Richard K. Lashof, who helped transform the field of geometric and differential topology into an important mathematical force in the second half of the 20th century, died Feb. 4 at his home in Alameda, Calif., after an eight-month illness. He was 87.
Lashof, a Professor Emeritus in Mathematics at the University of Chicago, collaborated with some of the greatest mathematicians of his day. "He was the key figure in sustaining the Chicago Mathematics Department as an international center for research and the training of topologists, many dozens of whom were to go on to pursue successful research careers at other leading universities," said Melvin Rothenberg, UChicago Professor Emeritus in Mathematics.
Topologists investigate the features and properties of objects that don't change when bent or stretched. The relationship between classical geometry and topology is mathematically deep and fundamental, Rothenberg said. "Many central and historic questions and unsolved problems, such as the Poincar'e Conjecture, a hundred-year-old problem that was solved in the last decade, are best viewed in this light."
The roots of geometric and differential topology go back to the work of the Swiss mathematician Leonhard Euler (1707-1783), and Jules Henri Poincar'e (1854-1912). The subject enjoyed a renaissance during the second half of the 20th century following a series of fundamental breakthroughs by a variety of mathematicians, Rothenberg said.
In building upon these breakthroughs, Lashof and his collaborators, along with many other mathematicians, "transformed the subject into one of the most significant and dynamic mathematical areas of the last 60 years," he said.
Among Lashof's collaborators were former UChicago Mathematics Professor S.S. Chern, recipient of the 1975 National Medal of Science; and Stephen Smale, Professor Emeritus in Mathematics at the University of California, Berkeley. Smale, a former Mathematics Instructor at UChicago, received the Fields Medal, the highest honor in mathematics, in 1966.
Rothenberg lauded Lashof as an outstanding and inspiring teacher and collaborator. "He was certainly my major mathematical influence, and the most exciting and fruitful period of my mathematics research were the years we spent working together."
Lashof was born Nov. 9, 1922 in Philadelphia. He received his bachelor's degree in chemical engineering from the University of Pennsylvania in 1943, then served as a communications officer in the U.S. Navy from 1943 to 1946. He earned his doctoral degree in mathematics from Columbia University in 1954.
He married Joyce Cohen Lashof on June 11, 1950 in Philadelphia. Joyce Lashof, who survives him, in 1973 became the first woman to head the Illinois Department of Public Health. She also headed the department of preventive medicine at Rush Presbyterian-St. Luke's Medical Center in Chicago, and served on the faculty at UChicago's Pritzker School of Medicine. She also is former dean of the School of Public Health at the University of California, Berkeley, the first female dean of a professional school at Berkeley.
Richard Lashof joined the UChicago faculty as an instructor in 1954. The National Science Foundation awarded him a senior postdoctoral fellowship in 1959. He was a member of the Institute for Advanced Study in Princeton, N.J., in 1960-61. He received UChicago's Quantrell Award for Excellence in Undergraduate Teaching in 1963.
He worked up the academic ranks to professor in 1964 and served as Mathematics Department chairman from 1967 to 1970. He directed the National Science Foundation Summer Institute for Inner City High School Students that was based at UChicago in 1964-65. The program brought in 160 sophomores and juniors from schools near the University that had high dropout rates and below-average achievement test scores.
In 1974, Lashof participated in the University's 28th annual Latke-Hamentash Debate, the traditional and still continuing comic face-off over the relative merits of the two delicacies of Jewish cuisine. He retired in October 1988.
In addition to his wife, Joyce, Lashof is survived by three children: Judith, Carol and Daniel; and six grandchildren: Elisabeth, Erica, Matthew, Samuel, Robin and SuMa. Family and friends will celebrate his life at a gathering scheduled for Saturday, April 3, at the Cardinal Point senior residential community in Alameda, Calif.
—Prof. Kunle Odunsi
