David Gale, a professor emeritus of mathematics at the University of California, Berkeley, and a puzzle lover who made fundamental contributions to economics and game theory, died March 7 at Alta Bates Medical Center in Berkeley following a heart attack. He was 86.

Gale, a resident of Berkeley and of Paris, France, applied his life-long love of mathematics and of problem solving to make discoveries that have been applied broadly within economics and operations research. His work has also had far-reaching implications for pure mathematics and for computer science.

"David was known for his elegance, which is a term of honor for math arguments that go directly to the point, that are simple, and, to our community, are beautiful," said one of Gale's former students, Joel Sobel, a professor of economics at UC San Diego.

Gale's 1960 book, "The Theory of Linear Economic Models," is a widely used reference work on linear optimization that brought to a broad audience ideas developed by Gale and his co-authors in the 1950s, according to Sobel. In recognition of this work on the theory of optimization, Gale shared the 1980 John von Neumann Theory Prize with Harold W. Kuhn and Albert W. Tucker. According to the prize citation, "Their research played a seminal role in laying the foundations of game theory, linear and non-linear programming - work that continues to be of fundamental importance to modern operations research and management science."

Sobel noted that the school systems of New York and Boston now match students with schools using procedures that are intellectual descendents of research Gale completed with Lloyd S. Shapley, now professor emeritus of economics at UCLA. This research involved the so-called stable matching or stable marriage problem. Gale and Shapley proved that, given an equal number of men and women who rank one another in terms of romantic interest, it is possible to pair them in marriage such that no two people would rather be married to each other than to their partners. The researchers also provided an algorithmic procedure to find a stable marriage. Gale and Shapley's theoretical work on this problem legitimized a procedure used to match newly graduated doctors to hospital residency programs.

David's "intellectual depth, originality of insight, and thorough liveliness were apparent from the beginning and have remained a source of joy and inspiration to all of us. His life's influence is a permanent heritage," wrote Kenneth Arrow, professor emeritus of economics at Stanford University and 1972 winner of the Nobel Prize in economics.

In a note to Gale's family, Harvard University economics professor Alvin Roth wrote that Gale "has had a giant influence in economics as well as in mathematics" and mentioned that he had nominated Gale and Shapley to the Nobel Committee for Economics. He added, "it was past time that David and Lloyd share that award. I'm sorry that this now won't happen. But David's work will be remembered for generations to come, in books and journal articles and seminars and workshops, as well as in the very concrete allocation procedures that have been built upon his insights."

According to Sylvia Nasar's 1998 book "A Beautiful Mind," Gale was one of the first people to recognize the significance of John Nash's concept of game-theoretic equilibrium. She wrote that Nash credited Gale, then an instructor at Princeton University, as being partly responsible for the simplicity of the proof of the theorem for which Nash shared the 1994 Nobel prize in economic sciences. That prize was awarded for "analysis of equilibria in the theory of non-cooperative games."

Gale also was an early contributor to general equilibrium theory and solved the Ramsey problem of optimal growth theory.

"He thought math was beautiful, and he wanted people to understand that," said his daughter, Katharine Gale. "But he was emphatic that the way for people to get the beauty and elegance of mathematics was to engage in it, not just be told about it."

She recalled that her father would discuss his mathematical work at the dinner table and share with his children his fascination with chess puzzles, card games, puzzle blocks and interlocking puzzles, as well as with all types of math games. Throughout his life, Gale would insist that visitors look at the newest puzzle he was working on. According to his daughter, just before his death, Gale e-mailed a colleague to discuss the mathematics of Sudoku, a popular game where players place numbers on a nine-by-nine grid.

Gale invented his own games, including Bridg-It, also known as the "Game of Gale," and Chomp, which can be played with a bar of chocolate.

About 30 years ago, Gale became convinced that the world needed a hands-on math museum, and he constructed at home some of his own rudimentary exhibits and puzzles out of bicycle chains, rubber and wood to demonstrate principles of mathematics and geometry, Katharine Gale said.

Although he eventually dropped the museum idea, saying it was too large an undertaking, David Gale developed an equivalent on the Internet in 2003 with $40,000 from the Sloan Foundation. MathSite (http://mathsite.math.berkeley.edu), which he promoted as "an interactive source for seeing, hearing, doing mathematics," received the 2007 Pirelli International Award for multimedia communication of mathematics, beating out several well-funded competitors, according to Gale's longtime partner, Sandra M. Gilbert, a feminist poet and professor emerita of English at UC Davis.

After his retirement from teaching, Gale began writing a recreational math column in the magazine Mathematical Intelligencer. He collected these columns in his 1998 book, "Tracking the Automatic Ant and Other Mathematical Explorations."

