C M Gleason Popular Books

C M Gleason Biography & Facts

Andrew Mattei Gleason (1921–2008) was an American mathematician who made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in math­e­mat­ics teaching at all levels. Gleason's theorem in quantum logic and the Greenwood–Gleason graph, an important example in Ramsey theory, are named for him. As a young World War II naval officer, Gleason broke German and Japanese military codes. After the war he spent his entire academic career at Harvard University, from which he retired in 1992. His numerous academic and scholarly leadership posts included chairmanship of the Harvard Mathematics Department and the Harvard Society of Fellows, and presidency of the American Mathematical Society. He continued to advise the United States government on cryptographic security, and the Commonwealth of Massachusetts on math­e­mat­ics education for children, almost until the end of his life. Gleason won the Newcomb Cleveland Prize in 1952 and the Gung–Hu Distinguished Service Award of the American Mathematical Society in 1996. He was a member of the National Academy of Sciences and of the American Philosophical Society, and held the Hollis Chair of Mathematics and Natural Philosophy at Harvard. He was fond of saying that math­e­mat­ic­al proofs "really aren't there to convince you that something is true‍—‌they're there to show you why it is true." The Notices of the American Mathematical Society called him "one of the quiet giants of twentieth-century mathematics, the consummate professor dedicated to scholarship, teaching, and service in equal measure." Biography Gleason was born on November 4, 1921, in Fresno, California, the youngest of three children; his father Henry Gleason was a botanist and a member of the Mayflower Society, and his mother was the daughter of Swiss-American winemaker Andrew Mattei. His older brother Henry Jr. became a linguist. He grew up in Bronxville, New York, where his father was the curator of the New York Botanical Garden. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, winning a scholarship to Yale University. Though Gleason's mathematics education had gone only so far as some self-taught calculus, Yale mathematician William Raymond Longley urged him to try a course in mechanics normally intended for juniors. So I learned first year calculus and second year calculus and became the consultant to one end of the whole Old Campus ... I used to do all the homework for all the sections of [first-year calculus]. I got plenty of practice in doing elementary calculus problems. I don't think there exists a problem‍—‌the classical kind of pseudo reality problem which first and second-year students are given‍—‌that I haven't seen. One month later he enrolled in a differential equations course ("mostly full of seniors") as well. When Einar Hille temporarily replaced the regular instructor, Gleason found Hille's style "unbelievably different ... He had a view of mathematics that was just vastly different ... That was a very important experience for me. So after that I took a lot of courses from Hille" including, in his sophomore year, graduate-level real analysis. "Starting with that course with Hille, I began to have some sense of what mathematics is about." While at Yale he competed three times (1940, 1941 and 1942) in the recently founded William Lowell Putnam Mathematical Competition, always placing among the top five entrants in the country (making him the second three-time Putnam Fellow). After the Japanese attacked Pearl Harbor during his senior year, Gleason applied for a commission in the US Navy, and on graduation joined the team working to break Japanese naval codes. (Others on this team included his future collaborator Robert E. Greenwood and Yale professor Marshall Hall Jr.) He also collaborated with British researchers attacking the German Enigma cipher; Alan Turing, who spent substantial time with Gleason while visiting Washington, called him "the brilliant young Yale graduate mathematician" in a report of his visit. In 1946, at the recommendation of Navy colleague Donald Howard Menzel, Gleason was appointed a Junior Fellow at Harvard. An early goal of the Junior Fellows program was to allow young scholars showing extraordinary promise to sidestep the lengthy PhD process; four years later Harvard appointed Gleason an assistant professor of mathematics, though he was almost immediately recalled to Washington for cryptographic work related to the Korean War. He returned to Harvard in the fall of 1952, and soon after published the most important of his results on Hilbert's fifth problem (see below). Harvard awarded him tenure the following year. In January 1959 he married Jean Berko whom he had met at a party featuring the music of Tom Lehrer. Berko, a psycholinguist, worked for many years at Boston University. They had three daughters. In 1969 Gleason took the Hollis Chair of Mathematics and Natural Philosophy. Established in 1727, this is the oldest scientific endowed professorship in the US. He retired from Harvard in 1992 but remained active in service to Harvard (as chair of the Society of Fellows, for example) and to mathematics: in particular, promoting the Harvard Calculus Reform Project and working with the Massachusetts Board of Education. He died on October 17, 2008 from complications following surgery. Teaching and education reform Gleason said he "always enjoyed helping other people with math"‍—‌a colleague said he "regarded teaching mathematics‍—‌like doing mathematics‍—‌as both important and also genuinely fun." At fourteen, during his brief attendance at Berkeley High School, he found himself not only bored with first-semester geometry, but also helping other students with their homework‍—‌including those taking the second half of the course, which he soon began auditing. At Harvard he "regularly taught at every level", including administratively burdensome multisection courses. One class presented Gleason with a framed print of Picasso's Mother and Child in recognition of his care for them. In 1964 he created "the first of the 'bridge' courses now ubiquitous for math majors, only twenty years before its time." Such a course is designed to teach new students, accustomed to rote learning of mathematics in secondary school, how to reason abstractly and construct mathematical proofs. That effort led to publication of his Fundamentals of Abstract Analysis, of which one reviewer wrote: This is a most unusual book ... Every working mathematician of course knows the difference between a lifeless chain of formalized propositions and the "feeling" one has (or tries to get) of a mathematical theory, and will probably agree that helping the student to reach that "inside" view is the ultimate goal of mathematical education; but he will usually give up any attempt at .... Discover the C M Gleason popular books. Find the top 100 most popular C M Gleason books.