| Proof of the sum of independent Poisson random variables by the multinomial theorem | Proof | Probability theory and stochastic processes |
| Proof that a product of two finite cyclic groups is cyclic iff their orders are coprime | Proof | Group theory and generalizations |
| Proof of Pascal's rule from the recursive definition | Proof | Combinatorics |
| Proof of the chain rule for a composition with a curve | Proof | Real functions |
| Proof of the classification of complex quadratic forms by rescaling a diagonal form | Proof | Number theory |
| Proof that the Gram–Schmidt vectors are orthogonal | Proof | Linear and multilinear algebra; matrix theory |
| Proof that a composition of surjections is surjective | Proof | Mathematical logic and foundations |
| Proof of the second isomorphism theorem for vector spaces | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the continuous image of a connected set is connected | Proof | General topology |
| Proof that a differentiable function is convex iff its derivative is increasing | Proof | Real functions |
| Proof of the multiplicativity of the Legendre symbol from Euler's criterion | Proof | Number theory |
| Proof of the polarisation identity | Proof | Functional analysis |
| Proof that the solutions of Pell's equation are powers of the fundamental solution | Proof | Number theory |
| Proof of Selberg trace formula for compact hyperbolic surfaces | Proof | |
| Proof that the cumulative distribution function determines the distribution, by the π-λ theorem | Proof | Probability theory and stochastic processes |
| Proof that the harmonic series diverges by grouping terms | Proof | Sequences, series, summability |
| Proof of the law of total probability for an event and its complement | Proof | Probability theory and stochastic processes |
| Proof of the vector triple product formula by coordinates | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the principal logarithm is holomorphic off the branch cut | Proof | Special functions |
| Proof of Fermat's little theorem in the form a^p = a | Proof | Number theory |
| Proof that i squared is minus one | Proof | Field theory and polynomials |
| Proof of Fermat's Last Theorem for n = 4 | Proof | Number theory |
| Proof of the expectation of a product of independent random variables by simple functions | Proof | Probability theory and stochastic processes |
| Proof of the existence of nontrivial solutions of Pell's equation by Dirichlet approximation | Proof | Number theory |
| Proof of Euler's partition theorem by Glaisher's bijection | Proof | Combinatorics |
| Proof of the linearity of differentiation | Proof | Real functions |
| Proof that the logarithm grows slower than any power | Proof | Real functions |
| Proof of the angle addition formulas by differentiation | Proof | Special functions |
| Proof of the Euler product formula | Proof | Number theory |
| Proof that the interior is the largest open subset | Proof | General topology |
| Proof that the size of an orbit times the size of the stabiliser is the order of the group | Proof | Group theory and generalizations |
| Proof of the mean value theorem for integrals | Proof | Real functions |
| Proof of the Dirichlet convolution formula over ordered pairs | Proof | Number theory |
| Proof that R/M is a field iff M is maximal | Proof | Commutative algebra |
| Proof of Lyndon's interpolation theorem | Proof | |
| Proof that a prime is a Gaussian prime if and only if it is 3 modulo 4 | Proof | Number theory |
| Proof of Vandermonde's identity by induction | Proof | Combinatorics |
| Proof of von Dyck's theorem | Proof | Group theory and generalizations |
| Proof of Bessel's inequality | Proof | Functional analysis |
| Proof of the monotonicity of probability | Proof | Probability theory and stochastic processes |
| Proof that a continuous image of a compact set is compact | Proof | General topology |
| Proof of Dirichlet's test by summation by parts | Proof | Sequences, series, summability |
| Proof that the closure is the smallest closed superset | Proof | General topology |
| Proof that exp z = 1 iff z is an integer multiple of 2πi | Proof | Special functions |
| Proof of the absorption laws in a lattice | Proof | Order, lattices, ordered algebraic structures |
| Proof that moments are derivatives of the moment-generating function at zero | Proof | Probability theory and stochastic processes |
| Proof that a quotient of continuous functions is continuous | Proof | Real functions |
| Proof of Lyapunov's stability theorem | Proof | Ordinary differential equations |
| Proof of the cardinality of the power set by indicator functions | Proof | Mathematical logic and foundations |
