44 influential journal articles

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 graphs1 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-similarity2 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 variations2 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


  • (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

No Disrespect Meant (on MathSciNet institution codes)

According to The Free Dictionary, the title is one of the meanings of the acronym NDM. Recently MathSciNet began to append the suffix NDM to the institution codes which it uses to indicate an author’s affiliation. So, instead of

1-SRCS: “This author is at Syracuse.”

you sometimes see

1-SRCS-NDM: “This author is at Syracuse. No disrespect meant.”

This change appears to be very recent (all papers with the -NDM suffix that I’ve seen were indexed in 2012) and its likely goal is to keep the unsuffixed codes, such as 1-SRCS, for the output of math departments only. MathSciNet long used the suffix -P for physics, as in 1-SRCS-P. But if physicists did not specifically mention their departmental affiliation, they could sneak in.

But no more! From now on, the lack of departmental affiliation marks you with the suffix -NDM, which I guess expresses the frustration of MathSciNet staff: “No Department, #*&$%*^!”. It is not to be confused with the code 1-NDM, which stands for Notre Dame math department. When the Notre Dame code acquires this suffix, is becomes 1-NDM-NDM.

Moral: to be admitted into the unsuffixed club, you must show your credentials, i.e., put your department in the author address field. Your name will not be enough, even if it is Terence Tao or Richard P. Stanley. No disrespect meant.

Apropos of et al

I have 111 MathSciNet reviews posted, and there are three more articles on my desk that I should be reviewing instead of blogging. Even though I think of canceling my AMS membership, I don’t mind helping the society pay their bills (MathSciNet brings about 37% of the AMS revenue, according to their 2010-11 report.)

Sure, reviews need to be edited, especially when written by non-native English speakers like myself. Still, I’m unhappy with the edited version of my recent review:

This was the approach taken in the foundational paper by J. Heinonen et al. [J. Anal. Math. 85 (2001), 87-139]

The paper was written by J. Heinonen, P. Koskela, N. Shanmugalingam, and J. T. Tyson. Yes, it’s four names. Yes, the 14-letter name is not easy to pronounce without practice. But does the saving of 45 bytes justify omitting the names of people who spent many months, if not years, working on the paper? Absolutely not. The tradition of using “et al” for papers with more than 3 authors belongs to the age of typewriters.

P.S. I don’t think MathSciNet editors read my blog, so I emailed them.

P.P.S. The names are now restored. In the future I’ll be sure to add in “comments to the editor” that names should not be replaced by et al.