World's Best Scientists 2026 revealed!
Communications on Pure and Applied Mathematics
H-index 26

Communications on Pure and Applied Mathematics

Ranking & Metrics

Discipline name Position Best Scientists Publications D-Index
Mathematics 35 98 140 26

Additional Metrics

Number of Best Scientists*: 106
Documents by Best Scientists*: 148
Top 100 Ranked Scientists*: 5
SCIMAGO H-index: 127
SCIMAGO SJR: 3.848
Impact Factor: 2.7

Overview

Top Research Topics at Communications on Pure and Applied Mathematics?

The aim of Communications on Pure and Applied Mathematics is to expand the discussion of research in Mathematical analysis, Pure mathematics, Nonlinear system, Mathematical physics and Boundary value problem. The studies tackled, which mainly focus on Mathematical analysis, apply to Boundary (topology) as well. Boundary value problem, which encompasses Free boundary problem and Mixed boundary condition, is the main subject of the journal.

In it, Stochastic partial differential equation and First-order partial differential equation are investigated in conjunction with one another to address concerns in Elliptic partial differential equation research. The First-order partial differential equation study featured in Communications on Pure and Applied Mathematics draws connections with the study of Numerical partial differential equations.

  • Mathematical analysis (48.53%)
  • Pure mathematics (15.07%)
  • Nonlinear system (8.90%)

What are the most cited papers published in the journal?

  • Orthonormal bases of compactly supported wavelets (7315 citations)
  • Stable signal recovery from incomplete and inaccurate measurements (5996 citations)
  • Optimal approximations by piecewise smooth functions and associated variational problems (4509 citations)

Research areas of the most cited articles at Communications on Pure and Applied Mathematics:

The journal publications investigate areas of study like Mathematical analysis, Nonlinear system, Pure mathematics, Mathematical physics and Partial differential equation. The journal articles cover various topics on Mathematical analysis such as Boundary value problem, Elliptic partial differential equation, Uniqueness, Differential equation and Hyperbolic partial differential equation. The Elliptic partial differential equation research presented in the most cited papers focuses mostly on Stochastic partial differential equation and, on occasion, topics in First-order partial differential equation.

What topics the last edition of the journal is best known for?

  • Quantum mechanics
  • Mathematical analysis
  • Algebra

The previous edition focused in particular on these issues:

Mathematical analysis, Applied mathematics, Pure mathematics, Mathematical physics and Measure (mathematics) are among the topics commonly tackled in Communications on Pure and Applied Mathematics. The work on Mathematical analysis tackled in Communications on Pure and Applied Mathematics brings together disciplines like Flow (mathematics) and Boundary (topology). The Boundary (topology) works, particularly on Free boundary problem are tackled in it.

Topics in Applied mathematics were tackled in line with various other fields like Well posedness, Class (set theory), Uniqueness and Limit (mathematics). The research on Pure mathematics tackled can also make contributions to studies in the areas of Function (mathematics), Zero (complex analysis) and Metric (mathematics). The Mathematical physics works featured in it incorporate elements from Distribution (mathematics) and Hamiltonian (quantum mechanics).

The most cited articles from the last journal are:

  • Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations (22 citations)
  • Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points (21 citations)
  • The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve (19 citations)

Papers citation over time

A key indicator for each journal is its effectiveness in reaching other researchers with the papers published at that venue.

The chart below presents the interquartile range (first quartile 25%, median 50% and third quartile 75%) of the number of citations of articles over time.

The top authors publishing in Communications on Pure and Applied Mathematics (based on the number of publications) are:

  • Fanghua Lin (50 papers) published 1 paper at the last edition,
  • Louis Nirenberg (36 papers) absent at the last edition,
  • Peter D. Lax (35 papers) absent at the last edition,
  • Luis A. Caffarelli (35 papers) absent at the last edition,
  • Harold N. Shapiro (34 papers) absent at the last edition.

The overall trend for top authors publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top authors.

Only papers with recognized affiliations are considered

The top affiliations publishing in Communications on Pure and Applied Mathematics (based on the number of publications) are:

  • Courant Institute of Mathematical Sciences (619 papers) published 15 papers at the last edition, 4 less than at the previous edition,
  • Princeton University (118 papers) published 4 papers at the last edition, 4 less than at the previous edition,
  • Stanford University (82 papers) published 3 papers at the last edition, 1 more than at the previous edition,
  • University of Chicago (74 papers) published 1 paper at the last edition the same number as at the previous edition,
  • New York University (70 papers) published 1 paper at the last edition, 3 less than at the previous edition.

The overall trend for top affiliations publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top affiliations.

Publication chance based on affiliation

The publication chance index shows the ratio of articles published by the best research institutions in the journal edition to all articles published within that journal. The best research institutions were selected based on the largest number of articles published during all editions of the journal.

