Samuel Eilenberg, 84, Dies; Mathematician at ColumbiaSamuel Eilenberg, an eminent mathematician and collector of Asian art, died on Friday at the Isabella Geriatric Center in upper Manhattan, where he had been for three months. He was 84 and had been a longtime resident of the Upper West Side of Manhattan.
He had been in poor health for the last three years, said Robert L. Poster, one of the co-executors of his estate.
Dr. Eilenberg retired in 1982 as a University Professor, the highest professorial rank, at Columbia University, where he had taught since 1947. He was born in Warsaw and moved in 1939 to the United States, where he became renowned for his work in the fields of algebraic topology and homological algebra. He served twice as chairman of Columbia's mathematics department, and taught at the University of Michigan from 1940 to 1946 and at Indiana University in 1946 and 1947.
In 1986, he was a co-winner, with Atle Selberg of the Institute for Advanced Study at Princeton, of the $100,000 Wolf Foundation Prize in Mathematics.
Beginning in the mid-1950's, Dr. Eilenberg amassed an art collection comprising many small sculptures and other artifacts, in bronze, silver, stone and other materials. The works were made between the 3d century B.C. and the 17th century in Indonesia, Pakistan, India, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. The collection came to be valued at more than $5 million.
Then in 1987, he gave more than 400 artifacts from the collection to the Metropolitan Museum of Art, which put on a show of holdings from his collection, ''The Lotus Transcendent: Indian and Southeast Asian Art From the Samuel Eilenberg Collection,'' in 1991 and 1992. In return for his generosity, the museum raised most of the $1.5 million necessary to create the Samuel Eilenberg Visiting Professorship of Mathematics at Columbia.
Another member of Columbia's mathematics department, Prof. John W. Morgan, said, ''The theme that runs through Sammy's mathematics is always to find the absolutely essential ingredients in any problem and work only with those ingredients and nothing else -- in other words, to get rid of all the superfluous information.''
When someone once asked Professor Eilenberg if he could eat Chinese food with three chopsticks, he answered, ''Of course,'' according to Professor Morgan. The questioner asked, ''How are you going to do it?'' and Professor Eilenberg replied, ''I'll take the three chopsticks, I'll put one of them aside on the table, and I'll use the other two.''
Dr. Eilenberg always applied that simplifying approach in his mathematical work, Professor Morgan said, and that helped him in his pioneering work in algebraic topology.
In the 1930's, 40's and 50's, he was one of the main researchers in algebraic topology, the use of algebraic techniques to study problems involving shapes. Professor Eilenberg also helped develop a related field, homological algebra.
He and a co-author, Prof. Norman E. Steenrod of Princeton University, collaborated in studying algebraic topology. They set out their findings in a 1952 book, ''Foundations of Algebraic Topology'' (Books on Demand), which is one of the primary sources in the field.
The two mathematicians developed axioms, or rules, for analyzing objects through algebraic topology.
''The Eilenberg-Steenrod axioms were crucial,'' Professor Morgan said, ''in exposing the essential features of the constructions of algebraic topology.''
Professor Eilenberg's mathematical work in algebraic topology began in his native Warsaw in the mid-1930's, while he was studying at the University of Warsaw. He received his doctorate there in 1936.
His many writings include the book ''Homological Algebra'' (Princeton, 1956) which he wrote with Henri Cartan.
Professor Eilenberg received Guggenheim and Fulbright Fellowships and was a member of the American Academy of Arts and Sciences and other professional groups.
His 1960 marriage to Natasha Chterenzon ended in divorce in 1969.
By ERIC PACE, February 3, 1998 © The New York Times Company