| Proof that the medians meet at the centroid | Proof | Geometry |
| Proof of the isolated zeros theorem by power series | Proof | Functions of a complex variable |
| Proof of the derivative of sine by term-by-term differentiation | Proof | Special functions |
| Proof of the well-ordering principle from strong induction | Proof | Mathematical logic and foundations |
| Proof of the uniqueness of the supremum | Proof | Order, lattices, ordered algebraic structures |
| Proof that n independent or n spanning vectors in an n-dimensional space form a basis | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the intersecting secants theorem by the power of a point | Proof | Geometry |
| Proof of the additivity of line integrals under concatenation | Proof | Real functions |
| Proof of Taylor's theorem with the Peano remainder | Proof | Approximations and expansions |
| Proof of the Bolzano–Weierstrass theorem by a monotone subsequence | Proof | Sequences, series, summability |
| Proof that the exponential of a sum of commuting matrices is the product of the exponentials | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the triangle inequality for integrals | Proof | Real functions |
| Proof that the minimal polynomial is irreducible | Proof | Field theory and polynomials |
| Proof of the solutions for repeated roots | Proof | Ordinary differential equations |
| Proof of the derivative of x^a by the chain rule | Proof | Real functions |
| Proof of the fundamental theorem of contour integration | Proof | Functions of a complex variable |
| Proof of Goursat's theorem by repeated subdivision | Proof | Functions of a complex variable |
| Proof of the generating function for partitions | Proof | Number theory |
| Proof of the division algorithm | Proof | Number theory |
| Proof that the cross product is perpendicular to its factors | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the formula for the modulus | Proof | Functions of a complex variable |
| Proof of Grönwall's inequality | Proof | Real functions |
| Proof that uniform limits of holomorphic functions are holomorphic, by Morera's theorem | Proof | Functions of a complex variable |
| Proof of the solutions for distinct real roots | Proof | Ordinary differential equations |
| Proof of angle-angle similarity with the law of sines | Proof | Geometry |
| Proof of Ping-pong lemma for several subgroups | Proof | |
| Proof of the change of basis rule for a bilinear form | Proof | Linear and multilinear algebra; matrix theory |
| Proof that a continuous injective function on an interval is strictly monotone | Proof | Real functions |
| Proof of L'Hôpital's rule from the Cauchy mean value theorem | Proof | Real functions |
| Proof of the Archimedean property in an Archimedean ordered field | Proof | Field theory and polynomials |
| Proof of the lifting-the-exponent lemma for odd primes | Proof | Number theory |
| Proof that a quotient is abelian iff the subgroup contains the commutator subgroup | Proof | Group theory and generalizations |
| Proof of Sylvester's law of inertia by comparing subspaces | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the sign of a cycle | Proof | Group theory and generalizations |
| Proof that finite-dimensional normed spaces are complete | Proof | Functional analysis |
| Proof of the general Leibniz rule by induction | Proof | Real functions |
| Proof of the Poincaré lemma for one-forms on convex sets | Proof | Global analysis, analysis on manifolds |
| Proof of the universal property of the quotient space | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the eigenvalues are the roots of the minimal polynomial | Proof | Linear and multilinear algebra; matrix theory |
| Proof that a continuous real function on a compact set attains its bounds | Proof | General topology |
| Proof that a convex function on an open interval is continuous | Proof | Real functions |
| Proof of the existence and uniqueness of the principal value of the argument | Proof | Functions of a complex variable |
| Proof of the mean of the Poisson distribution | Proof | Probability theory and stochastic processes |
| Proof of Wilson's theorem by pairing inverses | Proof | Number theory |
| Proof that the eigenvalues of a positive definite matrix are positive | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the sum of the first n natural numbers by induction | Proof | Combinatorics |
| Proof that the minimal polynomial divides every polynomial vanishing at the element | Proof | Field theory and polynomials |
| Proof of the Leibniz formula from the defining properties of the determinant | Proof | Linear and multilinear algebra; matrix theory |
| Proof that every walk contains a path | Proof | Combinatorics |
