Awarded some of the math world's highest honors, Keller was a professor emeritus of mathematics and of mechanical engineering at Stanford and a longtime member of the Geophysical Fluid Dynamics summer program at the Woods Hole Oceanographic Institution in Woods Hole, Massachusetts.

Known for his remarkable breadth in the physical sciences, the life sciences and engineering, Joe Keller demonstrated the significant impact of mathematics in understanding scientific phenomena and creating solutions for engineering problems. Considered by many as the Dean of Applied Mathematics, he was best known for his Geometrical Theory of Diffraction, a method for describing the propagation, scattering and diffraction of waves, especially as they bend around the edges and corners of an obstacle.

The theory, developed while he was on the faculty at New York University, built on work he had done during and after World War II using sonar to determine the presence and location of submarines and underwater land mines. This required transmitting sound waves through water and measuring and analyzing them as they weakened, bounced off objects and returned in altered form to be detected by a receiver. The theory can be applied whether the waves are acoustic, electromagnetic, elastic or fluid, and has become an indispensable tool for engineers and scientists working on applications such as radar, stealth technology and antenna design.

Keller studied many other issues related to national security, including the possibility that underwater explosions of atomic bombs might cause a tsunami a question that concerned the U.S. government as it prepared to test nuclear devices at Bikini Atoll more than half a century ago.

**The math of the natural world**

Keller's wide-ranging interests and gift for finding the mathematical essence of problems allowed him to contribute to many fields. He developed and used a mathematical method of approximation known as asymptotic analysis to tackle problems that cannot be solved exactly, and applied it to predict behavior throughout the domains of science. For example, he used the method to describe eigenvalue spectra in quantum mechanics, to develop optimal strategies for runners in a race, to study the propagation of nerve pulses, to model the development of the visual system in mammals such as kittens, and to understand the locomotion of worms and how it differs from that of snakes.

His lectures were paragons of clarity that elucidated mathematical ideas for everyone. For example, in one of his annual Christmas Lectures at NYU, he outlined a method for ranking the strengths of basketball teams that was later reinvented and used to rank webpages by the founders of Google. He drew inspiration from everything and inspired many. At a party, he might explain to a child how tiny soda bubbles assemble and form patterns in a glass, and later discuss the nuances of fluid dynamics or wave propagation with a colleague.

His intellectual curiosity and humor were recognized in two Ig Nobel Prizes for research that makes you laugh and then makes you think. The first of these, in 1999, honored his work explaining why teapots dribble and how to avoid it. The second, in 2012, recognized his discussion of the physical forces that make a jogger's ponytail swing horizontally even though the jogger is oscillating vertically.

"Keller has been an inspiration to generations of mathematicians, and fundamental and applied scientists, Professor Michael I. Weinstein of the Department of Applied Physics and Applied Mathematics at Columbia University said in 2014 when Columbia granted Keller an honorary doctorate. His work is characterized by deep creativity and startlingly elegant formulations with profound impact. This is combined with a sense of playfulness and joy in thinking mathematically about the world."

**Math runs in the family**

Joseph Bishop Keller was born July 31, 1923, in Paterson, New Jersey. His father, Isaac Keiles, was a native of Bialystok who fled Russian pogroms and whose name was changed to Keller at Ellis Island. His mother, Sarah Bishop, emigrated to Paterson as a baby from Hull, England, where her family had landed after similarly leaving Russia. Isaac Keller sold wholesale liquor in Paterson during Prohibition and later owned Keller's Bar and Grill there, while Sarah did the business's bookkeeping and later worked in a dress shop.

A knack for mathematics ran in the family. His younger brother, Herbert B. Keller, was also a noted applied mathematician and a professor at California Institute of Technology. The two worked together early in their careers and remained close throughout their lives. Their father often challenged his sons with mathematical puzzles to solve at the dinner table, they recalled.

Keller graduated from Paterson's East Side High School, where he ran track and competed on the math team. He received his secondary schooling at New York University, earning a BA in 1943, an MS in 1946 and a PhD in 1948. He remained there as a professor of mathematics until 1979, when he joined the Stanford faculty as a professor of mathematics and of mechanical engineering until 1993, when he earned emeritus status.

In 1963, Keller married Evelyn Fox Keller, the scientist and scholar of gender and science. They had two children, Sarah Keller and Jeffrey Keller, and divorced in 1976. He later met Alice Segers Whittemore, a professor of mathematics at Hunter College who was visiting NYU on a fellowship aimed at shifting her focus from pure mathematics to mathematical problems with practical applications in statistics and epidemiology. Keller was the mathematician assigned to oversee her transition into cancer research. The two became life partners, intensely devoted to each other, and moved together to Stanford, where she is currently a professor of epidemiology and biomedical data science at the Stanford School of Medicine.

Joe and Alice balanced their full lives as academics with simple routines and daily pleasures of jogging and cycling, good food, gathering with friends and reading the New York Times and the short stories of Somerset Maugham were among Keller's favorites. Both frugal and systematic, they asked a relative who worked in film to compile a list of recommended movies, and they worked their way through that list, checking the movies out from the Stanford library.

They shared the household duties, including meal preparation and post-dinner cleanup, but he was the one to assign seats to guests at the dinner table. He was very generous and always insisted on paying the tab when going out to dinner. He always closely checked the math on the restaurant bill and had concluded over time that most errors on the bill were in favor of the house.

Keller was a member of the National Academy of Sciences, a Foreign Member of the Royal Society of London and Honorary Professor of Mathematical Sciences at the University of Cambridge. He received some of the world's highest scientific honors, including the Wolf Prize in Mathematics (1997), the Frederick E. Nemmers Prize (1996), the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis (1995), the National Medal of Science (1988), the Timoshenko Medal (1984), the Eringen Medal (1981) and the von Karman Prize (1979). He was the Gibbs Lecturer of the American Mathematical Society (1977) and the von Neumann Lecturer of the Society of Industrial and Applied Mathematics (1983). His work earned him honorary doctorates from eight universities in the United States and Europe.

In awarding him the Wolf Prize in Mathematics, the Wolf Foundation noted that Keller brought a deep understanding of physics and a superb skill at asymptotics to an astonishing range of problems, adding, He is really the model of what a mathematician interested in a wide variety of physical phenomena can and should be.

Keller is survived by his wife, Alice S. Whittemore; his children, Sarah N. Keller of Bozeman, Montana, and Jeffrey M. Keller of Somerville, Massachusetts; stepdaughters Gayle Whittemore of Los Angeles and Margot Palermo of Brook Haven, New York; as well as 10 grandchildren and step-grandchildren, and several nieces and nephews.