Recipient of the 2017 Leroy P. Steele Prize for Lifetime Achievement, Jim Arthur has had an illustrious career, spread out over almost ﬁve decades, and has contributed in a profound manner to our understanding of the theory of automorphic forms. This tribute has colleagues and associates offering remembrances and assessments of his lifetime of achievements.
A common theme in mathematics is to study a particular mathematical structure and attempt to classify all instances of it. In 1981 a project to classify all of the finite simple groups appeared to be nearing its conclusion, while a plan to write a series of volumes that would contain the complete proof of this Classification Theorem began to take shape. Ronald Solomon provides a progress report on this monumental project.
The Langlands Program envisions deep links between arithmetic and analysis, and uses constructions in arithmetic to predict maps between spaces of functions on diﬀerent groups. The conjectures have shaped research for many years, and the richness of Langlands’ fundamental idea continues to expand.
Claude L. Schochet discusses how the irrational rotational C*-algebra arises in nature and how K-theory is used to get information out of it.
Bo’az Klartag and Elisabeth Werner describe four related open problems in asymptotic geometric analysis.
The latest report on the Conference Board of the Mathematical Sciences (CBMS) Survey was released in May, and it is brimming with both global and fine-grain information about undergraduate programs in the mathematical sciences throughout the US.
In computer science, formal methods are used to specify, develop, and verify hardware and software systems. Such methods hold great promise for mathematical discovery and verification of mathematics as well.
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Brendan Larvor reviews Roi Wagner's Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice.
The Norwegian Academy of Science and Letters has awarded the Abel Prize for 2018 to Robert P. Langlands of the Institute for Advanced Study, Princeton, “for his visionary program connecting representation theory to number theory.”
The prize citation reads in part: “The Wolf Foundation Prize for Mathematics in 2018 will be awarded to Professors Alexander Beilinson and Vladimir Drinfeld...for their groundbreaking work in algebraic geometry, in mathematical physics, and in representation theory..."