivalent measures Exponentiating by squaring Exponentiation Forgetting curve Four exponentials conjecture Fourier
List_of_exponential_topics
Aharoni-Korman conjecture also known as the fishbone conjecture Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Bunkbed conjecture Chinese
List_of_conjectures
are themselves transcendental? The four exponentials conjecture: the transcendence of at least one of four exponentials of combinations of irrationals Are
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
On algebraic independence of logarithms
unproven Schanuel's conjecture, and does not imply the six exponentials theorem nor, clearly, the still open four exponentials conjecture. The main reason
Baker's_theorem
Open problem on 3x+1 and x/2 functions
problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple
Collatz_conjecture
Matrix operation generalizing exponentiation of scalar numbers
ISSN 1095-7200.. Suzuki, Masuo (1985). "Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical
Matrix_exponential
On generating functions from counting points on algebraic varieties over finite fields
In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them
Weil_conjectures
Type of natural number
They showed that this would follow from a special case of the four exponentials conjecture in transcendental number theory, specifically that for any two
Colossally_abundant_number
Conjecture in number theory
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and
Abc_conjecture
Unproven conjecture in graph theory
is exponential in the iterated logarithm of n necessarily contains a cycle whose length is a power of two (Sudakov & Verstraëte 2008). The conjecture is
Erdős–Gyárfás_conjecture
Generates a forecast of future values of a time series
had been used previously, it was applied twice and four times to coincide with the Hadamard conjecture, while triple application required more than double
Exponential_smoothing
Geometry problem on tiling by hypercubes
In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes
Keller's_conjecture
Conjecture on zeros of the zeta function
problems in mathematics In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even
Riemann_hypothesis
Mathematical space
the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter
3-manifold
Unsolved problem in the mathematics of graph coloring
problems in mathematics In the mathematics of graph coloring, Cereceda’s conjecture is an unsolved problem on the distance between pairs of colorings of sparse
Cereceda's_conjecture
Arithmetic operation
Dave L. Renfro, Web pages for infinitely iterated exponentials Knobel, R. (1981). "Exponentials Reiterated". American Mathematical Monthly. 88 (4):
Tetration
3-regular graph with no 3-edge-coloring
problems in graph theory (such as the cycle double cover conjecture and the 5-flow conjecture), one encounters an interesting but somewhat mysterious variety
Snark_(graph_theory)
Collection of sets in which every two sets have the same intersection
conjecture was resolved as a consequence of a breakthrough on the cap set problem. Alon, Shpilka, and Umans had previously shown that an exponential upper
Sunflower_(mathematics)
Time for exponential decay to remove half of a quantity
running a statistical computer program. An exponential decay can be described by any of the following four equivalent formulas: N ( t ) = N 0 ( 1 2 )
Half-life
American mathematician (1943–2024)
of results and ideas for using it to prove the Poincaré conjecture and geometrization conjecture from the field of geometric topology. Hamilton's work on
Richard_S._Hamilton
Complex exponential in terms of sine and cosine
definitions of the trigonometric functions and the standard identities for exponentials are sufficient to easily derive most trigonometric identities. It provides
Euler's_formula
Algorithmically defined graph
scheme; this question, which Spinrad restated as a conjecture. Recent work has refuted this conjecture by providing a family of graphs with a forbidden
Implicit_graph
Unsolved problem in computer science
complexity. Exponential time hypothesis List of unsolved problems in computer science List of unsolved problems in mathematics Unique games conjecture A nondeterministic
P_versus_NP_problem
Number of form 2^(2^p-1)-1 with prime exponent
proof of the Goldbach conjecture". In the movie, this number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number
Double_Mersenne_number
Three groups
totally ordered, has exponential growth, and does not contain a subgroup isomorphic to the free group of rank 2. It is conjectured that F is not amenable
Thompson_groups
Australian and American mathematician (born 1975)
resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks
Terence_Tao
Partial differential equation
Thurston's geometrization conjecture, Hamilton produced a number of results in the 1990s which were directed towards the conjecture's resolution. In 2002 and
Ricci_flow
Points with no three in a line
{\displaystyle c_{p}^{n}} for some c p < p {\displaystyle c_{p}<p} . The cap set conjecture was solved in 2016 due to a series of breakthroughs in the polynomial
Cap_set
Type of Diophantine equation in number theory