| Proof of the Heine–Cantor theorem by a finite cover of balls | Proof | General topology |
| Proof of the decomposition into generalised eigenspaces | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the power series of the complex cosine | Proof | Special functions |
| Proof that holomorphic functions on a disc have primitives | Proof | Functions of a complex variable |
| Proof of Vieta's formulas | Proof | Field theory and polynomials |
| Proof of the general solution of an inhomogeneous linear equation | Proof | Ordinary differential equations |
| Proof of Bertrand's ballot theorem by reflection | Proof | Combinatorics |
| Proof of the universal property of the abelianisation | Proof | Group theory and generalizations |
| Proof that the orthogonal complement of the orthogonal complement is the subspace | Proof | Functional analysis |
| Proof that an injective endomorphism of a finite-dimensional space is surjective | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the Heine–Borel theorem in finite-dimensional normed spaces | Proof | Functional analysis |
| Proof that characteristic subgroups are normal | Proof | Group theory and generalizations |
| Proof of the recurrence for derangements by the image of the last point | Proof | Combinatorics |
| Proof that compact subsets of a Hausdorff space are closed | Proof | General topology |
| Proof of the angle bisector theorem and its converse with unit vectors | Proof | Geometry |
| Proof that the composition of continuous maps is continuous | Proof | General topology |
| Proof of the estimate for approximate solutions by a first-crossing argument | Proof | Ordinary differential equations |
| Proof that groups of prime order are cyclic | Proof | Group theory and generalizations |
| Proof that the characteristic of an integral domain is zero or prime | Proof | Commutative algebra |
| Proof of the Chinese remainder theorem for rings | Proof | Commutative algebra |
| Proof of epsilon-delta continuity at a point in metric spaces | Proof | General topology |
| Proof of the sum of independent normal random variables by characteristic functions | Proof | Probability theory and stochastic processes |
| Proof that a compact closed unit ball implies finite dimension | Proof | Functional analysis |
| Proof of the second derivative test | Proof | Real functions |
| Proof that the group of units of Z/pZ is cyclic by counting elements of each order | Proof | Number theory |
| Proof that the integers are a Euclidean domain | Proof | Number theory |
| Proof of Riemann's criterion for integrability | Proof | Real functions |
| Proof of the negation of an existential statement | Proof | Mathematical logic and foundations |
| Proof of the symmetry of binomial coefficients from the factorial formula | Proof | Combinatorics |
| Proof of Lagrange's four-square theorem by descent | Proof | Number theory |
| Proof of the angle sum of a triangle with sines and cosines | Proof | Geometry |
| Proof that congruence is compatible with addition | Proof | Number theory |
| Proof that groups of order p squared are abelian | Proof | Group theory and generalizations |
| Proof that the trace of a linear map does not depend on the basis | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the irreducibility of the cyclotomic polynomials by reduction modulo primes | Proof | Number theory |
| Proof of Class existence theorem | Proof | |
| Proof of the sequential characterization of limits | Proof | Real functions |
| Proof that the tensor products of basis vectors form a basis | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the Cauchy mean value theorem from Rolle's theorem | Proof | Real functions |
| Proof of Extension of Lagrange's theorem | Proof | Group theory and generalizations |
| Proof that the size of a conjugacy class is the index of the centraliser | Proof | Group theory and generalizations |
| Proof that the exponential function is strictly increasing | Proof | Special functions |
| Proof of the sum of binomial coefficients from the binomial theorem | Proof | Combinatorics |
| Proof of Taylor's theorem with the integral remainder by the fundamental theorem of calculus | Proof | Approximations and expansions |
| Proof of the power-reduction formulas | Proof | Special functions |
| Proof of the alternating sum of binomial coefficients from the binomial theorem | Proof | Combinatorics |
| Proof of the central limit theorem by characteristic functions | Proof | Probability theory and stochastic processes |
| Proof of Euler's criterion by counting quadratic residues | Proof | Number theory |
| Proof of the first isomorphism theorem for linear maps | Proof | Linear and multilinear algebra; matrix theory |