| Proof of continuous dependence on initial data by Grönwall's inequality | Proof | Ordinary differential equations |
| Proof of the Cayley–Hamilton theorem for linear maps | Proof | Linear and multilinear algebra; matrix theory |
| Proof of Thales's theorem by the dot product | Proof | Geometry |
| Proof of the uniqueness of inverses | Proof | Group theory and generalizations |
| Proof of the class equation | Proof | Group theory and generalizations |
| Proof of the polar form of a complex number | Proof | Functions of a complex variable |
| Proof of the derivative of a map into a product | Proof | Real functions |
| Proof that the trace is linear | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the identity theorem by connectedness | Proof | Functions of a complex variable |
| Proof of the integral of sine | Proof | Real functions |
| Proof of the maximum modulus principle by Cauchy's integral formula | Proof | Functions of a complex variable |
| Proof that row rank equals column rank by a factorization A = CR | Proof | Linear and multilinear algebra; matrix theory |
| Proof that limits are unique in Hausdorff spaces | Proof | General topology |
| Proof of the existence of maximal ideals by Zorn's lemma | Proof | Commutative algebra |
| Proof that arguments add under multiplication | Proof | Functions of a complex variable |
| Proof of Gauss's lemma on irreducibility over a UFD | Proof | Commutative algebra |
| Proof that a composition of continuous functions is continuous | Proof | Real functions |
| Proof of the theorem on friends and strangers | Proof | Combinatorics |
| Proof that repeating decimals are rational | Proof | Number theory |
| Proof of the exponential of a sum by the Cauchy product | Proof | Special functions |
| Proof of the law of total expectation | Proof | Probability theory and stochastic processes |
| Proof of the Möbius inversion formula | Proof | Number theory |
| Proof that cyclic groups of the same order are isomorphic | Proof | Group theory and generalizations |
| Proof of Cantor's intersection theorem | Proof | General topology |
| Proof that a finite field of order q is the splitting field of x^q - x | Proof | Field theory and polynomials |
| Proof of the existence and uniqueness of Laurent expansions on an annulus | Proof | Functions of a complex variable |
| Proof of the existence of inverses modulo n | Proof | Number theory |
| Proof of the first supplement to quadratic reciprocity from Euler's criterion | Proof | Number theory |
| Proof of Stirling's formula by a monotone sequence and the Wallis product | Proof | Approximations and expansions |
| Proof of Turán's theorem by Zykov symmetrization | Proof | Combinatorics |
| Proof of the divisibility rule for 9 | Proof | Number theory |
| Proof of the Casorati–Weierstrass theorem by Riemann's theorem | Proof | Functions of a complex variable |
| Proof of the Pythagorean trigonometric identity by differentiation | Proof | Special functions |
| Proof of Bézout's identity in a Euclidean domain | Proof | Commutative algebra |
| Proof that a linear isometry preserves the inner product by polarisation | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the multiplication rule | Proof | Probability theory and stochastic processes |
| Proof that an implication is equivalent to its contrapositive by a truth table | Proof | Mathematical logic and foundations |
| Proof of the number of permutations by counting injections | Proof | Combinatorics |
| Proof of the additivity of the integral over intervals | Proof | Real functions |
| Proof that a decreasing sequence bounded below converges | Proof | Sequences, series, summability |
| Proof of the term test | Proof | Sequences, series, summability |
| Proof that the exponential function is its own derivative, by term-by-term differentiation | Proof | Special functions |
| Proof that the reals are Archimedean from the completeness axiom | Proof | Real functions |
| Proof of the ratio test | Proof | Sequences, series, summability |
| Proof of Zorn's lemma from the axiom of choice by good chains | Proof | Mathematical logic and foundations |
| Proof of the second derivative test in several variables | Proof | Calculus of variations and optimal control; optimization |
| Proof that holomorphic functions are analytic | Proof | Functions of a complex variable |
| Proof that the divergence of a curl is zero | Proof | Real functions |
| Proof of the power series of the exponential function | Proof | Special functions |
| Proof that convergent sequences are bounded | Proof | Sequences, series, summability |
| Proof of the law of cosines with the dot product | Proof | Geometry |
| Proof of the converse of Wilson's theorem | Proof | Number theory |