He was internationally known as a wonderful mentor. Colleague Gabrielle Demange of L'École des Hautes Études en Sciences Sociales in Paris wrote to the family that Gale "was so kind with young people, with no a priori (assumptions) about their capacities. He was so easy to reach."

Another admiring colleague, mathematician Marilda Sotomayor of the Universidade São Paulo in Brazil, arranged "Gale's Feast," a celebration of his career, that was held last summer at the annual International Summer Festival on Game Theory at the State University of New York in Stony Brook and edited a collection of Gale's papers that will be published later this year.

Gale was born Dec. 13, 1921, in Manhattan and grew up in and around New York City. He attended Swarthmore College and graduated with a B.A. in 1943, obtained an M.A. from the University of Michigan in 1947, and earned his Ph.D. from Princeton in 1949.

After a year-long stint as an instructor at Princeton, he joined the Brown University mathematics department in 1950, where he remained until 1965 except for a year sabbatical at the RAND Corp. in Santa Monica, Calif. Following a year-long Miller Professorship at UC Berkeley, he was appointed a full professor in both mathematics and operations research in 1966. He also was appointed to the economics faculty in 1967.

Gale was elected to the National Academy of Sciences in 1983, received the Lester Ford Prize in 1980 and was named a fellow of the Econometric Society, the Center for Advanced Study in Behavioral Sciences and the American Academy of Arts and Sciences. He received a second Miller Professorship in 1971; a Fulbright Research Fellowship in Denmark in 1953, where he met his former wife Julie. B. Skeby, who died earlier this year; and two Guggenheim Fellowships, in 1962 and 1981.

Apart from his love of puzzles, Gale was an avid skier, tennis player, traveler and jazz aficionado.

"David was a passionate traveler, but especially in Paris, where he long had an office at the ancient École Polytechnique," said Gilbert, who in her 2000 book of collected poems, "Kissing the Bread," included a section of poems she wrote for Gale called "When She Was Kissed By The Mathematician." "He loved to explore the city, savoring the subtleties of jazz and French cuisine. It was a privilege to learn from him."

In addition to Gilbert, Gale is survived by three daughters, Kirsten Gale Cutler of Santa Rosa, Calif., Karen Gale of Sacramento, Calif., and Katharine Gale of Berkeley; and a sister, Ellen Dunning of Peabody, Mass.

By Robert Sanders, Media Relations, 18 March 2008

Gale, a resident of Berkeley and of Paris, France, applied his life-long love of mathematics and of problem solving to make discoveries that have been applied broadly within economics and operations research. His work has also had far-reaching implications for pure mathematics and for computer science.

"David was known for his elegance, which is a term of honor for math arguments that go directly to the point, that are simple, and, to our community, are beautiful," said one of Gale's former students, Joel Sobel, a professor of economics at UC San Diego.

Gale's 1960 book, "The Theory of Linear Economic Models," is a widely used reference work on linear optimization that brought to a broad audience ideas developed by Gale and his co-authors in the 1950s, according to Sobel. In recognition of this work on the theory of optimization, Gale shared the 1980 John von Neumann Theory Prize with Harold W. Kuhn and Albert W. Tucker. According to the prize citation, "Their research played a seminal role in laying the foundations of game theory, linear and non-linear programming - work that continues to be of fundamental importance to modern operations research and management science."

Sobel noted that the school systems of New York and Boston now match students with schools using procedures that are intellectual descendents of research Gale completed with Lloyd S. Shapley, now professor emeritus of economics at UCLA. This research involved the so-called stable matching or stable marriage problem. Gale and Shapley proved that, given an equal number of men and women who rank one another in terms of romantic interest, it is possible to pair them in marriage such that no two people would rather be married to each other than to their partners. The researchers also provided an algorithmic procedure to find a stable marriage. Gale and Shapley's theoretical work on this problem legitimized a procedure used to match newly graduated doctors to hospital residency programs.

David's "intellectual depth, originality of insight, and thorough liveliness were apparent from the beginning and have remained a source of joy and inspiration to all of us. His life's influence is a permanent heritage," wrote Kenneth Arrow, professor emeritus of economics at Stanford University and 1972 winner of the Nobel Prize in economics.

In a note to Gale's family, Harvard University economics professor Alvin Roth wrote that Gale "has had a giant influence in economics as well as in mathematics" and mentioned that he had nominated Gale and Shapley to the Nobel Committee for Economics. He added, "it was past time that David and Lloyd share that award. I'm sorry that this now won't happen. But David's work will be remembered for generations to come, in books and journal articles and seminars and workshops, as well as in the very concrete allocation procedures that have been built upon his insights."

