A service for mathematicians, by mathematicians
On the 30th anniversary of MathSciNet, Edward Dunne retraces the history of Mathematical Reviews and explains its importance
Tell us a little about your background and qualifications.
I have an undergraduate degree in Mathematics from Santa Clara University, a liberal arts university in the San Francisco Bay Area, and a PhD in Mathematics from Harvard University.
My research spans several areas of mathematics: algebra, geometry, differential equations, and mathematical physics. This breadth has been very useful in my career. I held academic positions at Oklahoma State University, Oxford University, and Rice University. I had several research visits to the University of Adelaide (Australia) and the University of Edinburgh (Scotland). For a time, I worked for Springer-Verlag in Heidelberg, Germany.
I currently live in Ann Arbor, Michigan (US), the home of Mathematical Reviews. I have worked for the AMS since 1997 – for the first 17 years, I was an editor for the AMS Book Program.
What is your job at AMS, and what does it involve?
My title is Executive Editor of Mathematical Reviews. The job has two parts. One is to oversee the running of the division of the American Mathematical Society known as Mathematical Reviews. With 72 employees, this is the largest division of the AMS. The primary function of Mathematical Reviews is to maintain and develop MathSciNet, the AMS’s database of the research literature in the mathematical sciences. The second part of my role is to oversee the editorial content of MathSciNet. The day-to-day editorial decisions are made by the 16 associate editors, who all have PhDs in mathematics or a related subject, as well as an established research record.
2026 marks the 30th anniversary of MathSciNet – can you tell us a bit about the history of MathSciNet and Mathematical Reviews?
Mathematical Reviews has two predecessors: the Jahrbuch über die Fortschritte der Mathematik, which ran from 1868 to 1942, and Zentralblatt für Mathematik und ihre Grenzgebiete, which was founded in 1931 and still operates as zbMATH Open. In the 1930s, the Nazis began interfering with the editorial work of Zentralblatt, which led to a strong sense among mathematicians globally that an alternative resource was needed.
At the time, the United States was seen as the logical place to found a new reviewing service, free from government interference. Otto Neugebauer, one of the co-founders of Zentralblatt, moved from Europe to the US to found such a new journal, while also taking up a professorship at Brown University, in Providence, Rhode Island. Mathematical Reviews was founded under the auspices of the American Mathematical Society. Many of the early issues had sponsorship from mathematical societies around the world, as well as from several private sources. The first issue was sponsored by the AMS, the Mathematical Association of America, Academia Nacional de Ciencias Exactas, Fisicas y Naturales de Lima, Het Wiskundig Genootschap te Amsterdam, and the London Mathematical Society.
In 1965, Mathematical Reviews (MR) moved from Providence to Ann Arbor, to take advantage of two resources available at the University of Michigan: its excellent library and its large, world-class Mathematics Department. In the 1980s, MR began using a database, rather than index cards and paper records, as our workflow. In 1989, MathSci Disc was released, providing a database version of Mathematical Reviews on a CD-ROM – and, in 1996, a web-based version, MathSciNet, was released. So, we are celebrating the 30th birthday of our online database!
What makes MathSciNet an essential tool for mathematics?
There are several things that make MathSciNet essential. First, it is a service for mathematicians, by mathematicians. The backing of the world’s largest mathematical society is a very important factor in the success of MathSciNet.
Our editorial oversight committee, which is appointed by the leadership of the AMS, sets editorial guidelines representing the standards of the Society. Moreover, we benefit by having colleagues who work in other areas supporting the mathematics profession: books and journals publishing, meetings and conferences, membership, and professional programs.
Second, the material indexed in MathSciNet is not randomly collected by bots crawling the internet. There are editorial processes for selecting which journals will be covered and for selecting which articles in those journals will be included.These decisions are made by research mathematicians, following the guidance provided by the AMS.
Mathematicians trust what they find in MathSciNet because we have followed such standards for 85 years. Senior mathematicians mentoring early career mathematicians will advise them to send their papers only to journals that are indexed in MathSciNet. Finally, MathSciNet includes reviews, which are written by volunteer researchers around the world. There are currently over 27,000 researchers who serve as reviewers for MR.
MathSciNet provides reviews of many of the indexed publications – can you tell us about the reviewers?
The reviewers are essential to what we do. Active researchers either contact us to volunteer to be reviewers or are invited by our editors. The volunteers reach us by one of several email addresses, such as mathrev@ams.org. Usually, they know about reviewing because they are using MathSciNet. Those who are invited are found as our editors do their regular work.
