Same idea as 44 Great Books, but for journal articles. Influence is measured by the number of citations on MathSciNet, and as such is subject to chronological and geographical bias. Italic indicates I took a look at the paper, whether or not I got anything out of it.

The earliest paper on the list was published in 1938 (see Geometry), the latest in 2000 (see K-theory). Half were published in 1977 or later.

Area | Title | Author | Year |
---|---|---|---|

General | A level-set approach for inverse problems involving obstacles | Santosa | 1995 |

History and biography | Mathematical problems for the next century | Smale | 1998 |

Mathematical logic and foundations | Linear logic | Girard | 1987 |

Combinatorics | On the evolution of random graphs^{1} |
Erdős, Rényi | 1960 |

Order, lattices, ordered algebraic structures | A lattice-theoretical fixpoint theorem and its applications | Tarski | 1955 |

General algebraic systems | Algebras whose congruence lattices are distributive | Jónsson | 1967 |

Number theory | Modular elliptic curves and Fermat’s last theorem | Wiles | 1995 |

Field theory and polynomials | Factoring polynomials with rational coefficients | Lenstra, Lenstra, Lovász | 1982 |

Commutative algebra | Tight closure, invariant theory, and the Briançon-Skoda theorem | Hochster, Huneke | 1990 |

Algebraic geometry | Resolution of singularities of an algebraic variety over a field of characteristic zero | Hironaka | 1964 |

Linear and multilinear algebra; matrix theory | The invariant theory of n×n matrices | Procesi | 1976 |

Associative rings and algebras | On the deformation of rings and algebras | Gerstenhaber | 1964 |

Nonassociative rings and algebras | Lie superalgebras | Kac | 1977 |

Category theory; homological algebra | Des catégories abéliennes | Gabriel | 1962 |

K-theory | The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space | Yu | 2000 |

Group theory and generalizations | Representations of Coxeter groups and Hecke algebras | Kazhdan, Lusztig | 1979 |

Topological groups, Lie groups | L’algèbre de Fourier d’un groupe localement compact | Eymard | 1964 |

Real functions | Analysis on measure chains—a unified approach to continuous and discrete calculus | Hilger | 1990 |

Measure and integration | Fractals and self-similarity^{2} |
Hutchinson | 1981 |

Functions of a complex variable | Quasiconformal maps in metric spaces with controlled geometry | Heinonen, Koskela | 1998 |

Potential theory | A symmetry problem in potential theory | Serrin | 1971 |

Several complex variables and analytic spaces | Real hypersurfaces in complex manifolds | Chern, Moser | 1974 |

Special functions | Differential-difference operators associated to reflection groups | Dunkl | 1989 |

Ordinary differential equations | Ordinary differential equations, transport theory and Sobolev spaces | DiPerna, Lions | 1989 |

Partial differential equations | User’s guide to viscosity solutions of second order partial differential equations | Crandall, Ishii, Lions | 1992 |

Dynamical systems and ergodic theory | A shallow water equation on the circle | Constantin, McKean | 1999 |

Difference and functional equations | Approximate homomorphisms | Hyers, Rassias | 1992 |

Sequences, series, summability | A contribution to the theory of divergent sequences | Lorentz | 1948 |

Approximations and expansions | Basic calculus on time scales and some of its applications | Agarwal, Bohner | 1999 |

Harmonic analysis on Euclidean spaces | H^p spaces of several variables | Fefferman, Stein | 1972 |

Abstract harmonic analysis | Banach spaces related to integrable group representations and their atomic decompositions | Feichtinger, Gröchenig | 1989 |

Integral transforms, operational calculus | On singular integrals | Calderón, Zygmund | 1956 |

Integral equations | Traveling waves in a convolution model for phase transitions | Bates, Fife, Ren, Wang | 1997 |

Functional analysis | Dual variational methods in critical point theory and applications | Ambrosetti, Rabinowitz | 1973 |

Operator theory | Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces | Amann | 1976 |

Calculus of variations and optimal control | The concentration-compactness principle in the calculus of variations^{2} |
Lions | 1984 |

Geometry | A theorem in finite projective geometry and some applications to number theory | Singer | 1938 |

Convex and discrete geometry | On general minimax theorems | Sion | 1958 |

Differential geometry | On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation | Yau | 1978 |

General topology | A generalization of Tychonoff’s fixed point theorem | Fan | 1960 |

Algebraic topology | On the structure of Hopf algebras | Milnor, Moore | 1965 |

Manifolds and cell complexes | Differentiable dynamical systems | Smale | 1967 |

Global analysis, analysis on manifolds | Spectral asymmetry and Riemannian geometry | Atiyah, Patodu, Singer | 1975 |

Probability theory and stochastic processes | A mathematical theory of communication | Shannon | 1948 |

#### Notes

- (1) In combinatorics, the Erdős-Rényi paper is slightly behind
*Emergence of scaling in random networks*by Barabási and Albert (1999). I disqualified the latter for being published in*Science*. - (2) The 1981 paper by Hutchinson on fractals was classified under Calculus of variations, and would be the most cited in that category. However, this is an artifact of MSC which did not have a classification for Fractals until 1991. Now they are under Measure and Integration (28A80).
- (2) If I did not move Hutchinson’s paper to Measure and Integration, the winner there would be
*A relation between pointwise convergence of functions and convergence of functionals*by Brézis and Lieb (1983). Notably, this is a 5-page paper in the Proceedings of the AMS.

Finally, some trivia based on the combined lists of 44 books and 44 papers.

- Pierre-Louis Lions is the only person with three entries: most cited papers in ODE, PDE, and Calculus of Variations
- Juha Heinonen, Walter Rudin, and Stephen Smale have entries in two different MSC areas:
- Heinonen: most cited book in Potential Theory and most cited paper in One Complex Variable (another artifact of MSC: analysis on metric spaces is under MSC 30)
- Rudin: most cited books in General and in Several Complex Variables
- Smale: most cited papers in History/Biography and in Manifolds/Cell Complexes.

- Victor Kac and Eliah Stein occupy both top spots (book and paper) in the same area:
- Kac: Nonassociative Groups and Algebras
- Stein: Harmonic Analysis on Euclidean Spaces