IN MEMORIAM: GERALD E. SACKS, 1933–2019

Abstract

Gerald E. Sacks, age 86, Professor Emeritus of Mathematics at Harvard and M.I.T., passed away at his home in Falmouth, Maine, after a long illness. Sacks was born in Brooklyn and graduated from Brooklyn Technical High School. He initially was an engineering major, but interrupted his college studies at Cornell University to serve in the U.S. Army from 1953 to 1956. After returning to Cornell, he developed an interest in Mathematical Logic and continued his studies in that area, receiving his Ph.D. in 1961 as a student of J. Barclay Rosser. He began his academic career at Cornell University, but moved to M.I.T. in 1966, and later accepted a joint appointment at M.I.T. and Harvard. During his career, he held visiting positions at The Institute for Advanced Study and several prestigious universities. Sacks had a brilliant mind for Mathematics and an abiding curiosity about it. In addition, he had a magnetic personality, and was always a center of attention. He was a captivating speaker, and a witty and deep thinker. His knowledge and interests were broad, covering not only his field of expertise but also the major developments in mathematics as a whole and in the world at large. His interests were varied; he enjoyed reading and had an extensive library, wrote poetry, and was a movie buff with a fantastic recall of highlights of movies. He gave willingly of his time and encouragement to his students, colleagues, and friends, and that encouragement frequently bore fruit. One cannot overestimate the effect he had on his main area of interest, Computability Theory, not only through his innovative work, but also through the work of his more than 30 students and more than 750 mathematical descendents. Sacks began his work in Classical Computability Theory when the field was in its infancy. Kleene and Post had begun the study of degrees of unsolvability, or Turing degrees, and Post the study of the computably enumerable Turing degrees. The results of Friedberg and independently Muchnik (incomparable computably enumerable Turing degrees) and Spector (minimal degrees) stimulated interest in the area. But it was the pioneering work of Sacks in his monograph, Degrees of Unsolvability [1] that generated an exhaustive study of those degrees. Sacks’ work in that monograph covered many aspects of degree theory, and his innovative techniques produced several theorems that bear his name. Moreover, the importance of the results was equalled by the importance of the techniques he introduced. The degrees of unsolvability form an algebraic structure that provides a measure of the complexity of information inherent in an oracle attached