Srinivasa Ramanujan, who conjectured that it has only five integer solutions, and after Trygve Nagell, who proved the conjecture. It implies non-existence
Ramanujan–Nagell_equation
Exploring properties of the integers with complex analysis
Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Analytic number theory can be split up into two
Analytic_number_theory
Most basic type of physical force
inferred a field filling space and transmitting that force. Faraday conjectured that ultimately, all forces unified into one. In 1873, James Clerk Maxwell
Fundamental_interaction
Number divisible only by 1 and itself
withstood proof for decades: all four of Landau's problems from 1912 are still unsolved. One of them is Goldbach's conjecture, which asserts that every even
Prime_number
On solvability of Diophantine equations
finitely many components. This conjecture implies that the integers are not Diophantine over the rationals, and so if this conjecture is true, a negative answer
Hilbert's_tenth_problem
Complete coloring Edge coloring Exact coloring Four color theorem Fractional coloring Goldberg–Seymour conjecture Graph coloring game Graph two-coloring Harmonious
List_of_graph_theory_topics
Chinese-American mathematician (born 1949)
recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered
Shing-Tung_Yau
Observation on the growth of integrated circuit capacity
be sustained indefinitely: "It can't continue forever. The nature of exponentials is that you push them out and eventually disaster happens." He also noted
Moore's_law
Compounding sum paid for the use of money
up interest in Wiktionary, the free dictionary. Credit card interest Exponential growth Fisher equation Interest Interest rate Rate of return Rate of
Compound_interest
Particular kind of exponential sum
generally that complete exponential sums 'along' algebraic varieties have good estimates, depending on the Weil conjectures in dimension > 1. It has
Kloosterman_sum
Award for advancements in discrete mathematics
optimization. G. P. Egorychev and D. I. Falikman for proving Van der Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any
Fulkerson_Prize
results and several examples including the Chvátal graph, Branko Grünbaum conjectured that for every k {\displaystyle k} and ℓ {\displaystyle \ell } there
Chvátal_graph
Compact astronomical body
hair conjecture proposes that dynamic gravitational collapse always results in an object characterized with only these three properties. The conjecture is
Black_hole
appears in various contexts in elementary geometry. The Fermat–Catalan conjecture concerns a certain Diophantine equation, equating the sum of two terms
List_of_sums_of_reciprocals
Mathematical problem
of each integer edge-length, which he called the heterogeneous tiling conjecture. This problem was later publicized by Martin Gardner in his Scientific
Squaring_the_square
Number without repeated prime factors
by x + c x 1 / 5 log x . {\displaystyle x+cx^{1/5}\log x.} The abc conjecture would allow x + x o ( 1 ) {\displaystyle x+x^{o(1)}} . The squarefree
Square-free_integer
Dutch mathematician
CFOP is used for their 3x3x3 stages. He also wrote a book on Catalan's conjecture. Schoof's algorithm Schoof–Elkies–Atkin algorithm Homepage Counting points
René_Schoof
Graph with all vertices of degree 3
Lovász and Plummer conjectured that every cubic bridgeless graph has an exponential number of perfect matchings. The conjecture was recently proved,
Cubic_graph
General relativity model near spacetime singularities
for appropriately defined spatial scale factors. This is called the BKL conjecture. For most types of matter the effect of the matter fields on the dynamics
BKL_singularity
British mathematician
matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs
Paul_Seymour_(mathematician)
Size of largest complete graph made by contracting edges of a given graph
graphs with this Hadwiger number) to the four color theorem on colorings of planar graphs, and the conjecture has also been proven for k ≤ 5, but remains
Hadwiger_number
Increase in the rate of technological change through history
then predicting the future course of technological progress is merely conjecture. Therefore, if we are astonished by the connections Burke is able to weave
Accelerating_change
In mathematics, a statement that has been proven
be written down. The most prominent examples are the four color theorem and the Kepler conjecture. Both of these theorems are only known to be true by
Theorem
Algebraic curve in mathematics
Birch and Swinnerton-Dyer conjecture (BSD) is one of the Millennium problems of the Clay Mathematics Institute. The conjecture relies on analytic and arithmetic
Elliptic_curve
Geometry problem on grid points
points for every n {\displaystyle n} up to 70 {\displaystyle 70} , it is conjectured that fewer than 2 n {\displaystyle 2n} points can be placed in grids
No-three-in-line_problem
Set of decision problems
first-order theory of the real numbers with +, ×, = is in EXPSPACE and was conjectured to be EXPSPACE-complete in 1986. The coverability problem for Petri Nets
EXPSPACE
Algorithm checking for prime numbers
a given number is prime or composite without relying on mathematical conjectures such as the generalized Riemann hypothesis. The proof is also notable
