World's Best Scientists 2026 revealed!
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Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
122
Citations
80654
World Ranking
10
National Ranking
7

Physics

D-Index
102
Citations
66988
World Ranking
1518
National Ranking
798

Barry Simon publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Barry Simon sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 82 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 588 publications — 98th percentile

98% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Barry Simon D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Barry Simon sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 137 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 122 D-Index — 100th percentile

100% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2022 - Research.com Mathematics in United States Leader Award
  • 2019 - Member of the National Academy of Sciences
  • 2018 - Dannie Heineman Prize for Mathematical Physics, American Physical Society and American Institute of Physics
  • 2016 - Steele Prize for Lifetime Achievement
  • 2013 - Fellow of the American Mathematical Society
  • 2012 - Henri Poincaré Prize, International Association of Mathematical Physics
  • 2005 - Fellow of the American Academy of Arts and Sciences
  • 1988 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

Barry Simon is affiliated with the California Institute of Technology in the United States. Their research primarily focuses on mathematics, with a significant emphasis on mathematical physics, applied mathematics, and several intersecting subfields. The scientist's work spans a range of subjects including spectral theory in mathematical physics, mathematical functions and polynomials, and random matrices and applications.

The scientist has contributed to the fields of mathematical physics and theoretical and computational physics, with additional interests in quantum mechanics, graph theory, and analytic number theory. Their scientific output includes publications in various venues, highlighting sustained engagement with both preprint platforms and peer-reviewed journals.

  • Recent papers include "Twelve tales in mathematical physics: An expanded Heineman prize lecture" (2022) published in the Journal of Mathematical Physics
  • "The strong Gauss-Lucas theorem and analyticity of correlation functions via the Lee-Yang theorem" (2022) in the Journal of Mathematical Physics
  • "Widom Factors and Szego-Widom Asymptotics, a Review" (2022) in Operator theory
  • "Periodic Boundary Conditions for Periodic Jacobi Matrices on Trees" (2020) in arXiv (Cornell University)
  • "Remembrances of Harold Widom" (2022) in Notices of the American Mathematical Society

  • Frequent collaborators have included Jacob S. Christiansen, Maxim Zinchenko, Ари Лаптев, Pavel Kurasov, and Serguei Naboko.

  • Major publication venues for the scientist's work are arXiv (Cornell University), Journal of Mathematical Physics, Notices of the American Mathematical Society, Operator theory, and Journal of Mathematical Sciences.

The scientist has also contributed to the literature through book publications, with titles released by notable publishers:

  • Analysis as a Tool in Mathematical Physics (Springer Nature, 2020)
  • Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov (California Institute of Technology, 2020)

Awards received by the scientist reflect recognition by various mathematical and physical societies. These include the Dannie Heineman Prize for Mathematical Physics awarded jointly by the American Physical Society and American Institute of Physics in 2018, the Steele Prize for Lifetime Achievement in 2016, and election as a Member of the National Academy of Sciences in 2019.

  • Fellow of the American Mathematical Society (2013)
  • Henri Poincaré Prize, International Association of Mathematical Physics (2012)
  • Fellow of the American Academy of Arts and Sciences (2005)
  • Fellow of John Simon Guggenheim Memorial Foundation (1988)

Best Publications

  • Methods of Modern Mathematical Physics

    Michael Reed;Barry Simon

  • Trace ideals and their applications

    Barry Simon

  • Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry

    H. L. Cycon;Barry Simon

  • Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase

    Barry Simon

  • Functional integration and quantum physics

    Barry Simon

  • Orthogonal polynomials on the unit circle

    Barry Simon

  • The P(φ)[2] Euclidean (quantum) field theory

    Barry Simon

  • Methods of modern mathematical physics. III. Scattering theory

    M. Reed;B. Simon

  • Analysis of Operators

    Michael Reed;Barry Simon

  • The statistical mechanics of lattice gases

    Barry Simon

  • The Thomas-Fermi theory of atoms, molecules and solids

    Elliott H Lieb;Barry Simon

  • Coupling constant analyticity for the anharmonic oscillator

    Barry Simon;A Dicke

  • Schrödinger operators with magnetic fields. I. general interactions

    J. Avron;I. Herbst;B. Simon

  • Resonances in n-Body Quantum Systems With Dilatation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory

    Barry Simon

  • Schrödinger Semigroups

    Unknown

  • Homotopy and Quantization in Condensed Matter Physics

    J. E. Avron;R. Seiler;B. Simon

  • The Statistical Mechanics of Lattice Gases, Volume I

    Barry Simon

  • The bound state of weakly coupled Schrödinger operators in one and two dimensions

    Barry Simon

  • Brownian motion and harnack inequality for Schrödinger operators

    Michael Aizenman;B. Simon

  • Quantum Mechanics for Hamiltonians Defined as Quadratic Forms

    Barry Martin Simon

  • Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

    Freeman J. Dyson;Elliott H. Lieb;Barry Simon

Frequent Co-Authors

Fritz Gesztesy
Fritz Gesztesy Baylor University
Elliott H. Lieb
Elliott H. Lieb Princeton University
David Damanik
David Damanik Rice University
Ira Herbst
Ira Herbst University of Virginia
Rowan Killip
Rowan Killip University of California, Los Angeles
Svetlana Jitomirskaya
Svetlana Jitomirskaya University of California, Irvine
Helge Holden
Helge Holden Norwegian University of Science and Technology
Rupert L. Frank
Rupert L. Frank California Institute of Technology
Edward Davies
Edward Davies King's College London
Alexander Kiselev
Alexander Kiselev Duke University

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