James H. Bramble, the Cornell professor of mathematics who pioneered new methods in finite element mathematics and partial differential equations, died on July 20 at his home in Austin, Texas. He was 90.

Born in Annapolis, Maryland, on Dec. 1, 1930, Bramble was the son of Charles C. Bramble, a mathematician and the first director of research at Dahlgren Naval Proving Ground. Eventually, James H. Bramble would follow in his fathers steps as an innovative mathematician himself.

James Bramble, the professor’s son, described his father as “thoughtful like a mathematician,” but still caring — a dedicated family man.

“He had a lot of experience as a kid being fun and mischievous, and so he allowed some of that with us,” the younger James said. “He didn’t try to quash that curiosity out of us, he fostered it. And I think that played a big role in producing a dynamic family that had a lot of different interests.”

“He would never really give too much advice, but he was there when we needed him,” James continued. “I was lucky enough to become very close friends with him later in life.”

In 1953, Bramble received a bachelor’s degree from Brown University, followed by a Ph.D. from the University of Maryland in 1958. He then ventured outside academia to work for General Electric and the Naval Ordnance Laboratory.

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Over the course of his career, Bramble was a professor at three universities, beginning at the University of Maryland before coming to Cornell in 1968 and eventually leaving to join Texas A&M University.

“Jim was a builder. Every place he ever worked at … he started and built a group of highly productive faculty working on numerical solutions to differential equations. Throughout his career he was an integral part of an international group working on [infinite element mathematics],” said Prof. Emeritus Stephen Hilbert, mathematics, Ithaca College, and co-author of the Bramble-Hilbert Lemma, Bramble’s major discovery.

Bramble came to Cornell in 1968 recruited by Prof. Larry Payne, applied mathematics, to join an elite group on numerical analysis and finite element mathematics, including mathematics professors Lars Wahlbin and Al Schatz. Bramble became central to his field and his work is still widely cited.

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“The [four] of them really put Cornell on the map in this field … that was one of the centers of this kind of work,” said Prof. Emeritus Richard Falk, mathematics, Rutgers University and one of Bramble’s former advisees. “Cornell was a key place.”

Much of Bramble’s work focused on numerical solutions of partial differential equations, a mathematical tool used to model the behavior of quantities across disciplines like economics and physics, and applied in practices like fracking and weather prediction.

According to Hilbert and Falk, differential equations are usually not solvable in terms of elementary functions that one could write down. Mathematicians know a solution exists, but can’t find an exact formula to calculate the values of the solution. Because of this, they have to find solvable problems that approximate the problem they wish to solve. Bigger problem sets, often solved with computers, should yield a solution that better approximates the actual solution of the real-world problem.

Bramble’s work dealt with the accuracy of those computer algorithms and the relationship between giving more equations to an algorithm and the rate at which accuracy increases. The Bramble-Hilbert Lemma, a mathematical method that he co-authored with Hilbert, was a key step in allowing mathematicians to prove how fast the error between the problem solved by the computer algorithm and the problem in the real world goes to zero.

Hilbert said that the lemma came out of attempts by Bramble and himself to integrate the finite element method, a new method of generating approximations when working with differential equations, with work he had already done on finite differences.

The two mathematicians worked closely together — with Bramble as Hilbert’s doctoral adviser — and Hilbert followed Bramble to Ithaca, working part-time at Ithaca College while completing his dissertation. The pair worked together for many hours each day on equations.

“The first thing about Bramble was that he was definitely a more collaborative type of person than a ‘I go off in the closet and I do great stuff and then I pop out of the closet and say here it is’ type,” Hilbert said.

Bramble was an innovator in the finite element method — which takes a region in which one seeks a solution to a differential equation and subdivides it into smaller shapes to approximate the unknown solution by using simple functions on each piece. In 1970, he helped found the Finite Element Circus, a bi-annual conference where academics discussed new developments in the theory and applications of the finite element method. The conference continues to meet to this day.

“He was very tenacious,” Falk said. “If you want to do research in mathematics you need to be tenacious, because sometimes these things go on a long time and you’re stuck and some people would give up. But the ones who are successful don’t give up, they keep going. He was like that.”

His contributions to Cornell and the field of mathematics were more than theoretical. He edited the journal *Mathematics of Computation* for 25 years and worked as the journal’s chief editor for eight years. He also served on Cornell’s mathematics department as associate chair, director of undergraduate studies and graduate faculty representative, and spent six years as the director of Cornell’s Center for Applied Mathematics.

Bramble also advised 22 doctoral students over his career, including Hilbert.

“When I talked to other graduate students, I [realized that] was very fortunate,” Hilbert said. “A lot of graduate students … would get to see [their] adviser[s] once every two weeks for an hour, and he would say, ‘What do you have for me?’”

“This was much more — we brainstormed, we thought about stuff, we said ‘Let’s look at this, let’s look at that,’” he continued.

Hilbert recalled a particular memory, when he and Bramble were both unable to solve an equation they were working on.

“I remember we both left, we went home and when we came back the next day he said, ‘I’ve got the answer!’ and I said ‘I’ve got the answer!’” Hilbert said.

He recalls that Bramble asked him to show his answer first — not something he would have expected from an adviser other than Bramble — so that he would “know that I had actually solved the problem on my own.”

Outside of the academy, Bramble loved to travel and made friends across the world. He went frequently to Sweden to see the country, visit other mathematicians and, in 1985, receive an honorary doctorate from Chalmers University in Sweden.

Bramble’s colleagues remember him as a fun-loving man, as well as a brilliant and dedicated academic who worked until he was 80, driving two hours from Austin to the Texas A&M campus each week to meet with advisees.

“When I got into math, I was a little nervous … [that] these guys are gonna be a bunch of nerds … but Bramble was always a fun guy to be with,” Hilbert said. “He liked to party, he had lots of friends all over the place.”

Prof. Bramble is survived by his four children, stepson, eight grandchildren and his first wife.