Over the course of Mathematical Reviews’ 75-year history, there have been many famous researchers who were also active reviewers. As pointed out by Norman Richert in his article Mathematical Reviews Celebrates 75 Years, the first issue of *Mathematical Reviews* (in January 1940) had some prominent mathematicians as reviewers, including: Lars Ahlfors, Richard Courant, Paul Erdős, Einar Hille, Alston S. Householder, D. H. Lehmer, Saunders Mac Lane, George Pólya, and John von Neumann. The complete roster is here. Fortunately for *Mathematical Reviews,* many prominent mathematicians have written reviews – sometimes a lot of reviews – over the years. This post lists some award-winning mathematicians and gives links to their reviews.

*Fields Medalists*

Medalist |
# of Reviews |

Michael Francis ATIYAH | 229 |

Pierre-Louis LIONS | 218 |

Lars Valerian AHLFORS | 170 |

Laurent SCHWARTZ | 100 |

Cédric VILLANI | 98 |

Gerd FALTINGS | 76 |

Jean BOURGAIN | 40 |

Alain CONNES | 25 |

Vaughan F.R. JONES | 24 |

Heisuke HIRONAKA | 24 |

Terence TAO | 15 |

Efim ZELMANOV | 15 |

John Willard MILNOR | 12 |

There are many fine examples of reviews by Fields Medalists. They vary greatly in length. Atiyah, for instance, was capable of getting to the essence of a paper in a few sentences. Other times, he gave details, such as in his review of Bott’s paper on the Borel-Weil-Bott theorem. His review of the paper by Kodaira, Nirenberg, and Spencer on deformations of complex structures is telegraphic. A surprising number of the reviews by Lions are just one, two, or three sentences, but still get the job done: 1, 2, 3. Villani’s review of Golse and Saint-Raymond’s paper on the Navier-Stokes limit of the Boltzmann equation verges on being a short course. Sometimes the important point is not what’s in the paper: Vaughan Jones reviews a paper by Uffe Haagerup, telling us what is *not* used in the paper (automorphisms).

*Abel Prize Winners*

Year |
Laureate |
# of reviews |

2004 | Michael Atiyah | 229 |

2007 | Srinivasa Varadhan | 105 |

2009 | Mikhail Gromov | 101 |

2005 | Peter Lax | 60 |

2010 | John Tate | 29 |

2015 | Louis Nirenberg | 23 |

2011 | John Milnor | 12 |

Many of these prominent mathematicians wrote reviews of papers by other prominent mathematicians, such as Lax’s review of a paper by Gȧrding or Tate’s review of a paper by Iwasawa. But John Milnor wrote a review of one of Don Porter’s only three papers.

*Winners of Other Prizes*^{(1)}

Abdus Salam, who won the Nobel Prize in Physics in 1979, wrote over 100 reviews. For instance, he wrote the review of the original (1954) paper by Yang and Mills that gave us Yang-Mills theory. His review is a bit brief, and didn’t point out the amazing consequences this would have. However, few others recognized the value of this paper before 1960. In 1972, t’Hooft and Veltman worked out the renormalization for Yang-Mills, which gave the theory a push and helped to earn t’Hooft and Veltman a Nobel Prize.

Subramanyan Chandrasekhar, who won the Nobel Prize in Physics in 1983 wrote a lot of reviews. His first review was in the second volume of *Mathematical Reviews* on a paper (in German) by Walter Fricke.

Peter Higgs, who won the Nobel Prize in Physics in 2013, wrote roughly 100 reviews. Higgs is famous for his work on particle physics. Yet he wrote plenty of reviews of papers on general relativity, for instance reviews of at least ten papers by Charles Misner, beginning with this paper.

##### (1) It is probably only in a blog about mathematics that Nobel Prizes would be described as “other prizes”.

### Become a reviewer!

You don’t need to be a Fields Medalist, an Abel Prize Laureate, or a Nobel Laureate to write reviews. The minimum requirement is that you are mathematically active. To find out more, you can read Reviewing for Mathematical Reviews, by Michael A. Jones, published in *MAA Focus*. We also have a Guide for Reviewers, which gets into the details. If you are interested in becoming a reviewer, contact us at mathrev@ams.org. We will be glad to hear from you, and you will be keeping very good company.