| Proof that a matrix with two equal rows has determinant zero | Proof | Linear and multilinear algebra; matrix theory |
| Proof that a C^1 map with invertible derivative is a local homeomorphism and an open map | Proof | Real functions |
| Proof that almost sure convergence implies convergence in probability | Proof | Probability theory and stochastic processes |
| Proof that monotone functions are Riemann integrable | Proof | Real functions |
| Proof that the product of primitive polynomials is primitive | Proof | Commutative algebra |
| Proof of the closed formula for Catalan numbers by the reflection principle | Proof | Combinatorics |
| Proof of the canonical isomorphism with the double dual | Proof | Linear and multilinear algebra; matrix theory |
| Proof that maximal ideals are prime | Proof | Commutative algebra |
| Proof of Well-ordering theorem | Proof | Mathematical logic and foundations |
| Proof that a function is surjective iff it has a right inverse | Proof | Mathematical logic and foundations |
| Proof that finite subgroups of the multiplicative group of a field are cyclic | Proof | Field theory and polynomials |
| Proof of the double negation law by a truth table | Proof | Mathematical logic and foundations |
| Proof that the logarithm is the inverse of the exponential | Proof | Special functions |
| Proof that power series converge uniformly on smaller intervals inside the radius of convergence | Proof | Functions of a complex variable |
| Proof of Liouville's formula | Proof | Ordinary differential equations |
| Proof of the extreme value theorem by the Bolzano–Weierstrass theorem | Proof | Real functions |
| Proof of the first isomorphism theorem for rings | Proof | Associative rings and algebras |
| Proof of the spectral theorem for self-adjoint operators by induction on the dimension | Proof | Operator theory |
| Proof that compact subsets of a metric space are bounded | Proof | General topology |
| Proof of the derivative of the logarithm by the inverse function rule | Proof | Special functions |
| Proof of differentiation under the integral sign | Proof | Real functions |
| Proof of the product of the gcd and the lcm | Proof | Number theory |
| Proof that the order of the group of units of Z/nZ is Euler's totient | Proof | Number theory |
| Proof of the law of quadratic reciprocity by counting lattice points | Proof | Number theory |
| Proof of the uniqueness of finite fields of a given order | Proof | Field theory and polynomials |
| Proof of the formula for the transpose of a product | Proof | Linear and multilinear algebra; matrix theory |
| Proof that subgroups of cyclic groups are cyclic | Proof | Group theory and generalizations |
| Proof of the Laplace expansion along a row by the Leibniz formula | Proof | Linear and multilinear algebra; matrix theory |
| Proof that holomorphic functions with nonzero derivative are conformal | Proof | Functions of a complex variable |
| Proof that the product of countable sets is countable | Proof | Mathematical logic and foundations |
| Proof of the discrete Grönwall inequality | Proof | Real functions |
| Proof of Eisenstein's criterion | Proof | Field theory and polynomials |
| Proof that the subgroups of a finite cyclic group correspond to the divisors of its order | Proof | Group theory and generalizations |
| Proof of the product formula for the moment-generating function of a sum of independent random variables | Proof | Probability theory and stochastic processes |
| Proof that compactness and sequential compactness agree in metric spaces | Proof | General topology |
| Proof of the Tietze extension theorem by successive approximation | Proof | General topology |
| Proof that every connected graph has a spanning tree, by a maximal acyclic edge set | Proof | Combinatorics |
| Proof of the Schröder–Bernstein theorem | Proof | Mathematical logic and foundations |
| Proof that a ring homomorphism is injective iff its kernel is zero | Proof | Associative rings and algebras |
| Proof of the coefficient formula for a product of power series | Proof | Commutative algebra |
| Proof of Hoeffding's inequality via Hoeffding's lemma and the Chernoff bound | Proof | Probability theory and stochastic processes |
| Proof of the number of subsets of a finite set by indicator functions | Proof | Combinatorics |
| Proof of the Cauchy condensation test | Proof | Sequences, series, summability |
| Proof that the kernel is a normal subgroup | Proof | Group theory and generalizations |
| Proof that the reals have the cardinality of the continuum | Proof | Mathematical logic and foundations |
| Proof of the Cartan–Dieudonné theorem by induction on the dimension | Proof | Geometry |
| Proof that the exponential function is positive | Proof | Special functions |
| Proof of Apollonius's theorem from the parallelogram law | Proof | Geometry |
