Born in Cornwall, Ontario, he moved to Winnipeg a few years later. He received a Bachelor of Science from the University of Winnipeg in 1946. He received a Master of Science in 1947 and Ph.D. in Mathematics in 1950 from the University of Chicago.

Divinsky served as a mathematics professor, and also as an assistant dean of science, at the University of British Columbia. He was also featured in many segments relating to mathematics and chess on the Discovery Channel Canada program @discovery.ca, now called Daily Planet. During the first two seasons of the show, he presented a weekly contest segment emphasizing math puzzles.

Divinsky has served on the Vancouver School Board, and as analderman on Vancouver's city council.

Divinsky tied for 3rd-4th places in the Closed Canadian Chess Championship, Toronto 1945, with 9.5/12, along with John Belson; the joint winners were Daniel Yanofsky and Frank Yerhoff at 10.5/12. In the 1951 Closed Canadian Chess Championship, held at Vancouver, Divinsky scored 6/12 to tie for 5th-7th places. He represented Canada twice at the Chess Olympiads, in 1954 at Amsterdam (second reserve board, 0.5/1), and in 1966 at Havana (second reserve board, 4.5/8). He served for 15 years, from 1959-1974, as editor of the magazine Canadian Chess Chat. He has played an important role in chess organization in Canada since the 1950s. He first became Canada's representative to FIDE (the World Chess Federation), in 1987, served again in this post in the mid-2000s, and is a member of the Canadian Chess Hall of Fame.

He has also written several books on chess (see bibliography below). Chess historian Edward Winter in a 1992 review was very critical of Divinsky's The Batsford Chess Encyclopedia, calling it "A Catastrophic Encyclopedia". In 2008, Winter selected it as one of the five worst chess books in English from the past two decades. His 1989 review of Divinsky and Raymond Keene's book Warriors of the Mind was also negative.

Divinsky met Kim Campbell, 22 years younger, while she was an undergraduate student at the University of British Columbia in the late 1960s. Their relationship continued while Campbell did graduate work at the London School of Economics, and the two were married in 1972. Divinsky was involved with administration at UBC, was a member of the Vancouver School Board, and was an influence in interesting Campbell in political activity. The two divorced in 1983; their marriage produced no children.