| Proof that Cauchy sequences are bounded | Proof | Sequences, series, summability |
| Proof of the first isomorphism theorem | Proof | Group theory and generalizations |
| Proof of Kőnig's theorem by alternating paths | Proof | Combinatorics |
| Proof of the formula for the variance as the mean of the square minus the square of the mean | Proof | Probability theory and stochastic processes |
| Proof of Hölder's inequality for sums | Proof | Real functions |
| Proof of the formula for the inverse of a product | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the only ideals of a field are zero and the whole field | Proof | Field theory and polynomials |
| Proof of the formula for the distance from a point to a line | Proof | Geometry |
| Proof of Darboux's theorem from the extreme value theorem | Proof | Real functions |
| Proof that a function with bounded derivative is Lipschitz | Proof | Real functions |
| Proof that C^1 functions are strictly differentiable | Proof | Real functions |
| Proof of Cauchy's integral formula for derivatives | Proof | Functions of a complex variable |
| Proof of the mean of the geometric distribution | Proof | Probability theory and stochastic processes |
| Proof of the description of the open sets of a metric space | Proof | General topology |
| Proof of the Ping-pong lemma for infinite cyclic subgroups | Proof | |
| Proof of the Banach fixed point theorem by iteration | Proof | Operator theory |
| Proof that an orthonormal family is linearly independent | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the tower law for indices | Proof | Group theory and generalizations |
| Proof of the derivative of arcsine by the inverse function rule | Proof | Special functions |
| Proof of the triangle inequality for real numbers | Proof | Real functions |
| Proof of the derivative of tangent by the quotient rule | Proof | Special functions |
| Proof that an intersection of subgroups is a subgroup | Proof | Group theory and generalizations |
| Proof of the epsilon-N definition of the limit of a sequence | Proof | Sequences, series, summability |
| Proof of quadratic reciprocity for the Jacobi symbol | Proof | Number theory |
| Proof that the convergents of an irrational number converge to it | Proof | Number theory |
| Proof of the quotient rule from the product and reciprocal rules | Proof | Real functions |
| Proof of the dimension of the annihilator by a dual basis | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the Pythagorean theorem and its converse with the dot product | Proof | Geometry |
| Proof of the Frattini argument | Proof | Group theory and generalizations |
| Proof that a zero derivative on a connected open set implies constant | Proof | Real functions |
| Proof of the existence of nth roots of complex numbers | Proof | Field theory and polynomials |
| Proof of the primitive element theorem | Proof | Field theory and polynomials |
| Proof of Rouché's theorem by the argument principle and continuity | Proof | Functions of a complex variable |
| Proof of the first fundamental theorem of calculus | Proof | Real functions |
| Proof of the intercept theorem with vectors | Proof | Geometry |
| Proof of the law of sines from the law of cosines | Proof | Geometry |
| Proof that the interior is open | Proof | General topology |
| Proof of Schwarz's theorem for C^2 functions by the mean value theorem | Proof | Real functions |
| Proof of the multiplicativity of the totient function | Proof | Number theory |
| Proof of the inclusion–exclusion principle by counting each element | Proof | Combinatorics |
| Proof of the simplicity of the alternating group by three-cycles | Proof | Group theory and generalizations |
| Proof of the power series of the complex logarithm | Proof | Functions of a complex variable |
| Proof that compactness of a subset can be tested with open sets of the ambient space | Proof | General topology |
| Proof that the modulus is multiplicative | Proof | Functions of a complex variable |
| Proof of the density of the irrationals | Proof | Real functions |
| Proof of Euler's theorem on Eulerian circuits by a longest trail | Proof | Combinatorics |
| Proof of the existence of prime factorization | Proof | Number theory |
| Proof of the formula for the dimension of the orthogonal complement | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the sign is a homomorphism | Proof | Group theory and generalizations |
| Proof of the comparison test | Proof | Sequences, series, summability |
| Proof that the trace of a product is symmetric | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the existence of an eigenvalue over an algebraically closed field | Proof | Linear and multilinear algebra; matrix theory |
Math 2.0