According to Sylvia Nasar's 1998 book "A Beautiful Mind," Gale was one of the first people to recognize the significance of John Nash's concept of game-theoretic equilibrium. She wrote that Nash credited Gale, then an instructor at Princeton University, as being partly responsible for the simplicity of the proof of the theorem for which Nash shared the 1994 Nobel prize in economic sciences. That prize was awarded for "analysis of equilibria in the theory of non-cooperative games."

Gale also was an early contributor to general equilibrium theory and solved the Ramsey problem of optimal growth theory.

"He thought math was beautiful, and he wanted people to understand that," said his daughter, Katharine Gale. "But he was emphatic that the way for people to get the beauty and elegance of mathematics was to engage in it, not just be told about it."

She recalled that her father would discuss his mathematical work at the dinner table and share with his children his fascination with chess puzzles, card games, puzzle blocks and interlocking puzzles, as well as with all types of math games. Throughout his life, Gale would insist that visitors look at the newest puzzle he was working on. According to his daughter, just before his death, Gale e-mailed a colleague to discuss the mathematics of Sudoku, a popular game where players place numbers on a nine-by-nine grid.

Gale invented his own games, including Bridg-It, also known as the "Game of Gale," and Chomp, which can be played with a bar of chocolate.

About 30 years ago, Gale became convinced that the world needed a hands-on math museum, and he constructed at home some of his own rudimentary exhibits and puzzles out of bicycle chains, rubber and wood to demonstrate principles of mathematics and geometry, Katharine Gale said.

Although he eventually dropped the museum idea, saying it was too large an undertaking, David Gale developed an equivalent on the Internet in 2003 with $40,000 from the Sloan Foundation. MathSite (http://mathsite.math.berkeley.edu), which he promoted as "an interactive source for seeing, hearing, doing mathematics," received the 2007 Pirelli International Award for multimedia communication of mathematics, beating out several well-funded competitors, according to Gale's longtime partner, Sandra M. Gilbert, a feminist poet and professor emerita of English at UC Davis.

After his retirement from teaching, Gale began writing a recreational math column in the magazine Mathematical Intelligencer. He collected these columns in his 1998 book, "Tracking the Automatic Ant and Other Mathematical Explorations."

He was internationally known as a wonderful mentor. Colleague Gabrielle Demange of L'École des Hautes Études en Sciences Sociales in Paris wrote to the family that Gale "was so kind with young people, with no a priori (assumptions) about their capacities. He was so easy to reach."

Another admiring colleague, mathematician Marilda Sotomayor of the Universidade São Paulo in Brazil, arranged "Gale's Feast," a celebration of his career, that was held last summer at the annual International Summer Festival on Game Theory at the State University of New York in Stony Brook and edited a collection of Gale's papers that will be published later this year.

Gale was born Dec. 13, 1921, in Manhattan and grew up in and around New York City. He attended Swarthmore College and graduated with a B.A. in 1943, obtained an M.A. from the University of Michigan in 1947, and earned his Ph.D. from Princeton in 1949.

After a year-long stint as an instructor at Princeton, he joined the Brown University mathematics department in 1950, where he remained until 1965 except for a year sabbatical at the RAND Corp. in Santa Monica, Calif. Following a year-long Miller Professorship at UC Berkeley, he was appointed a full professor in both mathematics and operations research in 1966. He also was appointed to the economics faculty in 1967.

Gale was elected to the National Academy of Sciences in 1983, received the Lester Ford Prize in 1980 and was named a fellow of the Econometric Society, the Center for Advanced Study in Behavioral Sciences and the American Academy of Arts and Sciences. He received a second Miller Professorship in 1971; a Fulbright Research Fellowship in Denmark in 1953, where he met his former wife Julie. B. Skeby, who died earlier this year; and two Guggenheim Fellowships, in 1962 and 1981.

Apart from his love of puzzles, Gale was an avid skier, tennis player, traveler and jazz aficionado.

"David was a passionate traveler, but especially in Paris, where he long had an office at the ancient École Polytechnique," said Gilbert, who in her 2000 book of collected poems, "Kissing the Bread," included a section of poems she wrote for Gale called "When She Was Kissed By The Mathematician." "He loved to explore the city, savoring the subtleties of jazz and French cuisine. It was a privilege to learn from him."

In addition to Gilbert, Gale is survived by three daughters, Kirsten Gale Cutler of Santa Rosa, Calif., Karen Gale of Sacramento, Calif., and Katharine Gale of Berkeley; and a sister, Ellen Dunning of Peabody, Mass.

By Robert Sanders, Media Relations, 18 March 2008