Frontier, page 5

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 601–750 in each list.

Statements with no proof

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

Name	Tag	Kind	Evidence
Totient of a prime	0HY1MXMEN9	statement	none
Eigenvalues of a positive definite matrix are positive	0HYC2RHD3M	statement	none
Injective iff it has a left inverse	0HYFEEZAEM	statement	none
Modulus is multiplicative	0HYNZE940T	statement	none
Mean value property	0HYPR64JM2	statement	none
Solutions of Pell's equation are powers of the fundamental solution	0J1TT091TN	statement	none
Polar decomposition	0J2C7BDJQA	statement	none
Conjugacy classes of the symmetric group correspond to cycle types	0J438GAC8K	statement	none
The symmetric group on five or more letters is not solvable	0J53NE674D	statement	none
Congruence is compatible with powers	0J5VGJYYC3	statement	none
Intersecting secants theorem	0J5XR7BW2S	statement	none
Lyapunov's stability theorem	0J6A752DTZ	statement	none
Associativity of composition	0J6AKYZQT8	statement	none
Kuratowski's theorem	0J6G5NJC5R	statement	none
Rearrangements of an absolutely convergent series have the same sum	0J76TP9FGD	statement	none
Logarithm of a quotient	0J7PHRBNNS	statement	none
Sperner's theorem	0J87V9K1GE	statement	none
Taylor's theorem in several variables	0J8T4K4YTE	statement	none
Determinant of a block triangular matrix	0J9TVTNB4K	statement	none
Ratio formula for the radius of convergence	0JBMYAA9QH	statement	none
Vector calculus identities	0JC5X4HWR2	statement	none
Sign is a homomorphism	0JEJJCB0EX	statement	none
The cumulative distribution function determines the distribution	0JEVZAFDY6	statement	none
Turán's theorem	0JG1KZSPFZ	statement	none
Eigenspaces of a self-adjoint operator are orthogonal	0JHGAV9H25	statement	none
Cauchy's estimates	0JJRENWMP6	statement	none
Abelian simple groups have prime order	0JJV80RXHD	statement	none
Cauchy's theorem	0JM7PA288B	statement	none
Lindemann–Weierstrass theorem	0JNCBFMPXR	statement	none
Convolution theorem for the Laplace transform	0JNMJEDD93	statement	none
Fundamental theorem of algebra	0JP0W07Y9A	statement	none
Kőnig's theorem	0JP0ZF57PN	statement	none
Subgroups of abelian groups are normal	0JPDTEDCFD	statement	none
Order of the general linear group over a finite field	0JQ1KNQW2K	statement	none
Weierstrass approximation theorem	0JQE130DHW	statement	none
Estimate for approximate solutions	0JTPMCCZT2	statement	none
Tychonoff's theorem	0JTRSJKCFB	statement	none
An orthonormal family is linearly independent	0JWM6GJNQW	statement	none
L'Hôpital's rule	0JWT4PPQ7B	statement	none
Divergence theorem	0JX86PSSA9	statement	none
Legendre's theorem on continued fractions	0JXTQ392ZM	statement	none
Lifting-the-exponent lemma	0JYF6PTKEW	statement	none
Power rule	0JZGW75C5Z	statement	none
Laplace transform of a derivative	0K090GVHVN	statement	none
Distance from a point to a plane	0K1E2S6Z69	statement	none
Lipschitz functions are uniformly continuous	0K1EWAR6AF	statement	none
Determinant of a triangular matrix	0K1KKMFHYH	statement	none
Integral of 1/x	0K1N1Y4EGZ	statement	none
Brahmagupta–Fibonacci identity	0K2DMACEZ4	statement	none
Logarithm of a product	0K2FNY6DYV	statement	none
Minkowski's theorem	0K387S2PKQ	statement	none
Factor theorem	0K3MWA7DMC	statement	none
Determinant of a matrix with two equal rows	0K4VQB7HWR	statement	none
Complement of an open set is closed	0K67Q60Z8P	statement	none
Isolated zeros theorem	0K83KEJ43P	statement	none
Compactness and sequential compactness agree in metric spaces	0K8SGQSV7G	statement	none
Continuous image of a compact set is compact	0K9AAJ8G51	statement	none
Inverse function theorem	0K9HSJFCMJ	statement	none
General Leibniz rule	0K9QCK6WJC	statement	none
Determinant via the Schur complement	0KA7A4ENVJ	statement	none
Sum of binomial coefficients	0KAMF19NV8	statement	none
Subgroups of cyclic groups are cyclic	0KB1ND7XDS	statement	none
Distributive law	0KBEMAJAYA	statement	none
Stirling's formula	0KC0F51T6A	statement	none
Bolzano–Weierstrass theorem	0KDJD249DT	statement	none
Classification of Pythagorean triples	0KF3J2KAER	statement	none
The alternating group is generated by three-cycles	0KFZ0QX83G	statement	none
A polynomial over a field has at most as many roots as its degree	0KJVQV3E0F	statement	none
One-sided limits of a monotone function exist	0KJXHN0TW0	statement	none
Hausdorff maximal principle	0KM4KVR9MV	statement	none
Determinant of a linear map is the determinant of its matrix	0KMN32XGPF	statement	none
Strong induction	0KMVFSHFGZ	statement	none
The exponential function is strictly increasing	0KN2V7840E	statement	none
Ceva's theorem	0KN93VDSXA	statement	none
Variance under scaling	0KVQ9D86BM	statement	none
Reduction modulo p test for irreducibility	0KWWEXW0RN	statement	none
