Math 2.0

Frontier, page 7

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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 901–1050 in each list.

Statements with no proof

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

NameTagKindEvidence
Existence of finite fields of every prime power order0T8M3YC5RGstatementnone
Axiom of extensionality0TB16T2C97statementnone
The successor function is injective0TBYMWPWWBstatementnone
Dirac's theorem on Hamiltonian cycles0TC99BRSSBstatementnone
C^k function characterised by continuous derivatives0TCBZMEYGNstatementnone
Product of the gcd and the lcm0TDY6JZHKSstatementnone
Remainder theorem0TEDQH56RWstatementnone
Reduction of a higher-order equation to a first-order system0TH9CPW3VSstatementnone
Third isomorphism theorem0TJ1V9DDPCstatementnone
Term-by-term differentiation0TJ8QBJX5Kstatementnone
Bounded derivative on a convex set implies Lipschitz0TKG7T3K0Estatementnone
An algebraic extension of an algebraic extension is algebraic0TPWS0K1BCstatementnone
Product of a subgroup and a normal subgroup is a subgroup0TXWV1JGG1statementnone
Characteristic polynomial does not depend on the basis0TYMASG33Ystatementnone
Surjective iff it has a right inverse0TYQNHVB4Cstatementnone
Row rank equals column rank0TZAG60ZYTstatementnone
Variance of a sum of independent random variables0V0778DCW9statementnone
Sign of a cycle0V0E04DWX2statementnone
Frobenius coin problem0V11FEXK08statementnone
Derivative of cosine0V2DV29EGTstatementnone
Intersection of subspaces0V33SPH7RRstatementnone
Continuous real function on a compact set attains its bounds0V4DET59NWstatementnone
Fibonacci numbers as sums of binomial coefficients0V4VB6MQDCstatementnone
Logarithm of a power0V948DE5KAstatementnone
First Sylow theorem0V98WY94B8statementnone
Product rule0V9A43H7WVstatementnone
Dirichlet's test0V9ME8GQE7statementnone
Multiplicativity of the Möbius function0VB9G5B034statementnone
Kummer's theorem0VBWK9XYDGstatementnone
Euler's theorem0VC4DVE7DQstatementnone
Morera's theorem0VDD7W0EKZstatementnone
Volume of a box0VEKNG02W0statementnone
Every polynomial has a root in some extension field0VG02M1FEZstatementnone
Product of continuous functions is continuous0VGMHCF4SCstatementnone
Continuity is equivalent to sequential continuity in metric spaces0VGPKZ8MRKstatementnone
Abel's identity0VGWKX2JHBstatementnone
Subsequences of a convergent sequence converge to the same limit0VHAVXW08Vstatementnone
Finite-dimensional spaces are isomorphic iff they have equal dimension0VJBSK15SNstatementnone
De Morgan's laws for sets0VK0W4D5Y5statementnone
Size of a conjugacy class is the index of the centraliser0VK5V9P8G3statementnone
Banach fixed point theorem0VK6VEH345statementnone
Lagrange multipliers0VKKP8X6Q6statementnone
Cartan–Dieudonné theorem0VMWGYY35Qstatementnone
If 2^n + 1 is prime then n is a power of 20VN4H8M12Xstatementnone
Polynomials of degree two or three are irreducible iff they have no roots0VNE161QCKstatementnone
Pythagorean theorem0VP3A1290Kstatementnone
Rule of product0VPK4X73Q0statementnone
A tree on n vertices has n − 1 edges0VSNHTHK8Tstatementnone
Minimal polynomial divides every annihilating polynomial0VTAD25A3Gstatementnone
Order of a power0VVPQNVM8Sstatementnone
Term test0VVY4H92G2statementnone
Euler line0VX0CPRQTZstatementnone
Gradient is orthogonal to level sets0VXYV3NQQ1statementnone
Bézout's identity in a Euclidean domain0VY3WPP9Y3statementnone
Compact closed unit ball implies finite dimension0VZVV8VME5statementnone
Continuous functions on a closed bounded interval are uniformly continuous0W0TZDRF9Cstatementnone
Euler's formula for planar graphs0W1C598HMSstatementnone
Line integral as an integral over the parameter interval0W3W1VYWBPstatementnone
Complete subspaces are closed0W41XG4W60statementnone
Rank–nullity theorem0W4FSW1TVBstatementnone
Irrationality of e0W4GQSG7B6statementnone
Law of total probability for an event and its complement0W62TKMW7Vstatementnone
Epsilon-delta definition of continuity0W8YHHGCJGstatementnone
Chinese remainder theorem for rings0W97J8QED7statementnone
Time translation of solutions of an autonomous system0WA7ZR95V4statementnone
Trace of a linear map is the trace of its matrix0WCPH5Z7FAstatementnone
R/M is a field iff M is maximal0WD3SE7S1Xstatementnone
Euclid–Euler theorem0WETJCKNRGstatementnone
Sylvester's law of inertia0WFED3K3DQstatementnone
Newton's identities0WG2A3HE0Sstatementnone
A subspace of full dimension is the whole space0WGAXEK99Estatementnone
There is a natural number n with 1/n below any positive epsilon0WH916TJNYstatementnone