AKS_primality_test
Assignment of colors to edges of a graph
d-edge-colorable if and only if G is oddly d-edge-connected. This conjecture is a generalization of the four color theorem, which arises at d=3. Maria Chudnovsky,
Edge_coloring
Mathematical function, inverse of an exponential function
2001), Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials Abramowitz & Stegun, eds. 1972, p. 68 Sasaki, T.; Kanada, Y. (1982),
Logarithm
Subpermutation of a longer permutation
sequences |Avn(β)| where β is of length four: In the late 1980s, Richard Stanley and Herbert Wilf conjectured that for every permutation β, there is some
Permutation_pattern
How many integer lattice points there are in a circle
o\left(r^{1/2}(\log r)^{1/4}\right),} using the little o-notation. It is conjectured that the correct bound is | E ( r ) | = O ( r 1 / 2 + ε ) . {\displaystyle
Gauss_circle_problem
Study of numbers that are not solutions of polynomials with rational coefficients
is whether there is a closed-form expression for a number, including exponentials and logarithms as well as algebraic operations. There are various definitions
Transcendental_number_theory
Function describing an electron in an atom
that the resulting orbitals are products of a polynomial series, and exponential and trigonometric functions. (see hydrogen atom). For atoms with two
Atomic_orbital
Computer simulation with random inputs
Stochastic originally meant "pertaining to conjecture"; from Greek stokhastikos "able to guess, conjecturing": from stokhazesthai "guess"; from stokhos
Stochastic_simulation
since Euclid. Euler made progress toward the prime number theorem and conjectured the law of quadratic reciprocity. The two concepts are regarded as the
Contributions of Leonhard Euler to mathematics
Contributions_of_Leonhard_Euler_to_mathematics
Mathematical descriptions of the properties of certain cells in the nervous system
Radar-like detection procedure. As shown in Fig. 6, the key idea of the conjecture is to account for neurotransmitter concentration, neurotransmitter generation
Biological_neuron_model
Methodic assignment of colors to elements of a graph
counties of England in 1852, Francis Guthrie postulated the four color conjecture, noting that four colors were sufficient to color the map so that no regions
Graph_coloring
Statement in mathematical combinatorics
2^{2^{k^{1+o(1)}}}.} However, that was still far from the exponential bound conjectured by Erdős. It was not until 1998 when a major breakthrough was
Ramsey's_theorem
that is exponentially faster than any possible deterministic classical algorithm. 1994 – Andrew Wiles proves part of the Taniyama–Shimura conjecture and thereby
Timeline_of_mathematics
Algebraic structure
Weil conjectures concern the number of points on algebraic varieties over finite fields and the theory has many applications including exponential and
Finite_field
Triangular array of the binomial coefficients
triangle Multiplicities of entries in Pascal's triangle (Singmaster's conjecture) Pascal matrix Pascal's pyramid Pascal's simplex Proton NMR, one application
Pascal's_triangle
Property of a mathematical space
affairs was highly marked in the various cases of the Poincaré conjecture, in which four different proof methods are applied. The dimension of a manifold
Dimension
2008 British TV series or programme
surfaces; however in 1904 he came up with a topological problem, the Poincaré conjecture, that he could not solve; namely what are all the possible shapes for
The_Story_of_Maths
Product of numbers from 1 to n
{\displaystyle 16!=14!\cdot 5!\cdot 2!} . It would follow from the abc conjecture that there are only finitely many nontrivial examples. The greatest common
Factorial
Mathematical problem
by Jordan curves, then at least six colors are required. Four color theorem Hadwiger conjecture Soifer (2008), pp. 557–563; Shelah & Soifer (2003). Beckman
Hadwiger–Nelson_problem
Number, approximately 3.14
decimal digits of π appear to be evenly distributed, but no proof of this conjecture has been found. Mathematicians have attempted to extend their understanding
Pi
Interaction between subatomic particles
particle, except perhaps the Higgs boson. So far they remain entirely a conjecture: As of October 2021, no such neutrinos are known to actually exist. "MicroBooNE
Weak_interaction
Probability of shared birthdays
[1]. Brink 2012, Theorem 2 Brink 2012, Theorem 3 Brink 2012, Table 3, Conjecture 1 "Minimal number of people to give a 50% probability of having at least
Birthday_problem
Doubly exponential integer sequence
{a_{n}}{a_{n-1}^{2}}}=1.} Badea (1995) surveys progress related to this conjecture; see also Brown (1979). If i < j, it follows from the definition that
Sylvester's_sequence
Geoffrey C. Shephard (but never formally published by himself) and is conjectured to be complete: * self-dual McMullen showed that projectively unique
Projectively_unique_polytope
Complex-differentiable part of a Maass wave function
S2CID 7688222 Bringmann, Kathrin; Ono, Ken (2006), "The f(q) mock theta function conjecture and partition ranks" (PDF), Inventiones Mathematicae, 165 (2): 243–266
Mock_modular_form
Natural number
Foundation. Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.
