Israel M. Gelfand, one of the giants of 20th-century mathematics, whose work cleared paths for other thinkers in fields as diverse as physics and medical imaging, died on Monday in New Brunswick, N.J. He was 96.

The death, at Robert Wood Johnson University Hospital, was confirmed by his wife, Tatiana.

Dr. Gelfand did not achieve fame from attacking and solving famous, intractable problems. Instead, he was a pioneer in untrodden mathematical fields, laying the foundation and creating tools for others to use.

"People always compare him with great mathematicians like Euler or Hilbert or Poincaré," said Vladimir Retakh, a professor of mathematics at Rutgers, where Dr. Gelfand spent most of his time as a visiting professor after leaving the Soviet Union in 1989.

Dr. Retakh said Vladimir Arnold, a prominent Russian mathematician, had contrasted the approaches of the Soviet Union's two most famous mathematicians -- Dr. Gelfand and Andrei Kolmogorov, who was Dr. Gelfand's thesis adviser -- with a travel analogy.

"Suppose they both arrived in a country with a lot of mountains," Dr. Retakh said of Dr. Arnold's comparison. "Kolmogorov would immediately try to climb the highest mountain. Gelfand would immediately start to build roads."

Dr. Gelfand's pioneering work in a highly abstract field known as representation theory has proven crucial for physicists working with quantum mechanics. "It's kind of the main language people use there," said Andrei Zelevinsky, a professor of mathematics at Northeastern University in Boston.

Later work in another field, integral geometry, seemingly just as abstract and obscure, is now used to turn the raw data of M.R.I.'s and CAT scans into three-dimensional images. "This turned out to be a mathematical apparatus crucial for tomography," Dr. Zelevinsky said. "You need rather deep mathematics to do that."

Dr. Retakh said, "He was probably the last of the greatest who worked in almost every area of mathematics."

Dr. Gelfand also recruited talented mathematicians as students and collaborators, many of whom also achieved prominence. At Moscow State University, where he taught for decades, he held a legendary weekly series of math seminars that, instead of typical invited prepared talks, sometimes unfolded more like math improv.

"He's probably the most interesting person I've ever met," said Alexander B. Goncharov, a professor of mathematics at Brown University and one of Dr. Gelfand's students. "Unpredictable and very wise."

Dr. Retakh said that what a typical day's seminar would cover would not be known until it started, often with conversations before the seminar leading to Dr. Gelfand's choosing an impromptu speaker and an impromptu topic. "The joke was: 'We cannot tell what will be at the seminar. We can tell what it will not be. What it will not be is the talk that was announced,' " Dr. Retakh said.

For the speaker, it could be a difficult challenge, stretching for several hours, with Dr. Gelfand interrupting with questions, observations and sometimes cutting remarks. "He was not the most delicate, polite person in the world," Dr. Zelevinsky said.

But for the speaker and the attendees, the sessions also provided valuable insight into Dr. Gelfand's thinking.

He started a second seminar series, on biology, after leukemia struck one of his sons, Aleksandr. "The best Moscow biologists were happy to come and attend this seminar and give talks and hear very unusual opinion," said Simon Gindikin, a colleague at Rutgers.

Aleksandr succumbed to leukemia, but Dr. Gelfand continued work in biology, Dr. Retakh said.

Born in Ukraine near Odessa, Israel Moiseevich Gelfand never finished high school. He never attended college as an undergraduate. Dr. Gelfand went to Moscow when he was 16 or 17, working at odd jobs. Already interested in mathematics, he attended seminars, and at the age of 19, he was admitted directly into graduate school at Moscow State University, studying under Kolmogorov.

Dr. Gelfand completed his ordinary doctorate in 1935 and then a higher doctor of mathematics degree in 1940.

As a Jew, Dr. Gelfand was pushed out of a position at the prestigious Steklov Institute and then out of a full-time professorship at Moscow University. He then ended up at the Institute of Applied Mathematics. He was elected to the Soviet Academy of Sciences in 1953, but only as a second-tier corresponding member, and did not receive full membership in the academy until 1984.

In 1989, Dr. Gelfand left the Soviet Union for the United States. He spent a year at Harvard and the Massachusetts Institute of Technology until obtaining a position at Rutgers, where he resumed his seminar series on a smaller scale for several years.

Dr. Gelfand's awards include membership in the National Academy of Sciences and the Royal Society in Britain, and a MacArthur grant in 1994.

An earlier marriage, to Zorya Shapiro, ended in divorce.

In addition to his wife, Tatiana, he is survived by two sons from his first marriage, Sergei, of Providence, R.I., and Vladimir, of Chicago; a daughter, Tatiana, of Jersey City; four grandchildren and three great-grandchildren.

Dr. Gelfand, who often said, "You have to be fast only to catch fleas," sought to teach not only the rules of math, but also the beauty and exactness of the field.

"Mathematics is a way of thinking in everyday life," Dr. Gelfand said in a 2003 interview with The New York Times. "It is important not to separate mathematics from life. You can explain fractions even to heavy drinkers. If you ask them, 'Which is larger, 2/3 or 3/5?' it is likely they will not know. But if you ask, 'Which is better, two bottles of vodka for three people, or three bottles of vodka for five people?' they will answer you immediately. They will say two for three, of course."

