Math 2.0

Frontier, page 4

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 451–600 in each list.

Statements with no proof

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

NameTagKindEvidence
Polynomial ring over a UFD is a UFD0D6KH8Y59Nstatementnone
Zero is not a successor0D752BG155statementnone
The exponential function is convex0D7GRZ2ADXstatementnone
Variance of a sum0D86GJEZ39statementnone
Limits are unique in Hausdorff spaces0D8T984XEEstatementnone
Mean of the geometric distribution0DB0R4N5XXstatementnone
Matrix of the adjoint is the conjugate transpose0DBTE6HVBDstatementnone
Strong law of large numbers0DFWHQ839Tstatementnone
Finite extensions are algebraic0DFYTNZ6AMstatementnone
Commutativity of addition0DFZNHJ0S2statementnone
Cauchy's integral formula0DG10TVYPNstatementnone
Spectral theorem for Hermitian matrices0DGZBQWZWNstatementnone
Order of a permutation is the lcm of its cycle lengths0DH7HMXP9Fstatementnone
Estimation lemma0DJMGPN8K9statementnone
Cosets have the same cardinality as the subgroup0DKMBWTD7Pstatementnone
Basel problem0DMY75D6FVstatementnone
K[x] is a Euclidean domain0DQG39K2NHstatementnone
Universal property of the polynomial ring0DQMDSVSXJstatementnone
Bézout's identity0DQVHMYAGAstatementnone
Inequality of arithmetic and geometric means0DRF0F3XC9statementnone
The rationals are countable0DS9KWFDK2statementnone
Stone's representation theorem for finite Boolean algebras0DYS9C3HH5statementnone
Irrationality of the square root of 20DZGSDHD92statementnone
Number of nth roots of unity0E021GF2B8statementnone
Jordan–Hölder theorem0E088ZP533statementnone
Primitive root theorem0E0DNQK22Pstatementnone
Orbit-stabiliser theorem0E2HSCKZ6Cstatementnone
Dimension of the orthogonal complement0E2NYPVSP9statementnone
Law of total probability0E5G5FMT2Rstatementnone
Convergents converge to the number0E70M92FE3statementnone
Fermat's Last Theorem for n = 40E741HSMJ1statementnone
Riemann rearrangement theorem0E7VBYGFF7statementnone
Exponential of a sum0E8HNVBCSPstatementnone
Harmonic series diverges0E9M24KS9Jstatementnone
Chain rule in several variables0EAAS2EHDRstatementnone
A composite number has a prime factor at most its square root0EB6BBMQMCstatementnone
A finite integral domain is a field0EBE031B8Estatementnone
The multiplicative group of a finite field is cyclic0EBZ3G455Gstatementnone
Existence of the infimum0EDH403M21statementnone
Neyman–Pearson lemma0EE19CFEEFstatementnone
Rule of sum0EE2V3CHFKstatementnone
Boole's inequality0EGSEE9J9Rstatementnone
Prime number theorem0EHBY5Y84Nstatementnone
Liouville's theorem0EHKVRF4J6statementnone
Binomial theorem0EHWPWGHB2statementnone
Universal property of the abelianisation0EJ4PC8NJ6statementnone
Epsilon-delta continuity in metric spaces0EKGKY5TGHstatementnone
Existence of nontrivial solutions of Pell's equation0EM6C9SZN5statementnone
Inverse in terms of the adjugate0ENVM493VKstatementnone
Continuous image of a connected set is connected0EPD87YVG8statementnone
Convergence in probability implies convergence in distribution0EPTDZPJ83statementnone
Central limit theorem0EPZC4Z1FCstatementnone
QR decomposition0ERWG4NXQ9statementnone
Divisibility by 90ESHD7ZQDXstatementnone
Existence of an algebraic closure0ETGBAK2CCstatementnone
Gershgorin circle theorem0ETGP0XVCJstatementnone
Poincaré–Bendixson theorem0EW1X61ZT1statementnone
Impossibility of trisecting the angle0EWXPZCSZ0statementnone
The exponential function is its own derivative0EX9GFJ0B3statementnone
Cantor's intersection theorem0EZBG8SKJMstatementnone
Cauchy's integral formula for derivatives0F0H5P5DEDstatementnone
Prime elements are irreducible in an integral domain0F0K8DB9TDstatementnone
Superposition principle0F2VBPXNP9statementnone
Bounded linear maps are continuous0F3K4C7XYWstatementnone
Derivative vanishes at a local extremum0F405477F8statementnone
Divergence of a curl is zero0F56CMMC5Pstatementnone
g to the n equals 1 iff the order divides n0F5QC101Q7statementnone
Cayley–Hamilton theorem0F765KFC2Jstatementnone
Closed subsets of complete spaces are complete0FBXJZX3MKstatementnone
The gamma function extends the factorial0FDCW77H44statementnone
A subgroup whose index is the smallest prime divisor of the order is normal0FEBE9NC0Estatementnone
e as the limit of (1 + 1/n)^n0FEMF8JKAFstatementnone
Universal property of the quotient topology0FF2FJ8CH2statementnone
Inclusion–exclusion principle0FF7726C7Pstatementnone
