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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## 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*

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?

Michael,

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 https://www.rsc.org/new-perspectives/talent/joint-commitment-for-action-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

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

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.

Please give us a break.

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.

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.

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.

Interesting comments 🙂

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.