Math 2.0

Frontier, page 6

The gaps in the graph. People and agents can take each item as work. To claim an item, open an issue in the content repository.

This copy of the site has no build data, so the lists give no evidence levels.

1916 statements with no proof; 92 open conjectures and problems. Showing up to 751–900 in each list.

Statements with no proof

No proof node in the graph proves these statements. A source can still support them.

NameTagKindEvidence
Z/pZ is a field for p prime0NV6E43P4Astatementnone
Multiplicativity of the Legendre symbol0NW1JP7TBRstatementnone
Second Borel–Cantelli lemma0NWXRAMEE7statementnone
Weierstrass M-test0NX5NWAFC9statementnone
Sum of independent normal random variables0NXGPJWNFNstatementnone
Theorem on friends and strangers0NYM0ZGAK9statementnone
Angle-angle similarity0NZVJYZVTZstatementnone
Classification of isometries of the plane0P0XDY9FZNstatementnone
Second-order Taylor expansion0P30YYZN85statementnone
Negation of a universal statement0P3A06QNDPstatementnone
Sine is 2π-periodic0P4NQD746Kstatementnone
A function with bounded derivative is Lipschitz0P64VE79X3statementnone
Picard–Lindelöf theorem0P6KRD5B7Astatementnone
Compactness via open covers0P6PMJB4MAstatementnone
Linearity of expectation0P7PTC8DDEstatementnone
Vandermonde determinant0P84B554ASstatementnone
The exponential function is positive0P9BNBW2W3statementnone
Metric spaces are Hausdorff0P9DCDES73statementnone
Existence of a complementary subspace0P9T8WHNMHstatementnone
Continuity is equivalent to sequential continuity0PAQM3H57Xstatementnone
Law of sines0PASQ34GHGstatementnone
Order of the symmetric group0PCKBBMEXCstatementnone
Fermat's theorem on stationary points0PCVBRV9VJstatementnone
First supplement to quadratic reciprocity0PHBS78HKTstatementnone
Heine–Borel theorem in finite-dimensional normed spaces0PHT6NBYPBstatementnone
Alternating series test0PK8QH1W1Vstatementnone
Projections are continuous0PM88Z9W4Mstatementnone
Order of an inverse0PMT9YJZVWstatementnone
The continued fraction of a rational number terminates0PMY0YQYXXstatementnone
The Gaussian integers are a Euclidean domain0PN13BB7BTstatementnone
Argument principle0PN2BXRS8Gstatementnone
The constructible numbers form a field closed under square roots0PN9WMRWT7statementnone
Jordan's lemma0PNPG2PP9Hstatementnone
Interior is open0PNWCM559Pstatementnone
Determinant is multilinear in the rows0PPG793642statementnone
Second isomorphism theorem0PPP2J2DJVstatementnone
Probability of the complement0PQEBTYDZMstatementnone
Alternating sum of binomial coefficients0PQQGFAWSHstatementnone
Principal axis theorem0PR5P9Z4KMstatementnone
Dirichlet convolution of multiplicative functions is multiplicative0PR88XHDMBstatementnone
Expectation with respect to the binomial distribution0PVCTCKD3Cstatementnone
The exponential series has infinite radius of convergence0PVJRACB9Hstatementnone
Orthogonal complement of the orthogonal complement0PXN9G4MX1statementnone
Stolz–Cesàro theorem0Q3AKZV74Dstatementnone
Integral of a power0Q3HYFT9RQstatementnone
Darboux's theorem0Q5A47J48Dstatementnone
Holomorphic functions with nonzero derivative are conformal0Q7M6K6VD7statementnone
Third Sylow theorem0Q8DGAZSJ4statementnone
Reciprocal rule0QD4E5JYPTstatementnone
Holomorphic functions are infinitely differentiable0QEBN8DGVEstatementnone
Cayley–Hamilton theorem for linear maps0QEM68Y0DEstatementnone
Eigenvalues are the roots of the minimal polynomial0QF4ZEFG52statementnone
The algebraic numbers form a field0QFTETCHKBstatementnone
Gauss's lemma0QFV5Y1Z5Xstatementnone
Irrationality of pi0QHZX1PK8Vstatementnone
Dimension of the coordinate space0QK7FPE6VEstatementnone
Euclidean domains are principal ideal domains0QKVE1GD9Astatementnone
The Galois group has order at most the degree0QM98DNWVWstatementnone
Ratio test0QNY6ZBXPNstatementnone
Von Dyck's theorem0QPYHHNRXCstatementnone
Derivative of a map into a product0QQMXFTX0Astatementnone
Number of odd-degree vertices is even0QQQQCPZA8statementnone
In a UFD irreducible elements are prime0QRCFZKXH8statementnone
Recurrence for derangements0QRRYXG7V7statementnone
The reals form an ordered field0QSPNASE50statementnone
The group of units of Z/pZ is cyclic0QTHB6PE52statementnone
Frattini argument0QTZDKJEDVstatementnone
Dimension of a subspace0QW084460Estatementnone
Every element of a finite field of order q satisfies x^q = x0QWR8WTZEWstatementnone
Tangent–secant theorem0QX7E9KAAXstatementnone
Convergent sequences are Cauchy0QY87R9CY3statementnone
Continuity of the sum of a uniformly convergent series of functions0R0MYT0BJDstatementnone
Fubini's theorem0R0T1VWH5Xstatementnone
Abelian groups are solvable0R0X73XHATstatementnone
