World's Best Scientists 2026 revealed!
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Barry Simon
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Mathematics
USA
2026

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Mathematics 122 10 9 7 6 588 80654
Physics 102 1518 1440 798 745 371 66988

Barry Simon publications per year

The chart shows the history of publications by Barry Simon between 1968 and 2025, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. Barry Simon published across 58 years, from 1968 to 2025, averaging 11.3 papers a year. Output peaked at 59 publications in 2015. 14 of the 658 publications appeared in the last two years.

No. of publications
10 20 30 40 50
Bar chart. Horizontal axis: year, 1968 to 2025. Vertical axis: number of publications, 0 to 59. Peak 59 publications in 2015. 1968: 1 publication 1969: 8 publications 1970: 5 publications 1971: 7 publications 1972: 14 publications 1973: 19 publications 1974: 5 publications 1975: 12 publications 1976: 15 publications 1977: 12 publications 1978: 18 publications 1979: 12 publications 1980: 21 publications 1981: 17 publications 1982: 12 publications 1983: 17 publications 1984: 8 publications 1985: 11 publications 1986: 5 publications 1987: 9 publications 1988: 9 publications 1989: 2 publications 1990: 10 publications 1991: 6 publications 1992: 7 publications 1993: 13 publications 1994: 9 publications 1995: 19 publications 1996: 11 publications 1997: 8 publications 1998: 4 publications 1999: 7 publications 2000: 7 publications 2001: 1 publication 2002: 5 publications 2003: 9 publications 2004: 16 publications 2005: 29 publications 2006: 9 publications 2007: 11 publications 2008: 9 publications 2009: 9 publications 2010: 28 publications 2011: 21 publications 2012: 1 publication 2013: 4 publications 2014: 3 publications 2015: 59 publications 2016: 2 publications 2017: 12 publications 2018: 5 publications 2019: 48 publications 2020: 7 publications 2021: 5 publications 2022: 5 publications 2023: 6 publications 2024: 4 publications 2025: 10 publications
1968 2025

658 publications in total across all disciplines

View publications per year as a table
Barry Simon: publications per year, 1968 to 2025
Year Publications
1968 1
1969 8
1970 5
1971 7
1972 14
1973 19
1974 5
1975 12
1976 15
1977 12
1978 18
1979 12
1980 21
1981 17
1982 12
1983 17
1984 8
1985 11
1986 5
1987 9
1988 9
1989 2
1990 10
1991 6
1992 7
1993 13
1994 9
1995 19
1996 11
1997 8
1998 4
1999 7
2000 7
2001 1
2002 5
2003 9
2004 16
2005 29
2006 9
2007 11
2008 9
2009 9
2010 28
2011 21
2012 1
2013 4
2014 3
2015 59
2016 2
2017 12
2018 5
2019 48
2020 7
2021 5
2022 5
2023 6
2024 4
2025 10
Total 658
Download as CSV

Barry Simon publications per year - data summary

  • Barry Simon, a Mathematics scholar from California Institute of Technology, has 658 publications recorded across 58 years, from 1968 to 2025.
  • The oldest publication on record dates to 1968 and the most recent to 2025.
  • The most productive year is 2015, with 59 publications.
  • The least productive years with any output are 1968, 2001 and 2012, with 1 publication each.
  • The rate of publication averages 11.3 papers per year over the whole span, or 11.3 per year counting only the 58 years with at least one publication.
  • The last 5 years on the chart (2021-2025) hold 30 publications, 5% of the career total.
  • Split into equal eras - 1968-1987: 228 publications (11.4 per year); 1988-2007: 192 publications (9.6 per year); 2008-2025: 238 publications (13.2 per year).
  • Comparing the opening and closing eras, the overall trend of publication is broadly steady.

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.

No. of scientists
25 50 75 100
Bar chart with 100 bars. Horizontal axis: publications, 42–46 to 537+. Vertical axis: number of scientists, 0 to 112. Most scientists, 112, have 142–146 publications. The last bar groups every scientist with 537 publications or more. The highlighted bar, 537+ publications, is where this scientist sits. 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: 83 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 scientist 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientist 522–526 publications: 3 scientists 527–531 publications: 1 scientist 532–536 publications: 4 scientists 537+ publications: 100 scientists
42–46 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.

