Andrew Gleason in Black and White

Found Film Offers Glimpse of Department Past

It was a business-as-usual day in the fall of 2022 when a small but meaningful piece of department history was unearthed while cleaning out a third- floor office in the Harvard Science Center. A heavy, brown case sat innocuously on a shelf, safekeeping a 16mm black-and-white film shot in 1966. On it, Harvard professor emeritus Andrew Gleason gives an hour-long lecture about nim—a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles—and other oriented-graph games. More than a recording of an old lecture, the film is a time capsule. Frame by frame, it brings to life a mathematician who left an indelible mark on our department, made fundamental contributions to widely varied areas of mathematics, and was a leader in reform and innovation in mathematical pedagogy at all levels of education.

Department staff and faculty quickly took steps to preserve the film. This included procuring the services of a company that specializes in scanning motion picture film to digital files, Gamma Ray Digital. After a closer look, company president Perry Paolantonio identified it as a kinescope. “In the early days of television and before videotapes, they had to come up with a way to preserve live television broadcasts,” Paolantonio said. “A kinescope is a specialized film camera that’s pointed at a cathode- ray tube (CRT) display and records the video image to film.”

Our particular film was shot in a lecture hall using several video cameras routed into a switcher to cut between cameras. The effect of one angle cutting to another is accomplished live in the switcher during the lecture. The kinescope would have recorded the output of that switcher directly to our film.

That film was meant to be viewed in a dark room and was engineered with the human vision system in mind. It contains a lot more information than some scanners are able to pick up as its dynamic range is greater than most digital sensors. The scanner Gamma Ray Digital used is a very high resolution digital camera designed to capture everything to any of the common media file formats used for digital motion picture work. It helped that the film was in good physical condition, as well, with very little shrinking or warping.

It was also fortunate that it had not succumbed to “vinegar syndrome.” This type of degradation is inherent in the chemical nature of cellulose acetate plastic and its symptoms include a pungent vinegar smell (hence the name), followed eventually by shrinkage, embrittlement, and buckling of the gelatin emulsion. The progress of vinegar syndrome depends largely on storage conditions, but once it begins the process is irreversible and only speeds up as it goes along. The cool, dry conditions of the office in which the film was stored all these decades had spared it that fate, allowing us a glimpse of a mathematician in his prime.

California-born Andrew Gleason graduated Yale University in 1942, only to enlist in the Navy where he served as a cryptanalyst during World War II, cracking Japanese and German codes. He re-enlisted in 1950 and served as a code breaker in the Korean War for three years. His entire academic career, however, was spent at Harvard University, starting in 1946 when he was appointed a Junior Fellow of the Society of Fellows, a select group of young scholars given three year fellowships to pursue their studies without formal requirements. At that time, to be a Fellow meant he could achieve an academic career without having a Ph.D. And indeed, despite all he accomplished throughout his lifetime, Gleason never did pursue a doctoral degree.

Instead, he set about solving Hilbert’s Fifth, a problem that mathematician David Hilbert formulated in 1900. Gleason solved a key aspect of the problem alongside three others, which earned him the Newcomb Cleveland Prize from the American Association for the Advancement of Science in 1952 and respect in the world of mathematicians. Among theoretical physicists and philosophers concerned with the foundations of quantum mechanics, he was famous for Gleason’s theorem, elucidating a key point in quantum logic.

In 1969, Gleason was named the Harvard Hollis Professor of Mathematics and Natural Philosophy, the oldest endowed chair in the sciences in the United States. He became a Senior Fellow of the Society of Fellows in 1977 and chair from 1989 to 1996. Gleason received the Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service, the Mathematical Association of America’s most prestigious award, and served as president of the American Mathematical Society from 1981 to 1982. Despite his impressive list of accomplishments, honors, and awards, Gleason was most well-known among the people closest to him for his love of teaching.

“Anybody who knew Andy knew he was really interested in his students,” said his wife and prominent psycholinguist Jean Berko Gleason, professor emerita in the Department of Psychological and Brain Sciences at Boston University. “He respected them but he also didn’t want them to just learn formulas. He wanted them to understand the underlying principles of mathematics.” It was a well-known fact that Gleason genuinely enjoyed helping other people with math. According to Berko Gleason, he frequently helped his fellow Yale students complete their homework.

Gleason’s interest in the training of mathematicians led him to edit a compendium of three decades of William Lowell Putnam mathematical competition problems. At Harvard, he regularly taught at every level and was always engaged in math curriculum reform. He helped found the Calculus Consortium in 1986, which went on to publish an influential series of calculus reform textbooks for college and high school. Gleason was also the first chairman of the advisory committee that helped define New Math, a unique teaching approach briefly used in the United States during the ‘60s that embraced abstract reasoning and conceptual understanding of the principles of mathematics, and de-emphasized technical computing skills.

Professor emeritus Benedict Gross took Math 55 with Gleason in 1968-69 as an undergraduate student at Harvard, and later had him as his thesis advisor. “He made outstanding contributions to mathematical research and was one of the most talented and committed teachers in the department,” Gross said of his time as Gleason’s student. “His lectures were beautifully organized and he often provided mimeographed hand-written notes. His clarity of thought and his willingness to interact with undergraduates persuaded many of us—myself included—to enter the field of mathematics.”

Gross recalled that after graduating, he didn’t feel quite ready to dedicate himself to mathematics. Gleason advised him to take a year off, which he did on a traveling fellowship. “Once I was ready to return, it was his support that got me into graduate school,” Gross said. “I owe him a very great debt.”

All of this comes through in the man lecturing in black and white all the way from 1966. The film shows someone comprehensible, clear, and to the point, whose formulations carry a scintillating precision delivered with enthusiasm and wide-eyed wonder. “He was a man who never raised his voice and enjoyed mathematics too much to get caught up in fights with people,” Berko Gleason recalled. “When we got married, his mother wrote me a letter telling me how pleased she was that I was getting married and that I would be happy to know that her son was extremely even-tempered.”

You can view the full lecture film here.

This article is a part of the 2022-2023 Harvard Math Newsletter.