By KENNETH CHANG

Published: October 8, 2009 © New York Times

The death, at Robert Wood Johnson University Hospital, was confirmed by his wife, Tatiana.

Dr. Gelfand did not achieve fame from attacking and solving famous, intractable problems. Instead, he was a pioneer in untrodden mathematical fields, laying the foundation and creating tools for others to use.

"People always compare him with great mathematicians like Euler or Hilbert or Poincaré," said Vladimir Retakh, a professor of mathematics at Rutgers, where Dr. Gelfand spent most of his time as a visiting professor after leaving the Soviet Union in 1989.

Dr. Retakh said Vladimir Arnold, a prominent Russian mathematician, had contrasted the approaches of the Soviet Union's two most famous mathematicians -- Dr. Gelfand and Andrei Kolmogorov, who was Dr. Gelfand's thesis adviser -- with a travel analogy.

"Suppose they both arrived in a country with a lot of mountains," Dr. Retakh said of Dr. Arnold's comparison. "Kolmogorov would immediately try to climb the highest mountain. Gelfand would immediately start to build roads."

Dr. Gelfand's pioneering work in a highly abstract field known as representation theory has proven crucial for physicists working with quantum mechanics. "It's kind of the main language people use there," said Andrei Zelevinsky, a professor of mathematics at Northeastern University in Boston.

Later work in another field, integral geometry, seemingly just as abstract and obscure, is now used to turn the raw data of M.R.I.'s and CAT scans into three-dimensional images. "This turned out to be a mathematical apparatus crucial for tomography," Dr. Zelevinsky said. "You need rather deep mathematics to do that."

Dr. Retakh said, "He was probably the last of the greatest who worked in almost every area of mathematics."

Dr. Gelfand also recruited talented mathematicians as students and collaborators, many of whom also achieved prominence. At Moscow State University, where he taught for decades, he held a legendary weekly series of math seminars that, instead of typical invited prepared talks, sometimes unfolded more like math improv.

"He's probably the most interesting person I've ever met," said Alexander B. Goncharov, a professor of mathematics at Brown University and one of Dr. Gelfand's students. "Unpredictable and very wise."

Dr. Retakh said that what a typical day's seminar would cover would not be known until it started, often with conversations before the seminar leading to Dr. Gelfand's choosing an impromptu speaker and an impromptu topic. "The joke was: 'We cannot tell what will be at the seminar. We can tell what it will not be. What it will not be is the talk that was announced,' " Dr. Retakh said.

For the speaker, it could be a difficult challenge, stretching for several hours, with Dr. Gelfand interrupting with questions, observations and sometimes cutting remarks. "He was not the most delicate, polite person in the world," Dr. Zelevinsky said.

But for the speaker and the attendees, the sessions also provided valuable insight into Dr. Gelfand's thinking.

He started a second seminar series, on biology, after leukemia struck one of his sons, Aleksandr. "The best Moscow biologists were happy to come and attend this seminar and give talks and hear very unusual opinion," said Simon Gindikin, a colleague at Rutgers.

Aleksandr succumbed to leukemia, but Dr. Gelfand continued work in biology, Dr. Retakh said.

Born in Ukraine near Odessa, Israel Moiseevich Gelfand never finished high school. He never attended college as an undergraduate. Dr. Gelfand went to Moscow when he was 16 or 17, working at odd jobs. Already interested in mathematics, he attended seminars, and at the age of 19, he was admitted directly into graduate school at Moscow State University, studying under Kolmogorov.

Dr. Gelfand completed his ordinary doctorate in 1935 and then a higher doctor of mathematics degree in 1940.

As a Jew, Dr. Gelfand was pushed out of a position at the prestigious Steklov Institute and then out of a full-time professorship at Moscow University. He then ended up at the Institute of Applied Mathematics. He was elected to the Soviet Academy of Sciences in 1953, but only as a second-tier corresponding member, and did not receive full membership in the academy until 1984.

In 1989, Dr. Gelfand left the Soviet Union for the United States. He spent a year at Harvard and the Massachusetts Institute of Technology until obtaining a position at Rutgers, where he resumed his seminar series on a smaller scale for several years.

Dr. Gelfand's awards include membership in the National Academy of Sciences and the Royal Society in Britain, and a MacArthur grant in 1994.

An earlier marriage, to Zorya Shapiro, ended in divorce.

In addition to his wife, Tatiana, he is survived by two sons from his first marriage, Sergei, of Providence, R.I., and Vladimir, of Chicago; a daughter, Tatiana, of Jersey City; four grandchildren and three great-grandchildren.

Dr. Gelfand, who often said, "You have to be fast only to catch fleas," sought to teach not only the rules of math, but also the beauty and exactness of the field.

"Mathematics is a way of thinking in everyday life," Dr. Gelfand said in a 2003 interview with The New York Times. "It is important not to separate mathematics from life. You can explain fractions even to heavy drinkers. If you ask them, 'Which is larger, 2/3 or 3/5?' it is likely they will not know. But if you ask, 'Which is better, two bottles of vodka for three people, or three bottles of vodka for five people?' they will answer you immediately. They will say two for three, of course."

By KENNETH CHANG

Published: October 8, 2009 © New York Times