| Proof of the path independence of line integrals | Proof | Real functions |
| Proof of the Fibonacci recurrence from the definition | Proof | Number theory |
| Proof that a finite integral domain is a field | Proof | Commutative algebra |
| Proof that C^1 vector fields satisfy the Picard–Lindelöf hypotheses | Proof | Ordinary differential equations |
| Proof of the geometric formula for the dot product | Proof | Geometry |
| Proof of Jordan's lemma by Jordan's inequality | Proof | Functions of a complex variable |
| Proof that the real numbers are uncountable by nested intervals | Proof | Mathematical logic and foundations |
| Proof of the Weierstrass approximation theorem | Proof | Approximations and expansions |
| Proof of the alternating series test | Proof | Sequences, series, summability |
| Proof that subsequences of a convergent sequence converge to the same limit | Proof | Sequences, series, summability |
| Proof of the uniqueness of limits | Proof | Sequences, series, summability |
| Proof of Hilbert's basis theorem by leading coefficients | Proof | Commutative algebra |
| Proof that the Gaussian integers form a Euclidean domain | Proof | Number theory |
| Proof that uniform limits commute with integration | Proof | Sequences, series, summability |
| Proof of the rule of product | Proof | Combinatorics |
| Proof that the order of an element divides the order of the group | Proof | Group theory and generalizations |
| Proof of Stokes' theorem by pulling back to Green's theorem | Proof | Real functions |
| Proof of the logarithm of a quotient | Proof | Special functions |
| Proof that every positive integer is a square times a square-free integer | Proof | Number theory |
| Proof that the minimal polynomial divides every annihilating polynomial | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the residue formula at a simple pole | Proof | Functions of a complex variable |
| Proof of Euler's four-square identity by expansion | Proof | Number theory |
| Proof that holomorphic functions are infinitely differentiable | Proof | Functions of a complex variable |
| Proof that the integers are countable | Proof | Mathematical logic and foundations |
| Proof that Lipschitz functions are uniformly continuous | Proof | Real functions |
| Proof of the classification of subgroups of the integers | Proof | Group theory and generalizations |
| Proof of the integral equation form of an initial value problem | Proof | Ordinary differential equations |
| Proof of the residue theorem by subtracting principal parts | Proof | Functions of a complex variable |
| Proof that Fermat numbers are pairwise coprime | Proof | Number theory |
| Proof that the integral of a continuous function is an antiderivative | Proof | Real functions |
| Proof that subgroups of solvable groups are solvable | Proof | Group theory and generalizations |
| Proof of the degree of a product over an integral domain | Proof | Commutative algebra |
| Proof of the Gershgorin circle theorem by a largest coordinate | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the coordinate map is a linear isomorphism | Proof | Linear and multilinear algebra; matrix theory |
| Proof of strong induction from ordinary induction | Proof | Mathematical logic and foundations |
| Proof that linear maps on finite-dimensional normed spaces are continuous | Proof | Operator theory |
| Proof that there are exactly n nth roots of unity | Proof | Number theory |
| Proof of the open mapping theorem by the maximum modulus principle | Proof | Functions of a complex variable |
| Proof of the number of compositions by partial sums | Proof | Combinatorics |
| Proof of Taylor's theorem with the Cauchy remainder by the mean value theorem | Proof | Approximations and expansions |
| Proof that a subgroup whose index is the smallest prime divisor of the order is normal | Proof | Group theory and generalizations |
| Proof that power series are differentiable inside the radius of convergence | Proof | Functions of a complex variable |
| Proof that the determinant of a transpose equals the determinant | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the laws of exponents in a group | Proof | Group theory and generalizations |
| Proof of induction from an arbitrary base case | Proof | Mathematical logic and foundations |
| Proof that every finite tree with at least two vertices has a leaf, by a longest path | Proof | Combinatorics |
| Proof of the universal property of the quotient topology | Proof | General topology |
| Proof of the limit of a product of sequences | Proof | Sequences, series, summability |
| Proof of Cauchy's integral formula by a primitive of the difference quotient | Proof | Functions of a complex variable |
| Proof that the alternating group is generated by three-cycles | Proof | Group theory and generalizations |