| Proof that Fibonacci numbers are sums of binomial coefficients, by Pascal's rule | Proof | Number theory |
| Proof that a space is the direct sum of a finite-dimensional subspace and its orthogonal complement | Proof | Functional analysis |
| Proof that K[x]/(f) is a field iff f is irreducible | Proof | Field theory and polynomials |
| Proof of the derivative test for repeated roots | Proof | Commutative algebra |
| Proof that a composite number has a prime factor at most its square root | Proof | Number theory |
| Proof of the product rule | Proof | Real functions |
| Proof of Hall's theorem for bipartite graphs from Hall's marriage theorem | Proof | Combinatorics |
| Proof of the formula for the variance of a sum of independent random variables | Proof | Probability theory and stochastic processes |
| Proof that the Möbius function is the inverse of the constant function 1 | Proof | Number theory |
| Proof of the recurrence for Stirling numbers of the first kind | Proof | Number theory |
| Proof of the Vandermonde determinant by column operations | Proof | Linear and multilinear algebra; matrix theory |
| Proof that the units of Z/nZ are the residues coprime to n | Proof | Number theory |
| Proof that open balls form a basis of the metric topology | Proof | General topology |
| Proof of the monotone convergence theorem for sequences | Proof | Sequences, series, summability |
| Proof of Bayes' theorem | Proof | Statistics |
| Proof of Euclid's theorem using n! + 1 | Proof | Number theory |
| Proof of the Baire category theorem by nested closed balls | Proof | General topology |
| Proof that the number of odd-degree vertices is even | Proof | Combinatorics |
| Proof of Mantel's theorem by double counting | Proof | Combinatorics |
| Proof of the fundamental theorem of Galois theory | Proof | Field theory and polynomials |
| Proof that consecutive Fibonacci numbers are coprime | Proof | Number theory |
| Proof that the matrix exponential solves a linear system | Proof | Ordinary differential equations |
| Proof of Burnside's lemma by double counting | Proof | Group theory and generalizations |
| Proof of the characterization of the floor | Proof | Real functions |
| Proof that prime elements are irreducible in an integral domain | Proof | Commutative algebra |
| Proof of the Gauss–Wantzel theorem | Proof | Field theory and polynomials |
| Proof that continuity is equivalent to sequential continuity | Proof | Real functions |
| Proof of the generalized pigeonhole principle | Proof | Combinatorics |
| Proof that a subspace of a finite-dimensional space has smaller or equal dimension | Proof | Linear and multilinear algebra; matrix theory |
| Proof that absolutely convergent series in a Banach space converge | Proof | Sequences, series, summability |
| Proof of the Mercator series by term-by-term differentiation and Abel's theorem | Proof | Functions of a complex variable |
| Proof of the symmetry of second derivatives by a second difference | Proof | Real functions |
| Proof that in a PID a nonzero element is irreducible iff it generates a maximal ideal | Proof | Commutative algebra |
| Proof of the formula for the totient of a prime power | Proof | Number theory |
| Proof that adding a multiple of one row to another preserves the determinant | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the bijection principle | Proof | Combinatorics |
| Proof of the chain rule for Jacobian matrices | Proof | Real functions |
| Proof that the determinant is multilinear in the rows | Proof | Linear and multilinear algebra; matrix theory |
| Proof of the formula for the moment-generating function of the normal distribution | Proof | Probability theory and stochastic processes |
| Proof that open balls are open | Proof | General topology |
| Proof that power series are holomorphic in the disc of convergence | Proof | Functions of a complex variable |
| Proof of the fixed point congruence for p-group actions | Proof | Group theory and generalizations |
| Proof that a tree on n vertices has n − 1 edges, by removing a leaf | Proof | Combinatorics |
| Proof of the five colour theorem by Kempe chains | Proof | Combinatorics |
| Proof that a function with zero derivative on an open interval is constant | Proof | Real functions |
| Proof that a function with nonempty domain is injective iff it has a left inverse | Proof | Mathematical logic and foundations |
| Proof that Möbius transformations map circles and lines to circles and lines | Proof | Functions of a complex variable |
| Proof that the eigenspaces of a self-adjoint operator are orthogonal | Proof | Operator theory |
| Proof of Lagrange's theorem | Proof | Group theory and generalizations |
Math 2.0