View publications distribution as a table
Number of Mathematics scientists by publication count, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
Publications Scientists This scientist
42–46 3
47–51 5
52–56 7
57–61 20
62–66 14
67–71 25
72–76 19
77–81 35
82–86 50
87–91 60
92–96 86
97–101 84
102–106 83
107–111 90
112–116 99
117–121 90
122–126 91
127–131 109
132–136 110
137–141 98
142–146 112
147–151 102
152–156 88
157–161 106
162–166 83
167–171 102
172–176 77
177–181 81
182–186 78
187–191 71
192–196 92
197–201 64
202–206 69
207–211 64
212–216 62
217–221 58
222–226 53
227–231 50
232–236 46
237–241 46
242–246 46
247–251 43
252–256 29
257–261 45
262–266 30
267–271 33
272–276 34
277–281 30
282–286 31
287–291 21
292–296 34
297–301 26
302–306 10
307–311 17
312–316 23
317–321 13
322–326 16
327–331 26
332–336 13
337–341 13
342–346 16
347–351 17
352–356 12
357–361 18
362–366 18
367–371 9
372–376 11
377–381 8
382–386 8
387–391 9
392–396 9
397–401 8
402–406 11
407–411 6
412–416 6
417–421 9
422–426 8
427–431 5
432–436 8
437–441 8
442–446 4
447–451 4
452–456 4
457–461 2
462–466 2
467–471 4
472–476 3
477–481 3
482–486 6
487–491 3
492–496 5
497–501 5
502–506 1
507–511 6
512–516 4
517–521 1
522–526 3
527–531 1
532–536 4
537+ 100 588
Download as CSV

Barry Simon publication distribution in Mathematics in 2026 - data summary

  • The chart plots the publication count of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 100 ranges running from 42–46 to 537+ publications.
  • Barry Simon, a Mathematics scholar from California Institute of Technology, records 588 publications - the 98th percentile of the discipline.
  • 98% of ranked Mathematics scientists score the same or lower than Barry Simon, and about 2% score higher.
  • The median of the discipline falls in the 172–176 publications range, and Barry Simon ranks above the median.
  • The most crowded range is 142–146 publications, holding 112 scientists (3% of the field).
  • 47% of the field sits in the lowest quarter of the value range (up to 162–166 publications), so the distribution leans towards the lower end of the scale.
  • The final bar has no upper bound: it groups every scientist with 537 publications or more, 100 scientists in all (3% of the field).

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.

No. of scientists
50 100 150
Bar chart with 57 bars. Horizontal axis: D-Index, 30 to 86+. Vertical axis: number of scientists, 0 to 174. Most scientists, 174, have 30 D-Index. The last bar groups every scientist with 86 D-Index or more. The highlighted bar, 86+ D-Index, is where this scientist sits. 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: 138 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.

View D-Index distribution as a table
Number of Mathematics scientists by D-index, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
D-Index Scientists This scientist
30 174
31 151
32 174
33 117
34 136
35 127
36 145
37 153
38 150
39 150
40 138
41 136
42 93
43 108
44 115
45 112
46 103
47 75
48 59
49 67
50 60
51 57
52 59
53 62
54 60
55 50
56 42
57 54
58 50
59 42
60 41
61 35
62 40
63 21
64 31
65 27
66 29
67 19
68 25
69 17
70 18
71 12
72 14
73 13
74 18
75 9
76 11
77 10
78 9
79 16
80 12
81 10
82 5
83 5
84 13
85 6
86+ 99 122
Download as CSV

Barry Simon D-index placement in Mathematics in 2026 - data summary

  • The chart plots the discipline H-index (D-index) of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 57 ranges running from 30 to 86+ D-Index.
  • Barry Simon, a Mathematics scholar from California Institute of Technology, records 122 D-Index - the 100th percentile of the discipline.
  • 100% of ranked Mathematics scientists score the same or lower than Barry Simon, and about 0% score higher.
  • The median of the discipline falls in the 42 D-Index range, and Barry Simon ranks above the median.
  • The most crowded range is 30 D-Index, holding 174 scientists (5% of the field).
  • 58% of the field sits in the lowest quarter of the value range (up to 44 D-Index), so the distribution is heavily right-skewed and high scores are rare.
  • The final bar has no upper bound: it groups every scientist with 86 D-Index or more, 99 scientists in all (3% of the field).

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

External Links

Wikipedia of Barry Simon Personal website of Barry Simon Google Scholar page

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David Damanik

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Elliott H. Lieb

Princeton University

Publications: 131

Pavel Exner

Pavel Exner

Czech Technical University in Prague

Publications: 122

Jürg Fröhlich

Jürg Fröhlich

ETH Zurich

Publications: 122

Gerald Teschl

Gerald Teschl

University of Vienna

Publications: 84

Rupert L. Frank

Rupert L. Frank

California Institute of Technology

Publications: 84

Daniel Lenz

Daniel Lenz

Friedrich Schiller University Jena

Publications: 81

Bernard Helffer

Bernard Helffer

University of Nantes

Publications: 75

Jan Philip Solovej

Jan Philip Solovej

University of Copenhagen

Publications: 71

Abel Klein

Abel Klein

University of California, Irvine

Publications: 70

Fedor Sukochev

Fedor Sukochev

University of New South Wales

Publications: 69

Svetlana Jitomirskaya

Svetlana Jitomirskaya

University of California, Irvine

Publications: 55

Michael Röckner

Michael Röckner

Bielefeld University

Publications: 50

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Joel L. Lebowitz

Rutgers, The State University of New Jersey

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