When an editor is handling a paper, our internal database will inform the editor if any of the authors of the paper is not already a reviewer. Our editor can look up the author’s publication record to find out more about the author’s research. The editor can then send out an automated invitation letter (via email). People should have several papers published before becoming a reviewer. This ensures that the person is an active researcher but also helps the editors understand the person’s areas of expertise, so we know what papers to send to them.
The set of reviewers is truly international. Roughly two thirds of the reviewers come from Brazil, China, France, Germany, India, Iran, Italy, Japan, Spain, Turkey, and the United States. A good review will state the context of the work, describe the main results of the paper, and say something about the techniques used. It is great when the reviewer can reference related work that isn’t mentioned in the paper. Sometimes, the reviewer will go on to point out how the results or techniques might lead to further results. Our reviewers will sometimes find flaws in the paper, which we try to present as constructively as possible. If a result is stated as holding for all N, but only really works for N > 2, it is good to be able to point that out.
Mathematics has always been considered a ‘core’ subject within education. From AMS’ point of view, does this remain the case?
Yes – definitely. Mathematics is at the core of all the sciences. At some point, every science needs mathematics, both to explain the existing theories in a workable, predictable way, and to move the subject forward.
Social sciences have traditionally relied heavily on statistics and probability. That continues to be the case, but other mathematical subjects have increasing roles to play here, such as dynamical systems and network theory. Physics tends to rely heavily on calculus and related mathematics, even to state the basic objects of study. Velocity is the derivative of position. Acceleration is the derivative of velocity. Motion of any kind is naturally stated in terms of vectors.
At a higher level, the heart of general relativity is the nonlinear partial differential equation known as the Einstein equation, which has remarkable uses in differential geometry. Mathematics is core to education because it teaches problem solving in a way that extends broadly. The mathematician George Polya even wrote a famous book on the general principles of solving problems. Appropriately enough, it is titled How to Solve It.
What do you consider the biggest challenge facing scholarly communications (and AMS) right now?
The incredible growth of literature is overwhelming everyone. Some of the growth is following historical patterns that were established in the 1960s through 1980s. In mathematics, that rate held steady at about 4% more journal articles per year for a long time. More recently, the growth rate is much higher.
On top of the traditional growth, we are seeing paper mills that generate low-quality research that is clogging the system of refereeing and publication. Traditional researchers are also using new tools to boost their own productivity, either to accelerate their research or to speed up the writing of the paper. As a result, new tools are needed to digest all this output.
For hundreds of years, people wrote papers that other people read. As output increased, people used tools, such as databases and search engines, to find the papers to read. We are now faced with the prospect, however, that researchers will be using tools, such as AIs, to help write their papers and to help read them. Reading a mathematics paper takes time, usually weeks, sometimes months. Few people are going to have the time to read relevant papers thoroughly. They will use an LLM, or a tool derived from an LLM, to extract the gist of the paper. This is a fundamental change.
Looking forward 10 years, what one improvement would you like to see in the industry?
I would like for the industry to find a solution to the astonishing levels of publication. It is tempting to suggest doing this by setting high standards, but we need to remember that science (or any scholarship) is not only done by those at the top, but by a host of others. Indeed, most scientists are journeymen, whose work supports the whole structure.
We need to figure out how to continue to publish legitimate research at legitimate rates without destroying the heart of the research ecosystem.
Finally – you must be a busy person. But what do you get up to in your spare time? Any exciting hobbies or pastimes you want to tell us about?
I come from a family with lots of people in the arts: music, photography, painting. My older brother, a musician, has introduced me to friends as the “white sheep” of the family.
Having musical brothers and a musical mother, I enjoy music a lot. My spouse and I attend quite a few live musical performances. We have season tickets to a concert series (mostly classical and jazz) in Ann Arbor. There is a great venue for acoustic music in town, called The Ark, which is famous in certain circles. We often go to Detroit for other sorts of music. I also like bicycling, either for commuting or for getting out into the countryside.
Travel is fun, especially to visit family. Being the product of a liberal arts education, reading is important to me, both fiction and nonfiction. Finally, I can be a bit obsessive about crossword puzzles, especially the dailies from the New York Times and occasionally the cryptic puzzles from The Guardian.
Interview by Tim Gillett