MathSciNet at 25 – A Special Collection

MathSciNet® was launched 25 years ago, and soon became recognized as the best way to use the trusted, comprehensive resource for mathematics researchers that started over 80 years ago as Mathematical Reviews.  To celebrate, we are creating a special collection of exceptional reviews: MathSciNet at 25. The first group of 25 selected reviews is given below.  Throughout 2021, we will be adding to the collection.

MathSciNet indexes books and articles in more than 1,750 journals, with daily updates.  It is home to the complete information from Mathematical Reviews®, adding tens of thousands of expertly curated reviews of research papers and books each year.  MathSciNet is a rich, searchable database of reviews, abstracts, and bibliographic information spanning all areas of research in the mathematical sciences.  More than two and a half million direct links from MathSciNet ensure you reach the exact article you want to read.

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You can access the complete database, including eight decades of Mathematical Reviews, through your institution’s subscription. You can also take MathSciNet on the road with you via Remote Access.  If you are currently connected to your institution’s network, pair your device now so that you have direct access to the complete collection of reviews from anywhere.

MathSciNet at 25 – 25 Exceptional Reviews

The selection is organized by the 2020 Mathematics Subject Classification.  The title is linked to a freely available copy of each review.  The MR number is linked to the item and review in MathSciNet, allowing you to search further in the database using this review as a starting point.  Use the Collaboration Distance Calculator to discover how this bit of research connects with your own.

03 Mathematical logic and foundations

Muchnik degrees and Medvedev degrees of randomness notions. MR3890460
Reviewed by: Bjørn Kjos-Hanssen

Iterating symmetric extensions. MR3922788
Reviewed by: Eleftherios C. Tachtsis

Berkeley cardinals and the structure of L(Vδ+1). MR3893283
Reviewed by: Rupert McCallum

Another arithmetic of the even and the odd. MR3859203
Reviewed by: Victor V. Pambuccian

14 Algebraic geometry

Foundations of rigid geometry. I. MR3752648
Reviewed by: Christopher David Lazda

26 Real functions

Fractional differential equations. MR1658022
Reviewed by: Anatoly Kilbas

33 Special functions

Some new q-congruences for truncated basic hypergeometric series: even powers.MR4040632
Reviewed by: Chen Wang

 34  Ordinary differential equations

Theory and applications of fractional differential equations. MR2218073
Reviewed by: B. S. Rubin

35 Partial differential equations

Blow-up solutions for fully nonlinear equations: existence, asymptotic estimates and uniqueness. MR3935863
Reviewed by: Seunghyeok Kim

User’s guide to viscosity solutions of second order partial differential equations. MR1118699
Reviewed by: P. Szeptycki

An extension problem related to the fractional Laplacian. MR2354493
Reviewed by: Francesco Petitta

Superlinear Schrödinger-Kirchhoff type problems involving the fractional p-Laplacian and critical exponent. MR3993416
Reviewed by: Vincenzo Ambrosio

Partial differential equations. MR2597943
Reviewed by: Diego M. Maldonado

37 Dynamical systems and ergodic theory

Generating positive geometric entropy from recurrent leaves. MR3834666
Reviewed by: Carlos Meniño Cotón

Algorithmic aspects of branched coverings IV/V. Expanding maps. MR3852445
Reviewed by: Kevin M. Pilgrim

Unique equilibrium states for geodesic flows in nonpositive curvature. MR3856792
Reviewed by: Boris Hasselblatt

Cantor minimal systems. MR3791491
Reviewed by: Olena Karpel

47 Operator theory

Semigroups of linear operators and applications to partial differential equations. MR710486
Reviewed by: H. O. Fattorini

53 Differential geometry

A comprehensive introduction to sub-Riemannian geometry. MR3971262
Reviewed by: Luca Rizzi

60 Probability theory and stochastic processes

A mathematical theory of communication. MR26286
Reviewed by: J. L. Doob

Liouville quantum gravity and the Brownian map I: the QLE(8/3,0) metric. MR4050102
Reviewed by: Juhan Aru

On Wishart and noncentral Wishart distributions on symmetric cones. MR3939571
Reviewed by: Gérard Letac

68 Computer science

Invariance principle on the slice. MR3831003
Reviewed by: Michele Zito

81 Quantum theory

Casimir squared correction to the standard rotator Hamiltonian for the O(n) sigma-model in the delta-regime. MR3832694
Reviewed by: J. A. van Casteren

83 Relativity and gravitational theory

Exact solutions in three-dimensional gravity. MR3889027
Reviewed by: Daniele Gregoris

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10 Responses to MathSciNet at 25 – A Special Collection

  1. Michael says:

    Since this is a week the international mathematics community has set aside to celebrate women in mathematics and take note of continued inequalities, I wonder if someone from MR can comment on the gender balance of reviewers and articles represented in this list, and perhaps contextualize in terms of how MathSciNet reflects (or counters? or perpetuates?) gender bias in mathematical publishing and reviewing?

    • Edward Dunne says:


      Thank you for your comment. Mathematical Reviews does not collect demographic information about authors or reviewers. The information we have about authors comes from the publications. Several major publishers, including the AMS, have signed onto the Joint Commitment for Action on Inclusion and Diversity in Publishing However, I am not aware of any plans for publishers to share demographic information with third party services, such as MathSciNet.

      Since MathSciNet indexes the published literature, it is likely that MathSciNet reflects current and historical biases in mathematical publishing. Reviewers are drawn from the author database. Since we don’t have demographic data, I cannot compare the reviewers to the authors demographically. While I might expect them to be similar, they are unlikely to be identical as there is some self-selection in that a researcher has to agree to be a reviewer.

      Edward Dunne
      Executive Editor
      Mathematical Reviews

      • Michael says:

        Thanks Ed. I hope you will promote more reviews by women in your next installments!

      • Mat says:

        Great selection of reviews, Edward. I rather enjoyed reading these. And not once did I stop to wonder what the gender (or any other irrelevant characteristic) of the author might be. Happy to hear that the database does not collect demographic data and sincerely hope it does not in the future.

    • Paul says:

      Please give us a break.

  2. Christina Sormani says:

    What is the process for choosing which articles receive featured reviews, and who reviews them, and which are exceptional reviews? Is there a nomination process? Is there an editorial board? Are their representatives from every subfield? The selection of articles for featured review is perhaps the most difficult task as it required both expertice and foresight.

  3. Al says:

    I fail to understand the choice of reviews. At first, I thought MathSciNet wanted to recover Featured Reviews that vanished around 2005. Then I quickly understood that the aim was to recognize exceptional reviews and not exceptional papers/books as before. Looking at some reviews one can actually appreciate the work of some reviewers. On the other hand, I completely fail to understand why some reviews appeared here: for example the reviews contains one sentence and quotes several theorems from the paper.

  4. Md. Shafiqul Islam says:

    I am requesting to notify the Author, who is a member of AMS, once it includes in MR. Then the young members will get inspiration to do more research Further, I will be happy if we (Authors who are Members of AMS) get the list of Indexed Articles for the last 25 years free especially for developing countries and Middle-Income-Countries.

  5. Chingyuen Hui( George) says:

    Interesting comments 🙂

  6. Edward Teach says:

    What a strange selection. Some of these reviews are quite good, but some of them are completely pedestrian and in no way “exceptional”. In fact, some of them merely state hilariously technical theorems quoted directly from the papers without adding any context. The fact that 32% of the chosen reviews are concerned with fractional calculus or hardcore mathematical logic is also delightfully whimsical and perverse.

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