Abhyankar's conjecture | Archimedes' axiom | Baudet's conjecture | Bayes' theorem | bellows conjecture | Bertrand's postulate | Bieberbach conjecture | binomial theorem | Bolzano's theorem | Calabi conjecture | Cantor's theorem | casus irreducibilis | Catalan's conjecture | Cauchy-Frobenius lemma | Ceva's theorem | chain rule | Chinese remainder theorem | Condorcet jury theorem | de Morgan's laws | divergence theorem | ... (total: 63)

For a finite group G, let p(G) be the subgroup generated by all the Sylow p-subgroups of G. Then Abhyankar's conjecture posits that if X is a projective curve in characteristic p>0, and if x_0, x_1, ..., x_t are points of X (for t>0), then a necessary and sufficient condition that G occur as the Galois group of a finite covering Y of X, branched only at the points x_0, x_1, ..., x_t, is that the quotient group G/(p(G)) has 2g + t generators.

Archimedes' axiom states that given two magnitudes having a ratio, one can find a multiple of either which will exceed the other.

Baudet's conjecture posits that if C_1, C_2, ..., C_r are sets of positive integers and union _(i = 1)^rC_i = Z^+, then some C_i contains arbitrarily long arithmetic progressions.

Bayes' theorem states that P(A_i|A) = P(A_i)P(A|A_i)/( sum_(j=1)^NP(A_j)P(A|A_j)), where P(A_i) is the probability of an event A_i, P(A_i|A) is the conditional probability of A_i given that A has already occurred, the events are disjoint, and union _(i = 1)^NA_i = A.

The bellows conjecture posits that all flexible polyhedra keep a constant volume as they are flexed.

Bertrand's postulate posits that if n>3, then there is always at least one prime between n and 2n - 2.

The Bieberbach conjecture, now proved, posited that the nth coefficient in the power series of a univalent function is no greater than n.

The binomial theorem gives a formula for the algebraic expansion of powers of a binomial, namely (x + a)^ν = sum_(k=0)^∞(ν k)x^ka^(ν - k).

Bolzano's theorem states that if a continuous function defined on an interval is sometimes positive and sometimes negative, it must be zero at some point.

The Calabi conjecture states that a compact Kähler manifold has a unique Kähler metric in the same class whose Ricci form is any given 2-form representing the first Chern class. In particular, if the first Chern class vanishes, then there is a unique Kähler metric in the same class with vanishing Ricci curvature.

If (r, s) = 1, then every pair of residue classes modulo r and s corresponds to a simple residue class modulo rs.

The statements "it is not true that A or B is true" and "A is not true and B is not true" are equivalent. Similarly, the statements "it is not true that A and B are true" and "A is not true or B is not true" are equivalent.

Every polynomial P(z) of degree n has n values z_i (some of them possibly degenerate) for which P(z_i) = 0.

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

For each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.

The three-sphere is the only type of bounded three-dimensional space possible that contains no holes.

| formal statement Bertrand's postulate | for all _(n element Z, n>3)exists_(m element Z^+)n1 ∧ q>1 ∧ m>1 ∧ n>1 ∧ q^n!=8)p^m - q^n = 1 Euclid's second theorem | π(∞) = ∞ Euler's totient theorem | for all _({a, n}, (a, n) element (Z^+)^2 ∧ gcd(a, n) = 1)a^ϕ(n) mod n = 1 Fermat's last theorem | ¬exists_({a, b, c, n}, (a, b, c, n) element (Z^+)^4 ∧ n>2 ∧ abc!=0)a^n + b^n = c^n Fermat's little theorem | for all _({p, a}, p element P ∧ a element Z^+ ∧ a mod p!=0)(a^(p - 1) - 1) mod p = 0 Fermat's sandwich theorem | ¬exists_({m, n}, (m, n) element (Z^+)^2 ∧ m!=3 ∧ n!=5) left bracketing bar m^3 - n^2 right bracketing bar = 2 second fundamental theorem of calculus | for all _({a, b, c, f}, a5 ∧ n mod 2 = 1)exists_({i, j, k}, (i, j, k) element (Z^+)^3)n = p_i + p_j + p_k prime number theorem | lim_(n->∞)π(n)/(li(n)) = 1