Jack Graver likes to tell the story about a vocational aptitude test he took in sixth grade. It asked students which activities they preferred — things like fixing a bicycle, building things or working with people. When the results came back, they said he was best suited to be a teacher.

That gave everyone who knew him a good laugh.

“How the hell is this guy going to teach when he can’t get through his own courses?” Graver recalls them saying.

He was dyslexic before the word was widely known. To his teachers, he was just lazy. Reading and writing were extremely difficult and he failed German four times. A Latin professor even gave him a D and kindly asked him not to come back for the second semester.

This spring, Graver retires from the Department of Mathematics in the College of Arts and Sciences (A&S) after 60 years on the faculty. The “lazy” student who struggled to read and write has authored five books and dozens of research papers spanning multiple mathematical fields. One such paper, originally dismissed as of no practical value, became foundational to algorithm design a decade later. The aptitude test, it turns out, was right.

Finding His Way to Syracuse

Graver grew up in Cincinnati, Ohio, in a working-class family, with no path to college.

After two years in the Navy, he used the G.I. Bill to attend Miami University in Ohio, where he planned to study forestry. A mentor redirected him toward a mathematics major instead and another visiting mathematician took him under his wing. By the time Graver finished his Ph.D. at Indiana University in 1964, his philosophy of teaching was already taking shape.

His first faculty position was a postdoctoral instructorship at Dartmouth. Combinatorics, the field of math related to counting and properties of finite structures, was more active in Canada than in the United States at the time. As it emerged as his specialty, Graver interviewed at the Universities of Alberta and Manitoba. Both offered him positions, but he still opted to interview at Syracuse University.

“This was a very, very friendly place,” he says. “One of the most collegial schools.”

Graver chose Syracuse and has been here ever since.

Working in the Corners

In a document he calls his “Mathematical Obituary,” Graver describes the research philosophy that guided his career with characteristic frankness. Rather than compete with the hotshots of the day who worked on the big, popular problems, he learned to “work in the corners,” that is, find the connections others had walked past.

“I wasn’t setting out to make big changes,” he writes. “I just wanted to understand things better, and the research followed.”

That approach produced a body of work that moved across a variety of mathematical fields — algebraic topology, combinatorics and graph theory, rigidity theory, integer linear programming and, most recently, the combinatorial structure of fullerenes. His 1975 paper “On the Foundation of Integer Linear Programming I” was dismissed by its original referee as interesting but of no practical value. A decade later, as computer memory expanded, it became foundational to algorithm design. He still finds the reversal amusing.

His longest collaboration had been with colleague Mark Watkins. Their textbook “Combinatorics with Emphasis on the Theory of Graphs,” published in 1977 as volume 54 in Springer’s Graduate Texts in Mathematics series, remains a standard reference. Two decades later, the pair produced a second major work together. Graver also co-authored “Combinatorial Rigidity” with Brigitte and Herman Servatius, published by the American Mathematical Society, and wrote “Counting on Frameworks,” an accessible treatment of rigidity theory for the Mathematical Association of America.

Collaboration is a key element to Graver’s career.

“I like working with coauthors,” he says, in part because dyslexia makes solo writing slow and error-prone. He is currently working on another book with a former graduate student.