Rene Thom, 79, a French mathematician who was acknowledged as one of the world's premier thinkers in his field and who was a leader in trying to apply mathematics to some of the most puzzling problems of nature and society, died Oct. 25 in a small French town near Paris. He had vascular disease.

The work for which Dr. Thom was best known suggests its appeal by its name: catastrophe theory.

It was an effort to explain the seemingly inexplicable, to give a mathematical account of how the seemingly placid and predictable suddenly gives rise to the drastically different. Its goal was to show how epidemics arise, earthquakes occur, revolutions break out.

Its goal also was to explain how the world of smooth continuity and flowing curves found in schoolbook graphs and equations suddenly gives rise to the jarring jaggedness that mathematicians describe as discontinuity, and in effect brings chaos out of order.

Recognition of the power of modern mathematics helped raise hopes that catastrophe theory might grant the ability to explain, predict and possibly even forestall the most terrifying disasters. Dr. Thom sought to account for many of these explosive collapses of orderly behavior through creation of intricate geometric analogues.

So attractive were his ideas for years that his 1972 book, "Structural Stability and Morphogenesis," sold enough copies to make it a best-seller.

However, catastrophe theory appears never to have lived up to the fondest hopes entertained for it. It ultimately lacked, in the eyes of many critics, sufficient ability to foresee the genuinely unforeseen. Social scientists contended that many of the social phenomena to which it was applied could already be accounted for without it. Catastrophe theory was viewed as perhaps relying too much on intuition and not enough on formal mathematics.

In one of his better-known sayings, Dr. Thom had what might be viewed as a response: "If one must choose between rigor and meaning," he said, "I shall unhesitatingly choose the latter."

Although catastrophe theory had been seized upon as a means of better understanding hurricanes and heart attacks, prison riots and stock market crashes, perhaps even the extinction of the dinosaurs, it ultimately left unsolved many of the mysteries of the world and its inhabitants.

Yet it is credited with focusing new attention on explaining how small deviations in the workings of large systems ultimately lead to great departures. Mathematicians describe it as a precursor of one of the cutting-edge areas of their field: chaos theory. Moreover, some new predictive techniques in certain areas of science have been traced to it.

Artist Salvador Dali honored Dr. Thom in a 1983 work, "Topological Abduction of Europe: Homage to Rene Thom." It superimposed one of his equations on a disordered landscape.

Observations made by Dr. Thom suggest his sympathy for the questions of philosophy and his dissatisfaction with what he saw as the limitations imposed by traditional mathematical disciplines.

"I believe that proving," in the sense of demonstrating rigorous logical consistency, "is not a natural activity for mathematicians," he said.

In a remark that might have been applauded by many an impatient high school student, he said that "algebra is rich in structure but weak in meaning."

Of course, Dr. Thom, though he may have strayed from time to time from what was accepted mathematical fashion, was a deeply gifted mathematician, holder of the Fields Medal, regarded as the supreme honor in his field.

He was born to two storekeepers in a town near the Swiss border and showed an early penchant for mathematics that won him a scholarship. He received degrees in mathematics and in philosophy and continued with his studies during much of World War II. He earned a doctorate in 1951, and in that year visited this country, where he met Albert Einstein.

He returned to France, taught and did research and moved in 1964 to the Institut des Hautes Etudes Scientifique, one of the foremost French scientific institutions.

In his writings, he provided insight into the combination of factors that led him to catastrophe theory. There was a colleague, he wrote, whose abilities overwhelmed him. "His technical superiority was crushing, His seminar attracted the whole of Parisian mathematics, whereas I had nothing new to offer. That made me leave the strictly mathematical world and tackle more general notions."

He remained on the Institut faculty until his retirement in 1988.

Survivors include his wife, Suzanne, and three children.