| Proof that a one-sided inverse of a square matrix is two-sided | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the reduction modulo p test for irreducibility | Proof | Field theory and polynomials |
| Proof that the determinant of a matrix exponential is the exponential of the trace | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the gamma function extends the factorial | Proof | Special functions |
| Proof that homomorphisms preserve identity and inverses | Proof | Group theory and generalizations |
| Proof of Kolmogorov's zero–one law | Proof | Probability theory and stochastic processes |
| Proof of the monotonicity of the integral | Proof | Real functions |
| Proof of the comparison test for improper integrals | Proof | Sequences, series, summability |
| Proof of the first derivative test | Proof | Real functions |
| Proof that the eigenvalues are the roots of the characteristic polynomial | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the boundedness theorem by Bolzano–Weierstrass | Proof | Real functions |
| Proof that a finite intersection of open sets of a metric space is open | Proof | General topology |
| Proof that a matrix and its transpose have the same trace | Proof | Linear and multilinear algebra; matrix theory |
| Proof that every element of a finite field of order q satisfies x^q = x | Proof | Field theory and polynomials |
| Proof that the exterior derivative squares to zero | Proof | Global analysis, analysis on manifolds |
| Proof of Legendre's formula by counting multiples of prime powers | Proof | Number theory |
| Proof of Markov's inequality | Proof | Probability theory and stochastic processes |
| Proof of the irrationality of square roots of non-squares | Proof | Number theory |
| Proof that a set is compact iff it is complete and totally bounded | Proof | General topology |
| Proof of the factor theorem | Proof | Commutative algebra |
| Proof that the Dirichlet convolution of multiplicative functions is multiplicative | Proof | Number theory |
| Proof that Lipschitz maps are uniformly continuous | Proof | Real functions |
| Proof that the closure is closed | Proof | General topology |
| Proof of the Picard–Lindelöf theorem in integral form | Proof | Ordinary differential equations |
| Proof of the intersecting chords theorem by the power of a point | Proof | Geometry |
| Proof that distinct eigenvalues imply diagonalisable | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the ratio formula for the radius of convergence | Proof | Functions of a complex variable |
| Proof that cosets have the same cardinality as the subgroup | Proof | Group theory and generalizations |
| Proof of the p-series test by Cauchy condensation | Proof | Sequences, series, summability |
| Proof of Carathéodory's theorem by removing points | Proof | Convex and discrete geometry |
| Proof of the rule of Sarrus | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the weak law of large numbers by characteristic functions | Proof | Probability theory and stochastic processes |
| Proof of the degrees along an Eulerian trail | Proof | Combinatorics |
| Proof of the superposition principle | Proof | Ordinary differential equations |
| Proof of Euler's formula by power series | Proof | Special functions |
| Proof of the number of invertible residues modulo n | Proof | Number theory |
| Proof of the existence of a prime divisor | Proof | Number theory |
| Proof that C^k functions are characterised by continuous derivatives | Proof | Real functions |
| Proof of the Chapman–Kolmogorov equation | Proof | Probability theory and stochastic processes |
| Proof of the multinomial theorem by induction on the number of terms | Proof | Combinatorics |
| Proof of the Cauchy–Binet formula by multilinearity | Proof | Linear and multilinear algebra; matrix theory |
| Proof of Dirac's theorem on Hamiltonian cycles from Ore's theorem | Proof | Combinatorics |
| Proof of the Euler line theorem by vectors | Proof | Geometry |
| Proof that continuous partial derivatives imply differentiability | Proof | Real functions |
| Proof that an algebraic extension of an algebraic extension is algebraic | Proof | Field theory and polynomials |
| Proof of Cantor's theorem by the diagonal argument | Proof | Mathematical logic and foundations |
| Proof that binary trees are counted by Catalan numbers | Proof | Combinatorics |
| Proof of the product rule in several variables | Proof | Real functions |
| Proof of the Chevalley–Warning theorem | Proof | Number theory |
| Proof of the vector calculus identities | Proof | Real functions |
| Proof of the comparability of cardinals from Zorn's lemma | Proof | Mathematical logic and foundations |
| Proof of the divisibility rule for 3 | Proof | Number theory |
| Proof that a set is open if and only if its complement is closed | Proof | General topology |
| Proof that a product of compact sets is compact by the tube lemma | Proof | General topology |
| Proof that abelian simple groups have prime order | Proof | Group theory and generalizations |
| Proof of the rank–nullity theorem by extending a basis of the kernel | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the symmetric group on five or more letters is not solvable | Proof | Group theory and generalizations |
| Proof of the anticommutativity of the cross product | Proof | Linear and multilinear algebra; matrix theory |
| Proof that every real number has a decimal expansion, with digits from the floor | Proof | Number theory |
| Proof of Menelaus's theorem by a linear function | Proof | Geometry |
| Proof of the fundamental theorem of calculus | Proof | Real functions |
| Proof that the chromatic number of a complete bipartite graph is 2 | Proof | Combinatorics |
| Proof of the well-ordering theorem from Zorn's lemma | Proof | Mathematical logic and foundations |
| Proof that a series of nonnegative terms converges iff its partial sums are bounded | Proof | Sequences, series, summability |
| Proof of the Riemann rearrangement theorem by a greedy construction | Proof | Sequences, series, summability |