The chart below presents the percentage ratio of articles from top institutions (based on their ranking of total papers).Top affiliations were grouped by their rank into the following tiers: top 1-10, top 11-20, top 21-50, and top 51+. Only articles with a recognized affiliation are considered.

During the most recent 2021 edition, 0.00% of publications had an unrecognized affiliation. Out of the publications with recognized affiliations, 39.47% were posted by at least one author from the top 10 institutions publishing in the journal. Another 10.53% included authors affiliated with research institutions from the top 11-20 affiliations. Institutions from the 21-50 range included 25.00% of all publications and 25.00% were from other institutions.

Returning Authors Index

A very common phenomenon observed among researchers publishing scientific articles is the intentional selection of journals they have already attended in the past. In particular, it is worth analyzing the case when the authors participate in the same journal from year to year.

The Returning Authors Index presented below illustrates the ratio of authors who participated in both a given as well as the previous edition of the journal in relation to all participants in a given year.

Returning Institution Index

The graph below shows the Returning Institution Index, illustrating the ratio of institutions that participated in both a given and the previous edition of the conference in relation to all affiliations present in a given year.

The experience to innovation index

Our experience to innovation index was created to show a cross-section of the experience level of authors publishing in a journal. The index includes the authors publishing at the last edition of a journal, grouped by total number of publications throughout their academic career (P) and the total number of citations of these publications ever received (C).

The group intervals were selected empirically to best show the diversity of the authors' experiences, their labels were selected as a convenience, not as judgment. The authors were divided into the following groups:

  • Novice - P < 5 or C < 25 (the number of publications less than 5 or the number of citations less than 25),
  • Competent - P < 10 or C < 100 (the number of publications less than 10 or the number of citations less than 100),
  • Experienced - P < 25 or C < 625 (the number of publications less than 25 or the number of citations less than 625),
  • Master - P < 50 or C < 2500 (the number of publications less than 50 or the number of citations less than 2500),
  • Star - P ≥ 50 and C ≥ 2500 (both the number of publications greater than 50 and the number of citations greater than 2500).

The chart below illustrates experience levels of first authors in cases of publications with multiple authors.

Top Publications

  • The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve

    Song Mei;Andrea Montanari

    (2021)
    379 Citations
  • Lipschitz Bounds and Nonuniform Ellipticity

    Lisa Beck;Giuseppe Mingione

    (2020)
    159 Citations
  • Deterministic Guarantees for Burer-Monteiro Factorizations of Smooth Semidefinite Programs

    Nicolas Boumal;Vladislav Voroninski;Afonso S. Bandeira

    (2020)
    128 Citations
  • Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality

    Paul Bourgade;Horng Tzer Yau;Jun Yin

    (2020)
    76 Citations
  • Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations

    Renjun Duan;Shuangqian Liu;Shota Sakamoto;Robert M. Strain

    (2021)
    74 Citations
  • Transition Threshold for the 3D Couette Flow in Sobolev Space

    Dongyi Wei;Zhifei Zhang

    (2021)
    73 Citations
  • Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime

    Gérard Ben Arous;Gérard Ben Arous;Eliran Subag;Ofer Zeitouni

    (2020)
    62 Citations
  • Formation of shocks for 2D isentropic compressible Euler

    Tristan Buckmaster;Steve Shkoller;Vlad Vicol

    (2020)
    55 Citations
  • Global Solution for Massive Maxwell‐Klein‐Gordon Equations

    Sergiu Klainerman;Qian Wang;Shiwu Yang

    (2020)
    55 Citations
  • Global bifurcation of rotating vortex patches

    Zineb Hassainia;Nader Masmoudi;Miles H. Wheeler

    (2020)
    52 Citations

Related Online Degrees & Career Pathways

Pursuing Mathematics in the USA opens doors to diverse career paths and advanced degrees. Complementary fields such as marketing, business, human resources, and healthcare increasingly value the analytical skills developed through a mathematics background.

For those interested in blending quantitative skills with business strategy, exploring a master's degree in marketing online can provide valuable expertise in data-driven marketing and consumer analysis.

Similarly, ambition for leadership roles can be accelerated with a 1 year MBA programs, which are designed for professionals seeking a fast-paced path to executive positions while building strong business acumen grounded in quantitative reasoning.

Human resource management also benefits from candidates with strong problem-solving skills. The best online human resource management masters degree programs integrate leadership, analytics, and strategy suited for those wanting to manage organizational talent efficiently.

Lastly, the intersection of mathematics and healthcare is growing. Students may consider online nursing degrees that incorporate data analytics and statistics to improve patient care and medical research.

Exploring these related online degrees can enrich your career opportunities, leveraging your mathematical skills in practical, high-demand professions.

Best Scientists Contributing to This Journal

Recently Published Articles