This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.

Algebra

  • Abhyankar's lemma
  • Aubin–Lions lemma
  • Bergman's diamond lemma
  • Fitting lemma
  • Injective test lemma
  • Hua's lemma (exponential sums)
  • Krull's separation lemma
  • Schanuel's lemma (projective modules)
  • Schwartz–Zippel lemma
  • Shapiro's lemma
  • Stewart–Walker lemma (tensors)
  • Whitehead's lemma (Lie algebras)
  • Zariski's lemma

Algebraic geometry

  • Abhyankar's lemma
  • Fundamental lemma (Langlands program)

Category theory

thumb|A commutative diagram that illustrates the five lemma

  • Five lemma
  • Horseshoe lemma
  • Nine lemma
  • Short five lemma
  • Snake lemma
  • Splitting lemma
  • Yoneda lemma

Linear algebra

  • Matrix determinant lemma
  • Matrix inversion lemma

Group theory

  • Burnside's lemma also known as the Cauchy–Frobenius lemma
  • Frattini's lemma (finite groups)
  • Goursat's lemma
  • Mautner's lemma (representation theory)
  • Ping-pong lemma (geometric group theory)
  • Schreier's subgroup lemma
  • Schur's lemma (representation theory)
  • Zassenhaus lemma

Polynomials

  • Gauss's lemma (polynomials)
  • Schwartz–Zippel lemma

Ring theory and commutative algebra

  • Artin–Rees lemma
  • Hensel's lemma (commutative rings)
  • Nakayama lemma
  • Noether's normalization lemma
  • Prime avoidance lemma

Universal algebra

  • Jónsson's lemma

Analysis

  • Fekete's lemma
  • Fundamental lemma of the calculus of variations
  • Hopf lemma
  • Sard's lemma (singularity theory)
  • Stechkin's lemma (functional and numerical analysis)
  • Vitali covering lemma (real analysis)
  • Watson's lemma

Complex analysis

  • Estimation lemma (contour integrals)
  • Hartogs's lemma (several complex variables)
  • Jordan's lemma
  • Lemma on the Logarithmic derivative
  • Schwarz lemma

Fourier analysis

  • Riemann–Lebesgue lemma

Differential equations

  • Borel's lemma (partial differential equations)
  • Grönwall's lemma
  • Lax–Milgram lemma
  • Pugh's closing lemma
  • Weyl's lemma (Laplace equation) (partial differential equations)

Differential forms

  • Poincaré lemma of closed and exact differential forms

Functional analysis

  • Cotlar–Stein lemma
  • Ehrling's lemma
  • Riesz's lemma

Mathematical series

  • Abel's lemma
  • Kronecker's lemma

Numerical analysis

  • Bramble–Hilbert lemma
  • Céa's lemma

Applied mathematics

alt=diagram of a length-8 fast Fourier transform |thumb|diagram of a length-8 fast Fourier transform

  • Danielson–Lanczos lemma (Fourier transforms)
  • Farkas's lemma (linear programming)
  • Feld–Tai lemma (electromagnetism)
  • Little's lemma (queuing theory)
  • Finsler's lemma

Control theory

  • Finsler's lemma
  • Hautus lemma
  • Kalman–Yakubovich–Popov lemma

Computational complexity theory

  • Isolation lemma
  • Switching lemma

Cryptography

  • Forking lemma
  • Leftover hash lemma
  • Piling-up lemma (linear cryptanalysis)
  • Yao's XOR lemma

Formal languages

  • Interchange lemma
  • Newman's lemma (term rewriting)
  • Ogden's lemma
  • Pumping lemma sometimes called the Bar-Hillel lemma

Microeconomics

  • Hotelling's lemma
  • Shephard's lemma

Combinatorics

  • Cousin's lemma (integrals)
  • Dickson's lemma
  • Littlewood–Offord lemma
  • Pólya–Burnside lemma
  • Sperner's lemma
  • Ky Fan lemma (combinatorial geometry)

Graph theory

  • Berge's lemma
  • Counting lemma
  • Crossing lemma
  • Expander mixing lemma
  • Handshaking lemma
  • Kelly's lemma
  • Kőnig's lemma
  • Szemerédi regularity lemma

Order theory

  • Higman's lemma
  • Ultrafilter lemma

Dynamical systems

  • Barbalat's lemma
  • Kac's lemma (ergodic theory)

Geometry

  • Shadowing lemma
  • Big-little-big lemma (mathematics of paper folding)
  • Gordan's lemma
  • Hilbert's lemma

Euclidean geometry

  • Archimedes's lemmas
  • Johnson–Lindenstrauss lemma (Euclidean geometry)

Hyperbolic geometry

  • Margulis lemma

Metric spaces

  • Lebesgue's number lemma (dimension theory)

Riemannian geometry

  • Gauss's lemma (Riemannian geometry)

Mathematical logic

  • Craig interpolation lemma
  • Diagonal lemma
  • Lindenbaum's lemma
  • Mostowski collapse lemma
  • Teichmüller–Tukey lemma also known as Tukey's lemma
  • Zorn's lemma; equivalent to the axiom of choice

Set theory

  • Covering lemma
  • Delta lemma
  • Dynkin lemma
  • Fodor's lemma
  • Fixed-point lemma for normal functions (axiomatic set theory)
  • Moschovakis coding lemma
  • Rasiowa–Sikorski lemma

Number theory

  • Bézout's lemma
  • Dwork's lemma
  • Euclid's lemma
  • Gauss's lemma
  • Hensel's lemma
  • Zolotarev's lemma
  • Siegel's lemma (Diophantine approximation)

Analytic number theory

  • Hua's lemma
  • Vaughan's lemma

Diophantine equations

  • Bhaskara's lemma

Sieve theory

  • Fundamental lemma of sieve theory

Probability theory

  • Borel–Cantelli lemma
  • Doob–Dynkin lemma
  • Itô's lemma (stochastic calculus)
  • Lovász local lemma
  • Stein's lemma
  • Wald's lemma

Statistics

  • Glivenko–Cantelli lemma
  • Neyman–Pearson lemma
  • Robbins lemma

Measure theory

  • Factorization lemma
  • Fatou's lemma
  • Frostman's lemma (geometric measure theory)
  • Malliavin's absolute continuity lemma

Topology

  • Lindelöf's lemma
  • Urysohn's lemma
  • Tube lemma

Differential topology

  • Morse lemma

Fixed-point theory

thumb|An example of a covering described by the Knaster–Kuratowski–Mazurkiewicz lemma

  • Knaster–Kuratowski–Mazurkiewicz lemma

Geometric topology

  • Dehn's lemma

Topological groups and semigroups

  • Ellis–Numakura lemma (topological semigroups)