| Proof that the multiplicative group of a finite field is cyclic | Proof | Field theory and polynomials |
| Proof of the finite intersection property characterisation of compactness | Proof | General topology |
| Proof that the real part of a holomorphic function is harmonic | Proof | Potential theory |
| Proof of the subgroup criterion | Proof | Group theory and generalizations |
| Proof of the product formula for the characteristic function of a sum of independent random variables | Proof | Probability theory and stochastic processes |
| Proof of the Cayley–Hamilton theorem with the adjugate | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the correspondence theorem | Proof | Group theory and generalizations |
| Proof that rearrangements of an absolutely convergent series have the same sum | Proof | Sequences, series, summability |
| Proof of the universal property of the tensor product from its construction | Proof | Linear and multilinear algebra; matrix theory |
| Proof that finite-dimensional spaces are isomorphic iff they have equal dimension | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the mean value theorem in several variables | Proof | Real functions |
| Proof of the product formula for the order of HK by counting pairs | Proof | Group theory and generalizations |
| Proof of the Picard–Lindelöf theorem | Proof | Ordinary differential equations |
| Proof that a set is closed if and only if it equals its closure | Proof | General topology |
| Proof of the mean value theorem from Rolle's theorem | Proof | Real functions |
| Proof of cancellation in congruences | Proof | Number theory |
| Proof of the addition formulas for hyperbolic functions | Proof | Special functions |
| Proof of the logarithm of a product | Proof | Special functions |
| Proof of the Wallis product by integrals of powers of sine | Proof | Number theory |
| Proof that congruence is compatible with powers | Proof | Number theory |
| Proof of the integral of 1/x | Proof | Real functions |
| Proof that continuity is equivalent to sequential continuity in metric spaces | Proof | General topology |
| Proof that the Cauchy product of absolutely convergent series converges absolutely to the product | Proof | Sequences, series, summability |
| Proof that the curl of a gradient is zero | Proof | Real functions |
| Proof that pi is greater than 3 by the alternating series estimate | Proof | Number theory |
| Proof of the product formula for the generating function of a sum of independent random variables | Proof | Probability theory and stochastic processes |
| Proof that slopes of a convex function are increasing | Proof | Real functions |
| Proof that sums and products of continuous functions are continuous | Proof | Real functions |
| Proof of the classification of isometries of the plane | Proof | Geometry |
| Proof that the determinant of a linear map does not depend on the basis | Proof | Linear and multilinear algebra; matrix theory |
| Proof of Lucas's theorem by generating functions | Proof | Number theory |
| Proof that every vector space has a basis, by Zorn's lemma | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the rank inequality for a product of matrices | Proof | Linear and multilinear algebra; matrix theory |
| Proof that independence means the joint law is the product of the marginals | Proof | Probability theory and stochastic processes |
| Proof that a bounded sequence converges iff its liminf and limsup agree | Proof | Sequences, series, summability |
| Niven's proof of the irrationality of pi | Proof | Number theory |
| Proof of the infinite pigeonhole principle | Proof | Combinatorics |
| Proof that the determinant is the product of the eigenvalues by comparing constant terms | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the product of a subgroup and a normal subgroup is a subgroup | Proof | Group theory and generalizations |
| Proof that Euclidean domains are principal ideal domains | Proof | Commutative algebra |
| Proof of the first Borel–Cantelli lemma | Proof | Probability theory and stochastic processes |
| Proof of Liouville's theorem by Cauchy's estimates | Proof | Functions of a complex variable |
| Proof of the law of excluded middle extended to the infinite | Proof | |
| Proof that orbits partition the set | Proof | Group theory and generalizations |
| Proof of the existence of an algebraic closure | Proof | Field theory and polynomials |
| Proof that the closure is the set of limits of sequences | Proof | General topology |
| Proof of continuity via open sets in metric spaces | Proof | General topology |
| Proof of the universal property of the quotient ring | Proof | Associative rings and algebras |
| Proof that the Cantor set is closed | Proof | General topology |
| Proof of the inscribed angle theorem by complex numbers | Proof | Geometry |
| Proof that continuous functions are Riemann integrable | Proof | Real functions |
| Proof of the mean value inequality | Proof | Real functions |
| Proof that the exponential function is strictly convex | Proof | Real functions |
| Proof of the law of excluded middle by a truth table | Proof | Mathematical logic and foundations |
| Proof of Bernoulli's inequality by induction | Proof | Real functions |
| Proof of Hurwitz's theorem by Rouché's theorem | Proof | Functions of a complex variable |
| Proof that an intersection of subspaces is a subspace | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the QR decomposition by clearing the first column | Proof | Linear and multilinear algebra; matrix theory |
| Proof that K[x] is a Euclidean domain | Proof | Commutative algebra |
| Proof of the exterior angle theorem from the angle sum | Proof | Geometry |
| Proof of the Arzelà–Ascoli theorem by total boundedness | Proof | General topology |
| Proof of the constant multiple rule | Proof | Real functions |
| Proof that similar matrices have the same characteristic polynomial | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the Cauchy–Schwarz inequality for expectations | Proof | Probability theory and stochastic processes |
| Proof of the cancellation laws | Proof | Group theory and generalizations |
Math 2.0