Fraction in lowest terms0R64A2CVN4statementnone
Universal property of the quotient ring0R74MZYNRBstatementnone
Compact subsets of a metric space are bounded0R7BTEWCJ2statementnone
Symmetry of binomial coefficients0R7JS3DP3Wstatementnone
pi is greater than 30R7SVNYTJSstatementnone
A linear isometry preserves the inner product0R7VXTYHYZstatementnone
Dimension of a tensor product0R84PF4JV7statementnone
A linear map is determined by its values on a basis0R8X9XA83Astatementnone
Integers modulo a prime form a field0R8YXRC9AJstatementnone
Characterization of the floor0R9B0B5458statementnone
Divisibility by 30R9D4CEJEBstatementnone
Gcd of Fibonacci numbers0R9F850CTHstatementnone
Limit of a sum of sequences0RAM4E07NRstatementnone
Bessel's inequality0RBT5PB74Kstatementnone
Cesàro means of a convergent sequence converge0RDRPBMNACstatementnone
Generating function of a sum of independent random variables0REMT01N36statementnone
Cauchy–Schwarz inequality0RFWW56Y22statementnone
Limit of the cumulative distribution function at infinity0RJ5TZH6G0statementnone
Logarithm is the inverse of the exponential0RKW2X63YRstatementnone
Cantor set is homeomorphic to the space of binary sequences0RQ8DHHR8Vstatementnone
Wedderburn's little theorem0RRNVX1VKAstatementnone
Jensen's inequality0RWMRTPC87statementnone
Every infinite set has a countably infinite subset0RWQ5VZ6VQstatementnone
Image of an intersection0RX7DDBYCKstatementnone
Distributivity of matrix multiplication0RXD6EZYBKstatementnone
Chain rule0RXX2PT1MQstatementnone
Structure theorem for finitely generated abelian groups0RY0B72XASstatementnone
Lucas's theorem0RY4GGMEQGstatementnone
Law of excluded middle0RYYK8PG4Sstatementnone
A nontrivial finite p-group has nontrivial centre0RZCTT30H5statementnone
Power-reduction formula for cosine0S049HG1W5statementnone
Size of an orbit times the size of the stabiliser0S19CWFZM2statementnone
Variation of constants formula for linear systems0S1KG0XE40statementnone
Abel's theorem0S4EMDQS2Fstatementnone
Convergent sequences are bounded0S4JF619V7statementnone
Inverse of a product0S4WTRE9GGstatementnone
Order of the group of units of Z/nZ is Euler's totient0S7495H4HMstatementnone
Hartman–Grobman theorem0S8WX8A4V9statementnone
Correspondence theorem0S9ZVZ34MDstatementnone
Derivative of tangent0SAMR34WXCstatementnone
Dirichlet convolution formula0SAR26CKPSstatementnone
Gradient theorem0SD237FEJDstatementnone
Product rule in several variables0SF85PY0QNstatementnone
Basis of a tensor product0SH5VT8QYAstatementnone
Closure is the smallest closed superset0SHC6Z304Zstatementnone
Irreducibility of the cyclotomic polynomials over the rationals0SK1VHZ5R2statementnone
Stability of linear systems via eigenvalues0SKVEMXJWFstatementnone
Edge bound for planar graphs0SM1REAVYJstatementnone
Erdős–Szekeres theorem0SNJM8HSD3statementnone
A space is the direct sum of a subspace and its orthogonal complement0SP7P0G7KQstatementnone
Existence of a prime divisor0SPBEDVNW1statementnone
Change of basis for a bilinear form0SPYAGE7T0statementnone
The Gaussian integers form a Euclidean domain0SPYEFH7H4statementnone
Principal value of the argument0SQSQP748Rstatementnone
Subgroups of the integers0SRATCFF1Wstatementnone
Characteristic subgroups are normal0SRE7K4E49statementnone
Hurwitz's theorem0SSKBQN58Mstatementnone
The degree of a constructible number is a power of two0SSSM1D475statementnone
Moments are derivatives of the moment-generating function at zero0STK8KEY9Gstatementnone
C^1 functions are strictly differentiable0STPPDXGMEstatementnone
Density of the rationals0STX0WRDNGstatementnone
Almost sure convergence implies convergence in probability0SVN6X695Kstatementnone
Primitive element theorem0SVX98HYV1statementnone
Möbius transformations map circles and lines to circles and lines0SXDHQM2MHstatementnone
Dimension of a quotient space0SXDQ6TN00statementnone
Order of the alternating group0SZ1KMNWVEstatementnone
Determinant is a coefficient of the characteristic polynomial0T0X8GTYYSstatementnone
Infinitely many primes congruent to 1 modulo n0T1BSD7H3Mstatementnone
Fundamental theorem of Galois theory0T1Q8D0FW8statementnone
Degree of a product0T233AZ1GEstatementnone
Power series of arctangent0T32ME0A6Hstatementnone
The cross product is perpendicular to its factors0T4QHJXSD4statementnone
First Borel–Cantelli lemma0T6WS7TT77statementnone
Cauchy–Riemann equations0T71SSYZ39statementnone
Integration in polar coordinates0T89W1QZ9Kstatementnone
The characteristic function determines the distribution0T8BYAFEXXstatementnone

Open conjectures and problems

No node in the graph resolves these conjectures and problems.

None.