The National Academy of Sciences (NAS) has honored 17 individuals with awards in recognition of their extraordinary scientific achievements in a wide range of fields spanning the physical, biological, and social sciences. Of the 17 chosen, four are Harvard faculty members:Michael J. Hopkins, professor of mathematics, is the recipient of the NAS Award in Mathematics. Hopkins is being honored for his research in algebraic topology, a field that studies algebraic invariants of the shape of continuous subsets in higher dimensional space. Hopkins has established important connections between algebraic topology and other areas of mathematics, and has contributed to the solution of a long-standing problem on the Kervaire invariant. Established by the American Mathematical Society in commemoration of its centennial, the award consists of a $5,000 prize for excellence of research in the mathematical sciences published within the past 10 years.Andrew H. Knoll, Fisher Professor of Natural History in the Department of Organismic and Evolutionary Biology, is the recipient of the Mary Clark Thompson Medal. Knoll is being recognized for his unparalleled contributions relating Precambrian life to Earth’s physical and chemical history and for innovative contributions on the paleophysiology and evolution of algae and angiosperms. Established in 1919, the Mary Clark Thompson Medal honors important services to geology and paleontology and is presented with a $15,000 prize.Jonathan B. Losos, the Monique and Philip Lehner Professor for the Study of Latin America and curator of herpetology in the Museum of Comparative Zoology at Harvard, is the recipient of the Daniel Giraud Elliot Medal. Losos is recognized for his novel and penetrating evolutionary studies of adaptive radiation in vertebrates, notably his comprehensive study of Anolis lizards in tropical America, as summarized in his recent book, “Lizards in an Evolutionary Tree: Ecology and Adaptive Radiation of Anoles.” Established by a gift from Margaret Henderson Elliot in 1917, the Elliot Medal recognizes “a most meritorious, recently published work in zoology or paleontology.” The medal is given every four years and carries an award of $15,000.Jason P. Mitchell, John L. Loeb Associate Professor of the Social Sciences in the Department of Psychology, will receive the Troland Research Award. Mitchell is being recognized for his insightful use of neuroimaging and behavioral methods to enrich our understanding of how people infer the thoughts, feelings, and opinions of others. This $50,000 research award is given annually to recognize unusual achievement by young investigators and to further empirical research within the broad spectrum of experimental psychology.