4000_(number)
include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative
List_of_theorems
Two raised to an integer power
hardware, and the data is stored in one or more octets (23), double exponentials of two are common in computing. The first 21 of them are: Also see Fermat
Power_of_two
Group that is also a differentiable manifold with group operations that are smooth
structure on G which turns it into a Lie group (see also Hilbert–Smith conjecture). If the underlying manifold is allowed to be infinite-dimensional (for
Lie_group
Used to count, measure, and label
and the Goldbach conjecture, which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution
Number
Quantum mechanics thought experiment
subjective experience of surviving quantum suicide. It is sometimes conjectured to be applicable to real-world causes of death as well. As a thought
Quantum suicide and immortality
Quantum_suicide_and_immortality
Swiss mathematician (1707–1783)
developed some of Fermat's ideas and disproved some of his conjectures, such as his conjecture that all numbers of the form 2 2 n + 1 {\textstyle 2^{2^{n}}+1}
Leonhard_Euler
Measure of a civilization's evolution
2023-08-27. Denning, Kathryn (2011-02-01). "Ten thousand revolutions: conjectures about civilizations". Acta Astronautica. SETI Special Edition. 68 (3):
Kardashev_scale
German physicist
{2}}} the speed of light. This finding was instrumental towards Maxwell's conjecture that light is an electromagnetic wave. He was the father of physicist
Rudolf_Kohlrausch
Task of computing complete subgraphs
require exponential size to detect cliques, or large polynomial size to detect cliques of bounded size. The Aanderaa–Karp–Rosenberg conjecture also states
Clique_problem
Mathematical graph theorem
matching. It was conjectured by Lovász and Plummer that the number of perfect matchings contained in a cubic, bridgeless graph is exponential in the number
Petersen's_theorem
Graph used in computational complexity theory and graph theory
these algorithms have been used to call into question the unique games conjecture. Let n be a positive integer, and let γ be a real number in the unit interval
Frankl–Rödl_graph
On the existence of arithmetic progressions in subsets of the natural numbers
{\displaystyle {\frac {N}{e^{O(\log N/\log \log N)}}}} , disproving an additional conjecture of Erdős and Turán that r 3 ( [ N ] ) = N 1 − δ {\displaystyle r_{3}([N])=N^{1-\delta
Roth's theorem on arithmetic progressions
Roth's_theorem_on_arithmetic_progressions
information on the topology and geometry (in the sense of the geometrisation conjecture of the manifold) and vice versa. A guiding principle is that the minimal
Curve_complex
Sequence of numbers ((2n) choose (n))
the OEIS) is seen in Wolstenholme's theorem. By the Erdős squarefree conjecture, proved in 1996, no central binomial coefficient with n > 4 is squarefree
Central_binomial_coefficient
Convex polytope of parenthesizations
tight when n is large enough, and conjectured that "large enough" means "strictly greater than 9". This conjecture was proved in 2012 by Lionel Pournin
Associahedron
List of scientists who are Christians
method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem. Heinrich Hertz (1857–1894): German physicist who first
List of Christians in science and technology
List_of_Christians_in_science_and_technology
Nonlinear partial differential equation
field theory. The quantum sine-Gordon equation should be modified so the exponentials become vertex operators L Q s G = 1 2 ∂ μ φ ∂ μ φ + 1 2 m 0 2 φ 2 − α
Sine-Gordon_equation
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
Biblical
four
Boy/Male
Hindu
Four-armed
Boy/Male
Bengali, French, Hebrew, Indian
Fair; Red; White
Boy/Male
Hindu, Indian
Four Faced; A Name for Varuna
Boy/Male
African, Arabic, Australian, Lebanese
Light
Boy/Male
Indian, Sanskrit
Four Legged; Another Name for Tortoise
Boy/Male
Tamil
Chaturbahu | சதà¯à®°à¯à®ªà®¾à®¹à¯Â
Four armed
Chaturbahu | சதà¯à®°à¯à®ªà®¾à®¹à¯Â
Boy/Male
Australian, Japanese
Four Seasons
Boy/Male
Muslim/Islamic
Light
Boy/Male
African
Rock.