Taylor's theorem with the integral remainder0WJGR81HBDstatementnone
Dimension theorem for vector spaces0WK0Y8RH1Mstatementnone
Sylvester's criterion0WKEF78PMVstatementnone
Cholesky decomposition0WKG8CYY6Astatementnone
Product of exponentials0WM7DJCM6Gstatementnone
Volume of a ball in R^30WMDV48VSNstatementnone
A prime is a Gaussian prime if and only if it is 3 modulo 40WMJSEFYFEstatementnone
Hoeffding's inequality0WPDNXGSSNstatementnone
Moment-generating function of a sum of independent random variables0WRZ170YEHstatementnone
Extreme value theorem0WS1A8E2P9statementnone
Cantor's theorem0WTEMGYV2Cstatementnone
Gram–Schmidt vectors are orthogonal0WXBGBTA3Dstatementnone
A monotone function has countably many discontinuities0WYTM4C9QGstatementnone
Number of injections0X0N833FF8statementnone
Hall's theorem for bipartite graphs0X2GJPNPFNstatementnone
Countable intersection of dense open sets is dense0X2T63GFQQstatementnone
The exterior derivative squares to zero0X308R2DBEstatementnone
Tietze extension theorem0X52TNMTCJstatementnone
Impossibility of squaring the circle0X7CVDE3BGstatementnone
Continuity of probability measures0X8HBKCSYBstatementnone
Uniform limit theorem0X9XT05JVCstatementnone
Handshaking lemma0XAP8WHNESstatementnone
Wallis product0XCYA4YERSstatementnone
Number of elements of each order in a cyclic group0XCYGCCX8Vstatementnone
Monotonicity of the cumulative distribution function0XD22PBMWAstatementnone
Multinomial theorem0XFC1VQYEKstatementnone
Euler's partition theorem0XFZ1BMF5Qstatementnone
Decomposition of a permutation into transpositions0XK6FECMW5statementnone
Poisson limit theorem0XKTZRWTXXstatementnone
Squeeze theorem0XMF00T4XQstatementnone
Dini's theorem0XRRYF1HPEstatementnone
Eisenstein's lemma0XSDBCP4RZstatementnone
The principal logarithm is holomorphic off the branch cut0XVGJE7Q04statementnone
A root of an integer is an integer or irrational0XWCKJZRYHstatementnone
Second fundamental theorem of calculus0XYAFCN0PTstatementnone
De Morgan's laws in a Boolean algebra0XYVDWGQX2statementnone
Absolutely convergent series converge0Y123X48GAstatementnone
Catalan recurrence0Y1MG9R5VNstatementnone
Gauss–Wantzel theorem0Y34JMJNE9statementnone
The order modulo p divides p − 10Y4B7P0GS8statementnone
Trace of a product is symmetric0Y4NF1DRKDstatementnone
Brooks' theorem0Y4TV2D5RQstatementnone
Fermat's Last Theorem0Y5X3SDBCZstatementnone
Tail sum formula for expectation0Y6QNF1J49statementnone
Existence of an orthonormal basis0Y85GYEGSFstatementnone
Distinct eigenvalues imply diagonalisable0Y95Z7MT02statementnone
Binary trees are counted by Catalan numbers0Y97E2DMB7statementnone
Comparability of cardinals0YBHSJMN3Jstatementnone
Identity theorem0YBVKMYX0Wstatementnone
Term-by-term integration0YBY3VYX0Kstatementnone
Matrix exponential as the solution of a linear system0YC8JT513Jstatementnone
Universal property of the tensor product0YDRV01R8Fstatementnone
Continuity via open sets0YF82GBTNDstatementnone
Sum of independent Poisson random variables0YH1M56SBNstatementnone
Irrationality of the square root of a prime0YHFMXJJAZstatementnone
Hilbert's basis theorem0YKA9J3XEEstatementnone
Existence of nth roots of complex numbers0YM6P6C206statementnone
Power series are holomorphic in the disc of convergence0YMP521ZR5statementnone
Fundamental theorem of contour integration0YQ458D7PFstatementnone
Intersecting chords theorem0YQQYET8YQstatementnone
Pascal's rule0YRG241HQQstatementnone
Closed balls are closed0YS40B38JDstatementnone
Homotopy invariance of line integrals of closed forms0YVVN6R715statementnone
Decomposition of a permutation into disjoint cycles0YWDAZPRPQstatementnone
Quadratic reciprocity for the Jacobi symbol0YY06KP3ZQstatementnone
Mercator series0YZXNE3HFRstatementnone
Power series of complex cosine0Z1G2F8DGYstatementnone
Diagonalisation of a quadratic form0Z3FEWZ8HAstatementnone
Decomposition into generalised eigenspaces0Z3GDY89T5statementnone
A function with nonnegative second derivative is convex0Z41C17TGPstatementnone
Burnside's lemma0Z47M1B2VSstatementnone
Determinant of the identity matrix0Z4BWARC38statementnone
Local homeomorphism from the inverse function theorem0Z8CSYVHDJstatementnone
Countable union of countable sets is countable0Z8FM54P86statementnone
Constant multiple rule0Z9JB71BS0statementnone
Dimension of the space of linear maps0Z9N1ER0W0statementnone
Cauchy criterion for sequences0ZA4AX4MW3statementnone
A complex number times its conjugate0ZB7J071WQstatementnone

Open conjectures and problems

No node in the graph resolves these conjectures and problems.

None.