### addition

━━ *n.* 付加, 増加, 加算; 付加物; 〔米・カナダ〕 増築部分.

**in addition (to)** （…に）加えて, その上.

**ad・di・tion・al** ━━ *a.* 付加の, 追加の.

## Albert W. Tucker

Extracts from an obituary by Sylvia Nasar in the*New York Times*, 1995-1-27, with a brief addition at the end by Martin J. Osborne.

Albert William Tucker ... was chairman of the mathematics department at Princeton University in the 1950's and 1960's, but effectively presided over it during World War II. ...

An admired teacher, Professor Tucker had a somewhat atypical trajectory that stretched from Princeton's heyday of John von Neumann and Albert Einstein through the Cold War years of military research to the anti-war demonstrations on campus of the early 1970's.

Professor Tucker's best-known work, in which he created the mathematical foundations of linear programming, was the product of a second career in mathematics that did not begin until he was 45 and swamped with wartime work, administrative duties and three boisterous young children.

Linear programming, or operations research, grew out of the logistical problems of the Army and Navy during World War II. It is a handy mathematical tool for maximizing the use of some scares resource. It is now used by the AT&T Corporation to design communications networks, by oil companies to run refineries and by the Navy to route its supply ships.

As a skilled communicator, he solved the problem of explaining game theory to psychology majors at Stanford in 1950 by dreaming up one of the most famous examples in all mathematics: the so-called Prisoners' Dilemma. [MJO: Nasar's claim that the Prisoner's Dilemma is one of the most famous examples in mathematics is surely incorrect. It is, however, a famous example in game theory, without question the most well-known strategic game. Further, Tucker did not "dream it up". The game originated with others; Tucker invented its well-known interpretation.]

It is a story of two criminals confronted with the choice of confessing or denying their crimes. For each, the consequences depend on what the other prisoner decides to do. If they guess right, they can go free. If both guess wrong, they both have the book thrown at them. Dr. Tucker's tale spurred a vast literature in philosophy, biology, sociology, political science and economics.

Mostly, though Dr. Tucker was the intellectual soul of Princeton's mathematics department. Martin Shubik, a professor economics at Yale University, recalled in an essay that the math department under Dr. Tucker was "electric with ideas and the sheer joy of the hunt."

"If a stray 10-year-old with bare feet, no tie, torn blue jeans and an interesting theorem walked into Fine Hall at teatime, someone would have listened," Professor Shubik wrote.

Professor Tucker was the mentor of a remarkable generation of mathematicians, including Ralph Gomory, the former research chief at I.B.M. who is now president of the Sloan Foundation of New York; Marvin Minsky, head of the artificial intelligence program at the Massachusetts Institute of Technology; and Jack Milnor, of the State University at Stony Brook, L.I., a winner of the Fields Medal, mathematics's equivalent of the Nobel Prize. He also trained the first generation of game theorists, including John Forbes Nash, Jr., who won a Nobel Memorial Prize in Economic Science last year.

Students flocked to Dr. Tuckers because of his willingness to back the more independent-minded ones. Dr. Von Neumann for example, disapproved of Dr. Nash's approach to game theory, but Professor Tucker, unfazed by Professor Von Neumann's glamour and prestige, encouraged Dr. Nash to pursue his own ideas. "He was extremely flexible as a thesis adviser and as an adviser in general," Dr. Nash said yesterday.

Dr. Tucker, a son of a high school teacher turned minister, came from a poor family in Ontario, Canada. No prodigy, Professor Tucker has to repeat his senior year of high school to retake the qualifying examination for a provincial scholarship he needed to attend college. After getting a B.A. in 1928 and M.A. in 1929 from the University of Toronto, he went to Princeton as a doctoral student.

As a first-year graduate student at Princeton, he taught calculus for a senior faculty member and protested that the professor was going too fast for his students until, finally, the professor tried to have him removed from the math department. After the dean of the faculty heard the particulars, however, Dr. Tucker was promoted.

After 1945, Professor Tucker never submitted a paper of his own for publication in a journal. He wrote conference papers with students, his son, Alan, said, but "he wanted to leave space in the journals for the next generation."

For example, the well-known Kuhn-Tucker theorem, a basic result in linear programming, never appeared in a journal but rather a volume of conference proceedings.

After his retirement in 1974, Professor Tucker tried to recapture some of the magic of Princeton's mathematics department in the 1940's. He organized a novel oral history project involving hundreds of taped interviews with former faculty members and students. He also procrastinated, his former colleagues recall fondly. His last book, published recently, was in the works for 18 years.

...

*Addition by Martin J. Osborne*: During Tucker's time as chair of the Math Department at Princeton, instructors in PhD courses did not award grades. At some point, the Dean of Graduate Studies demanded that they start doing so. Tucker's response was to invent the grade of "N"---meaning "no grade"! [Source: "Mathematics in the Movies" by Harold W. Kuhn (paper to be published, in Italian, in the proceedings of a conference on "Mathematics and Culture" in Venice, Italy,

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