Boy/Male
Biblical
Four.
Girl/Female
Indian, Telugu
Four Types
Boy/Male
Native American
Four bears.
Male
Icelandic
Icelandic form of Old Norse Friðþjófr, FRIÃÞJÓFUR means "peace-thief."
Boy/Male
Scottish
From the water.
Boy/Male
Hindu, Indian, Traditional
Four Faced; Another Name for Brahma
Girl/Female
Indian, Punjabi, Sikh
Tears of Eyes
Boy/Male
Hindu, Indian, Kannada, Telugu, Traditional
Four Armed
Boy/Male
Tamil
Chaturbahave | சதà¯à®°à¯à®ªà®¹à®¾à®µà¯‡
Four-armed
Chaturbahave | சதà¯à®°à¯à®ªà®¹à®¾à®µà¯‡
Boy/Male
Hindu, Indian, Punjabi, Sikh
Princess
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
Female
Czechoslovakian
, love peace (or world).
Female
Norwegian
Norwegian variant form of Scandinavian Birgit, BERGIT means "exalted one."
Surname or Lastname
English (Midlands)
English (Midlands) : habitational name from a place in Staffordshire, recorded as Bidolf in Domesday Book, from Old English bī ‘beside’ + dylf ‘digging’ (a putative derivative of delfan ‘to dig’), i.e. a mine or quarry.
Boy/Male
Australian, British, Christian, English
Heart; Mind and Spirit
Girl/Female
Australian, French, Greek
Shining; Bright; Similar to Helen
Boy/Male
Tamil
White
Boy/Male
Anglo, British, English
Shear Man
Boy/Male
Hindu
Love
Boy/Male
Hindu
Display, Signs
Female
Russian
(Иринушка) Pet form of Russian Irina, IRINUSHKA means "peace."
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
FOUR EXPONENTIALS-CONJECTURE
superl.
Loathsome; disgusting; as, a foul disease.
n.
Fixed or appointed time; conjuncture; a particular time or occasion; as, the hour of greatest peril; the man for the hour.
superl.
Covered with, or containing, extraneous matter which is injurious, noxious, offensive, or obstructive; filthy; dirty; not clean; polluted; nasty; defiled; as, a foul cloth; foul hands; a foul chimney; foul air; a ship's bottom is foul when overgrown with barnacles; a gun becomes foul from repeated firing; a well is foul with polluted water.
superl.
Scurrilous; obscene or profane; abusive; as, foul words; foul language.
v. t.
To sprinkle with flour.
n.
A symbol representing four units, as 4 or iv.
v. t.
To grind and bolt; to convert into flour; as, to flour wheat.
n.
Four things of the same kind, esp. four horses; as, a chariot and four.
superl.
Disagreeable; unpleasant; hence; cross; crabbed; peevish; morose; as, a man of a sour temper; a sour reply.
n.
The sum of four units; four units or objects.
a.
Having four wheels.
a.
Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function.
n.
See Foul ball, under Foul, a.
v. t.
To macerate, and render fit for plaster or mortar; as, to sour lime for business purposes.
n.
Strips of dressed skins with fur, used on garments for warmth or for ornament.
superl.
Cold and unproductive; as, sour land; a sour marsh.
n.
A naval vessel carrying seventy-four guns.
a.
Allowing passage in either of four directions; as, a four-way cock, or valve.
n.
A vehicle having four wheels.
a.
Having four corners or angles.