| Proof of the inverse in terms of the adjugate | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the eigenvalue criteria for stability of linear systems via the Jordan normal form | Proof | Ordinary differential equations |
| Proof of the density of the rationals | Proof | Real functions |
| Proof of Cavalieri's principle for Jordan measurable solids | Proof | Measure and integration |
| Proof of the number of functions between finite sets | Proof | Combinatorics |
| Proof of the Hausdorff maximal principle from Zorn's lemma | Proof | Mathematical logic and foundations |
| Proof of the de Moivre–Laplace theorem from the central limit theorem | Proof | Probability theory and stochastic processes |
| Proof that the p-adic valuation of a product is the sum of the valuations | Proof | Number theory |
| Proof of the fundamental theorem of arithmetic | Proof | Number theory |
| Proof that uniform convergence of derivatives allows term-by-term differentiation | Proof | Sequences, series, summability |
| Proof of the linearity of the derivative | Proof | Real functions |
| Proof that Dyck words are counted by Catalan numbers, by first return decomposition | Proof | Combinatorics |
| Proof of the universal property of the quotient group | Proof | Group theory and generalizations |
| Proof that a homomorphism is injective iff its kernel is trivial | Proof | Group theory and generalizations |
| Proof that the trace is a coefficient of the characteristic polynomial by the Leibniz formula | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the complex exponential is 2πi-periodic | Proof | Special functions |
| Proof of the third Sylow theorem | Proof | Group theory and generalizations |
| Proof of Riemann's theorem on removable singularities | Proof | Functions of a complex variable |
| Proof of Chebyshev's inequality | Proof | Probability theory and stochastic processes |
| Proof of the uniqueness of the derivative | Proof | Real functions |
| Proof of the parametric formula for line integrals | Proof | Real functions |
| Proof that stabilisers of points in the same orbit are conjugate | Proof | Group theory and generalizations |
| Proof of the correspondence theorem for rings | Proof | Associative rings and algebras |
| Proof of Euler's theorem by rearrangement | Proof | Number theory |
| Proof that the matrix of the adjoint is the conjugate transpose | Proof | Linear and multilinear algebra; matrix theory |
| Proof of Tarski's theorem about choice | Proof | |
| Proof of Cauchy's estimates | Proof | Functions of a complex variable |
| Proof of the Chernoff bound | Proof | Probability theory and stochastic processes |
| Proof that a metric space is complete if and only if each Cauchy sequence has a convergent subsequence | Proof | General topology |
| Proof of the derivative of arctangent | Proof | Special functions |
| Proof that a subgroup is normal iff its left and right cosets agree | Proof | Group theory and generalizations |
| Proof of the negation of a universal statement | Proof | Mathematical logic and foundations |
| Proof that the degree of a constructible number is a power of two | Proof | Field theory and polynomials |
| Proof of Cauchy's theorem by McKay's counting argument | Proof | Group theory and generalizations |
| Proof of the formula for the variance of the normal distribution | Proof | Probability theory and stochastic processes |
| Proof of the complement principle | Proof | Combinatorics |
| Proof that −1 is a square modulo p if and only if p is not 3 modulo 4 | Proof | Number theory |
| Proof that eigenvectors with distinct eigenvalues are linearly independent by induction | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the pigeonhole principle | Proof | Combinatorics |
| Proof that the absolute value is multiplicative | Proof | Real functions |
| Proof of the power series of cosine | Proof | Special functions |
| Proof of the squeeze theorem for sequences | Proof | Sequences, series, summability |
| Proof of the number of injections | Proof | Combinatorics |
| Proof of Grushko decomposition theorem | Proof | |
| Proof that a matrix is diagonalisable iff its minimal polynomial has distinct roots | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the order of the general linear group over a finite field by counting columns | Proof | Group theory and generalizations |
| Proof of the derivative of a continuous linear map | Proof | Real functions |
| Proof of the Cauchy–Riemann equations | Proof | Functions of a complex variable |
| Proof that compact Hausdorff spaces are normal | Proof | General topology |
| Proof of the existence of square roots of nonnegative reals | Proof | Real functions |
| Proof that the integers modulo a prime form a field | Proof | Number theory |
| Proof that if 2^n − 1 is prime then n is prime | Proof | Number theory |
Math 2.0