Radius of convergence of the binomial series	0KX1MXJ5MR	statement	none
Continuous partial derivatives imply differentiability	0KXSK8TEEB	statement	none
Derivative of x^a	0KY08TWDMQ	statement	none
Lagrange's four-square theorem	0KYYSMEVHH	statement	none
Quadratic formula	0KYZXYDGQZ	statement	none
Derivative of an inverse function	0M0RZ3HSB0	statement	none
Linearity of differentiation	0M0TKFRX2A	statement	none
Intercept theorem	0M1GFS6PVA	statement	none
Bernoulli's inequality	0M1MX28VXK	statement	none
Fermat's little theorem	0M25PRN3WQ	statement	none
Curl of a gradient is zero	0M2JRW1J0N	statement	none
Cayley's formula	0M2SSGSYPE	statement	none
The number of Sylow subgroups divides the index	0M3PYJ3TSE	statement	none
Four colour theorem	0M406JC8J1	statement	none
Every linearly independent set extends to a basis	0M4SXE5WW3	statement	none
Classification of the Platonic solids	0M4TCS0RRG	statement	none
Existence of inverses modulo n	0M67FWZWPQ	statement	none
The only ideals of a field are zero and the whole field	0M6G75E95E	statement	none
Universal property of the product topology	0M6W4XNST6	statement	none
Euler's criterion	0M7DEDKSYB	statement	none
Vieta's formulas	0M8EWQJ1YV	statement	none
Approximation property of the supremum	0M8TGGP9JP	statement	none
Schwarz lemma	0MB48XDBY3	statement	none
Monotonicity of the integral	0MBWQKM8QR	statement	none
A finite abelian group is cyclic iff its exponent equals its order	0MC0AQZSHE	statement	none
Orthogonal projection is the closest point	0MCDDSCB9Z	statement	none
Epsilon characterisation of Cauchy sequences	0MCK8K2D7Z	statement	none
Division algorithm for polynomials	0MES3KS0ZC	statement	none
Derivative of a polynomial	0MH1WK89PP	statement	none
Wronskian test for linear independence of solutions	0MHE4B1QCQ	statement	none
Every sequence has a monotone subsequence	0MHGJRZMTM	statement	none
A ring homomorphism is injective iff its kernel is zero	0MMCB8RXGA	statement	none
Continuum hypothesis	0MN2MER9WN	statement	none
Derivative as a little-o approximation	0MN882VJ4P	statement	none
Diagonalisable iff the minimal polynomial has distinct roots	0MPAJRB23T	statement	none
Compact Hausdorff spaces are normal	0MQQQ5NA2S	statement	none
Change of basis formula	0MQXVZEBMT	statement	none
A quotient is abelian iff the subgroup contains the commutator subgroup	0MS8QGA6S5	statement	none
Test for exactness	0MSCQNFTM8	statement	none
First isomorphism theorem for linear maps	0MTBGVZ4XJ	statement	none
Exponentials dominate powers in sequences	0MVTCFW42K	statement	none
A series of nonnegative terms converges iff its partial sums are bounded	0MX1HZBBXJ	statement	none
Mantel's theorem	0MXEHSCYCS	statement	none
Open connected subsets of R^n are path-connected	0MXN7AFBPE	statement	none
Compact subsets of a Hausdorff space are closed	0MYFJVMN7M	statement	none
Well-ordering theorem	0N109NG5ZX	statement	none
Irrationality of square roots of non-squares	0N10YRNNWV	statement	none
Completeness via Cauchy sequences	0N1ZWFJDN5	statement	none
The rationals form a field	0N2WPCC00T	statement	none
Limits preserve non-strict inequalities	0N32V0E3XJ	statement	none
Liouville's theorem on Diophantine approximation	0N3WFZEFPM	statement	none
Classification of conics by the discriminant	0N5NR32NQG	statement	none
Degree of a simple extension is the degree of the minimal polynomial	0N5QW9K7MH	statement	none
Mean value theorem for integrals	0N91N98EG5	statement	none
Ore's theorem	0NACHJYPKW	statement	none
Apollonius's theorem	0NAKHQ9XYY	statement	none
The integral of a continuous function is an antiderivative	0NC2A3HWGT	statement	none
Implicit function theorem for a surjective derivative	0NE2W2XPQJ	statement	none
Double negation law	0NFAGWH84K	statement	none
The minimal polynomial is irreducible	0NFEG48RDR	statement	none
Fundamental theorem of calculus	0NHGY0N0JB	statement	none
Bayes' theorem	0NM6E9VW04	statement	none
Variance as the mean of the square minus the square of the mean	0NMF95YK8W	statement	none
Epsilon-net characterisation of total boundedness	0NMGJJ19HD	statement	none
Trace is the sum of the eigenvalues	0NMXDCNNKR	statement	none
Closed formula for Catalan numbers	0NNDQVJ54Q	statement	none
Schwarz's theorem for C^2 functions	0NNQY8WCW6	statement	none
Triangle inequality for integrals	0NR82KMYKD	statement	none
Composition of continuous functions is continuous	0NRQPQX3VA	statement	none
Connected components are closed	0NRT0E2QT2	statement	none
Characteristic function of the normal distribution	0NS0TDA4E2	statement	none
Derivative of a map into R^n by components	0NS0X75RS1	statement	none
Discrete Grönwall inequality	0NTM3J5MFE	statement	none
Exterior angle theorem	0NTSE7EREA	statement	none

Open conjectures and problems

No node in the graph resolves these conjectures and problems.

None.