The reals form a field0FGENPMPJXstatementnone
Characterization of bridges0FHM8DB6PMstatementnone
Epsilon-delta uniform continuity0FHSDCQACYstatementnone
Chromatic number of a complete bipartite graph0FJBBCXYPSstatementnone
Bertrand's postulate0FJTGZA4GSstatementnone
Triangle inequality for norms0FJZMBX0ZZstatementnone
Simultaneous diagonalisation0FK17N4DKAstatementnone
Monotone convergence theorem for sequences0FM6N4R0VBstatementnone
Burnside's p^a q^b theorem0FMAQSB1SCstatementnone
Chinese remainder theorem0FNN9B4W64statementnone
Lévy's continuity theorem0FPWF7TTMBstatementnone
Inverse of a complex number0FQRAV5SKHstatementnone
Comparison test for improper integrals0FR1BDKK10statementnone
Heron's formula0FRBZ2X4HJstatementnone
The complex numbers form a field0FRSR10DWFstatementnone
Trace is a coefficient of the characteristic polynomial0FRYPZ6D0Xstatementnone
Infinite pigeonhole principle0FS3RHF6KEstatementnone
Determinant of a matrix with a zero row0FS6B46E5Tstatementnone
Bertrand's ballot theorem0FS972T0ZHstatementnone
Reversing a path changes the sign of a line integral0FSCXYG856statementnone
Multiplicativity of the totient function0FSJA9M43Wstatementnone
Second derivative test0FZFHK97P7statementnone
Transcendence of pi0G0F7FGCGPstatementnone
Sylvester's determinant theorem0G24VQ1088statementnone
The complex exponential is entire0G2YJN0H5Sstatementnone
Continuous dependence on initial data0G3DBXRRQJstatementnone
Automorphism group of a cyclic group0G4C8SJ6PVstatementnone
Derivative of the inverse function0G65751VSWstatementnone
Cauchy sequences are bounded0G6D8E7CTAstatementnone
Uniqueness of the complete ordered field0G8G1TH5WKstatementnone
Inscribed angle theorem0GA1V8NN8Cstatementnone
Derivative of arcsine0GA6G43EA9statementnone
Epsilon-delta definition of a limit0GBZDAFPX8statementnone
Induction from an arbitrary base case0GF6AJEBZ0statementnone
General solution of an inhomogeneous linear equation0GHWEH6H15statementnone
Universal property of the quotient group0GJ83E78A5statementnone
Cancellation in an integral domain0GJM24EXP9statementnone
Trace is linear0GJWQZCPZMstatementnone
Addition formulas for hyperbolic functions0GJZCE87WPstatementnone
Solution space of a homogeneous linear equation has dimension n0GK68PZ6KHstatementnone
Absolute value is multiplicative0GMV7GP8W0statementnone
Nilpotent groups are solvable0GNG2KVPZJstatementnone
Dirichlet's theorem on arithmetic progressions0GNVN3CA2Pstatementnone
Cardinality of the power set0GPFKS96T7statementnone
The medians meet at the centroid0GPQ67XV7Nstatementnone
Quotient of continuous functions is continuous0GR2APWTACstatementnone
Angles in the same segment are equal0GS0AW6JRYstatementnone
Thales's theorem0GSDHYMA1Tstatementnone
Cavalieri's principle0GTZ2F3PQYstatementnone
Bijection principle0GV2573FP4statementnone
Fundamental theorem of symmetric polynomials0GW1ZZH0R4statementnone
Integral of sine0GXCXCX3QNstatementnone
Units of Z/nZ are the residues coprime to n0GXNHEHQNAstatementnone
Second derivative test in several variables0GYDV9FE98statementnone
Divergence theorem on a rectangle in the plane0GZ3D8F921statementnone
The order of a finite field is a prime power0H5WWC8RZXstatementnone
Taylor's theorem with the Lagrange remainder0H5ZAZCX2Tstatementnone
Changing the order of integration0H60H1Q0SXstatementnone
Product of power series0H6KWAYS87statementnone
Every finite tree with at least two vertices has a leaf0H8Q4MANBDstatementnone
Rule of Sarrus0H8SZFFDXJstatementnone
Interior is the largest open subset0HAZEFH137statementnone
Induction on the integers0HBS1F00DNstatementnone
Union of open sets is open0HEF46RPEKstatementnone
Russell's paradox0HESMMSYEGstatementnone
Pigeonhole principle0HGVCWQGY3statementnone
Solutions for distinct real roots0HJ0HDA6W7statementnone
Second isomorphism theorem for rings0HJ4DTW6FNstatementnone
A sequence converges iff its liminf and limsup agree0HM732ZNVCstatementnone
Eigenvectors with distinct eigenvalues are linearly independent0HNMFG8F8Kstatementnone
Generalised Stokes theorem0HPHKCGEQ0statementnone
Green's theorem0HR3N02317statementnone
Solutions for repeated roots0HRVY67CNVstatementnone
Axiom of choice0HTGB13FE2statementnone
Rouché–Capelli theorem0HV1SKWPMSstatementnone
Limit comparison test0HW7BNHHGFstatementnone

Open conjectures and problems

No node in the graph resolves these conjectures and problems.

None.