Samuel Karlin was born in Yonova, Poland in 1924. His family, who were Orthodox Jews, emigrated to Chicago while he was still a small child. Karlin's early years in the USA were during the Great Depression, during which the family suffered financially. He abandoned religion in his early teens, and recalled later how first walking down the street without a yarmulke on his head was a milestone in his life.
Karlin took his first degree at the Illinois Institute of Technology, and his doctorate at Princeton University in 1947. His supervisor was Salomon Bochner, one of the great mathematical analysts of the last century. Bochner and Karlin had several traits in common: great mathematical ability, wide interests, Jewishness and a combative personality.
Karlin's thesis topic was on pure mathematics, in spaces of infinitely many dimensions. He married in 1947, and continued this line of work at the California Institute of Technology. Finding that he needed a second job for financial reasons, he also worked as a consultant at the RAND Corporation, then sponsored by the US Air Force and engaged in strategic planning for the Cold War. The new problems and contacts at RAND and his teaching duties at Cal Tech combined to turn Karlin from a pure mathematician working on abstract problems into an applied mathematician of very broad range.
The theory of games, recently developed by John von Neumann (1903-1957), was exactly what was needed for Karlin's work at RAND on modelling of conflict. Much of his work during the Forties and Fifties was on game theory; this culminated in the publication of Karlin's two-volume book Mathematical Methods and Theory in Games, Programming and Economics in 1959.
Game theory is closely linked to statistical decision theory, and Karlin had become interested in probability and statistics through sharing an office at RAND with David Blackwell. This led later on to his two influential books with Howard M. Taylor on stochastic processes, in 1966 and 1981, and a third on stochastic modelling in 1984.
Consultancy at RAND also led to contact with Kenneth J. Arrow (later to win the Nobel prize in economics, in 1972). With Arrow, he worked on a variety of optimisation problems in economics, operations research and management science. This led to his book Studies in the Mathematical theory of Inventory and Production in 1958, with Arrow and Herbert Scarf. Arrow's influence also led to Karlin's move to Stanford University in 1956, as a professor of mathematics and statistics; he was to remain in Stanford for the rest of his career.
Karlin's closest Stanford colleague was James L. McGregor, with whom he wrote many papers, most on the application of probability theory to problems in the life sciences. His shift of emphasis to biological problems was because this turned out to be the natural area of application for much of Karlin's mathematical work, but was partly accidental: McGregor was a devoted horticulturalist and camellia enthusiast, trying to raise a white camellia flower, which had not then been done.
The two great biological advances of the nineteenth century, Darwinian evolution and Mendelian genetics, were at first thought to be incompatible, but a synthesis was found between them through the work of Wright, Fisher and Haldane in the 1920s. The whole area proved a rich field of application for Karlin's mathematical skills, in the use of probability theory in models of population growth and genetics. The many papers with McGregor on birth and death processes and branching processes were particularly influential. Typically versatile, Karlin applied his work on total positivity, a topic in pure mathematics, to a range of problems in this area. A later interest was genetic epidemiology.
In 1982, Karlin realized that he needed to study DNA and proteins, and threw himself into this new field with characteristic energy and enthusiasm. His main contribution here was the development (with Amir Dembo and Ofer Zeitouni) of the computer programme BLAST (Basic Local Alignment Search Tool), now the most frequently used software in computational biology. It proved a very effective tool in the vast collective endeavour of mapping the human genome, and has been described as "the Google of biological research". So completely did Karlin throw himself into this work that, despite being a great mathematician, he came to think of himself, and describe himself, as a molecular biologist.
Karlin's published output was extraordinary, both in extent -- over 450 papers and (as author or coauthor) 10 books -- and in the range of different areas he worked in. He had 41 doctoral students. He was widely honoured: he was a member of the National Academy of Science and the American Academy of Arts and Sciences, and a Foreign Member of the London Mathematical Society. He received the National Medal of Sciences in 1989.
Karlin and his first wife Elsie had three children, all of whom became scientists -- Kenneth, a professor of chemistry at Johns Hopkins University, Baltimore, Manuel, a doctor in Portland, Oregon, and Anna, a professor of computer science at the University of Washington, Seattle. The marriage ended in divorce. Karlin divided his time from 1970 to 1976 between Stanford and the Weizmann Institute of Science in Rehovot, Israel. There one of his doctoral students was Dorit Carmelli, who later became his second wife.
Karlin had strong opinions, which he expressed robustly; colleagues speak of "a real workaholic, a dominating personality", and of him having "an outgoing personality, to put it mildly". He played tennis, and was a devoted football fan. His daughter recalls him as "the happiest person I have ever known, because he loved what he did so much".
He is survived by his wife, Dorit, his three children and a stepson.
Samuel Karlin, mathematician and molecular biologist, was born on June 8, 1924. He died on December 18, 2007 aged 83