The Yale University mathematics department, where Dr. Lang taught for more than 30 years before retiring last year, announced the death but gave no cause.

Throughout his life, Dr. Lang railed against inaccuracy and imprecision and felt that the scientific establishment unfairly suppressed dissident ideas.

Beginning around 1977, he adopted a more activist approach, writing letters and articles -- sometimes even buying newspaper advertisements -- to challenge research that he considered unscrupulous or sloppy. He would pull together his writings and add news articles, Congressional testimony and other documents into what he called files and mail the compiled documents to scientists, journalists and government officials.

"He just thought by presenting everyone all of the primary documents, everyone else would be able to see what he saw," said Kenneth A. Ribet, a professor of mathematics at the University of California, Berkeley. "It was a very effective tool."

Edward G. Dunne of the American Mathematical Society said: "Lang was always meticulous in his documentation. These things multiplied. People would be receiving 25-, 35-, 100-page documents from Lang."

One focus of Dr. Lang's ire was the Harvard political scientist Samuel P. Huntington. Dr. Lang mounted a one-man campaign against Dr. Huntington's nomination to the National Academy of Sciences in 1986, dismissing Dr. Huntington's use of mathematical equations to relate factors like economic development and political instability as "pseudoscience" and "nonsense" -- "a type of language which gives the illusion of science without any of its substance."

Dr. Lang also challenged Dr. Huntington's description of apartheid in South Africa in the 1960's as a "satisfied society." Dr. Huntington, who said the math was not meant to be rigorous but rather a "shorthand" of his arguments, twice failed to win election to the academy.

Controversially, beginning in the mid-1990's, Dr. Lang sided with skeptics who doubted that AIDS was caused by human immunodeficiency virus, arguing that the scientific evidence connecting them was weak and faulty. He criticized the denial of research money to Peter Duesberg, a skeptic on the H.I.V.-AIDS link.

He was never convinced otherwise. A week before his death, he mailed out his latest file, a dozen pages of letters and e-mail messages about two papers he had written about the AIDS debate that had been rejected by the Proceedings of the National Academy of Sciences.

Dr. Lang also threw in a whimsical document, "The Three Laws of Sociodynamics," which states, among other things, that "the power structure does what they want, when they want; then they try to find reasons to justify it."

Dr. Lang started his career as one of the nation's leading thinkers in fundamental mathematics, using aspects of geometry to study the properties of numbers, and evolved into a gifted but challenging teacher.

Decades of students discovered that if they did not pay attention in class, Dr. Lang would throw chalk. "He would rant and rave in front of his students," Dr. Ribet said. "He would say, 'Our two aims are truth and clarity, and to achieve these I will shout in class."'

He was a prolific author, having written more than 40 mathematics textbooks and research monographs and well over 100 research articles.

Born in Paris in 1927, Serge Lang moved to California with his family when he was a teenager.

He graduated from the California Institute of Technology in 1946 and received a Ph.D. in mathematics from Princeton in 1951. He taught at the University of Chicago before becoming a professor at Columbia in 1955.

Dr. Lang resigned his Columbia professorship in 1971 because of the university's handling of antiwar protesters.

He was elected to the National Academy of Sciences in 1985 and was a member of the American Mathematical Society, but forcefully challenged both bodies at times over the election of new members and other issues.

He resigned from the mathematical society in 1996, because the society's journal had refused to publish an article he wrote about AIDS.

"He described himself as a congenital troublemaker," said Paul Vojta of the University of California, Berkeley, who had been a postdoctoral student at Yale under Dr. Lang.

Dr. Lang's research focused on number theory and algebraic geometry. He won the Frank Nelson Cole Prize in 1960 from the American Mathematical Society for his insights on algebra.

**Kenneth Chang** and **Warren Leary**

September 25, 2005 © NY Times