... to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the American Mathematical Society in the preceding five years.

... for his paper "A Tale of Two Sieves".

... for their article "A Guide to Entropy and the Second Law of Thermodynamics".

... for their expository paper "Zeroes of zeta functions and symmetry".

... for his enlightening two-part article "Lattices, Linear Codes, and Invariants".

... for their stimulating article "Honeycombs and Sums of Hermitian Matrices".

... for his article "A Brief History of the Classification of the Finite Simple Groups".

... for his article "The Poincare Dodecahedral Space and the Mystery of the Missing Fluctuations".

... for his article "The Riemann Hypothesis"

... for their article "Expander graphs and their applications".

... for his article, "Recent Progress on the Poincaré Conjecture and the Classification of 3-Manifolds".

... for her article, "The Green-Tao Theorem on arithmetic progressions in the primes: An ergodic point of view" (Bull. Amer. Math. Soc. (N.S.) 43 (2006), no. 1, 3 23).

... for his article, "The character table for E8" (Notices of the AMS 54 (2007), no. 9, 1122-1134).

... for his article, "The Markov chain Monte Carlo revolution" (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179 205).

... for their article,  The algebra of grand unified theories (Bulletin Amer. Math. Soc., 47 (2010), no. 3, 483 552).

... for his article, "From Apollonius to Zaremba: Local-global phenomena in thin orbits", which appeared in Bull. Amer. Math. Soc. 50. This article introduces a new field of number theory that has proven to be extremely fruitful, even in shedding light on some ancient problems.

... for their article, "Mysteries in Packing Regular Tetrahedra," which appeared in Notices of the AMS, Volume 59, No. 11, (2012), 1540-1549. The article leads the broad range of Notices readers through the 2000-year history of the subject, including its appearance in 1900 in Hilbert's 18-th problem, into its mathematical heart.

... for his paper "Earth's Carbon Cycle: A Mathematical Perspective", Bulletin of the AMS (2015). He gives the reader an understanding of the Earth's carbon cycle by applying classical ideas from applied mathematics to the data at hand.

... for their article "The Computation of Previously Inaccessible Digits of $\pi^{2}$ and Catalan's Constant," Notices of the AMS, August 2013.

... for his article "A Conceptual Breakthrough in Sphere Packing," published in the February 2017 issue of the Notices of the AMS.

... for "From rational billiards to dynamics on moduli spaces". Bulletin of the AMS. 53: 41–56. 2016.

... for the article "What are Lyapunov exponents, and why are they interesting?", Bulletin of the AMS, Volume 54, January 2017, Pages 79–105

... for the article "The Mathematics of Joan Birman," Notices of the AMS, 66 (2019), 341–353

... for "Five Stages of Accepting Constructive Mathematics". Bulletin of the AMS. 54 (3): 481–498.

... for "Heegaard Floer homology". Notices of the AMS. 68 (1): 19–33.

... for her article "Getting a handle on the Conway knot," Bulletin of the American Mathematical Society, 59 (2021), 19–29

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