Dr. René Thom, the French mathematician whose catastrophe theory once held out hope of predicting unruly phenomena like earthquakes, prison riots and the outbreak of war, died on Oct. 25 in Bures-sur-Yvette, near Paris, where he had worked at the Institute of Advanced Scientific Studies. He was 79.
The cause was vascular disease, his colleagues said.
Dr. Thom's expertise was in topology, which studies the shapes and symmetries of abstract geometric objects. From this lofty mathematical vantage point, cubes appear identical to spheres (one can be smoothly transformed into the other) and doughnuts and coffee cups are fundamentally the same.
This unifying perspective has found practical footholds -- computer scientists speak of the topology of a network -- but Dr. Thom resided on a higher Platonic plane, where the messy distinctions of reality seem to blur together, revealing a few underlying patterns.
''He was obsessed with forms, far beyond their mathematical geometric interest,'' said Dr. David Ruelle, who worked with him at the institute. ''He would enjoy staring at a topographic map, imagine what the landscape would look like from a certain viewpoint, then go to that point and compare reality with what he had imagined.''
This passion to understand the world geometrically led him to invent catastrophe theory, which sought to quantify how continuous actions (sailing along the smooth surface of a lake) could suddenly give way to discontinuous change (plunging over a waterfall). Such events, he believed, could be described with their own topography: abstract mathematical forms, with names like the cusp, the swallowtail and the butterfly, that could be used to chart and even predict life's surprises, bringing them within reach of reason.Continue reading the main story
The theory, brought public in his 1972 book ''Structural Stability and Morphogenesis,'' caused a sensation, and soon prognosticators both amateur and professional were applying his ideas to biology, sociology and, predictably, the stock market.
Late in his career, Salvador Dali painted ''Topological Abduction of Europe: Homage to René Thom'' (1983), an aerial view of a seismically fractured landscape juxtaposed with the equation that strives to explain it.
Born in Montbéliard, near the Swiss border, René Frédéric Thom was reputed to have learned by the age of 10 to visualize in four dimensions. After studying in Paris, earning a doctorate in mathematics in 1951, he went on to teach in Grenoble and Strasbourg.
In 1958 his work on an influential theory called cobordism, which Dr. Ruelle described as lying at the border between algebra and geometry, earned him the Fields Medal, the closest honor in mathematics to a Nobel Prize.
This early success left him free to pursue his interests in many directions. At the Institute of Advanced Scientific Studies, where he became a professor in the early 1960's, he wrote papers not just on topology but also on linguistics, philosophy and theoretical biology.
A shy, somewhat reserved man, Dr. Thom liked to gently prod his colleagues into questioning their assumptions. ''He was never aggressive and always had a sparkle in his eye,'' said Dr. Jean-Pierre Bourguignon, director of the institute.
While Dr. Thom's influence in mathematics has become deeply rooted, catastrophe theory did not live up to its promise of useful predictions. Nor did Dr. Thom's contributions to other fields always sit well with colleagues.
In his book ''What Mad Pursuit,'' Dr. Francis Crick recalls being approached by Dr. Thom at a meeting in the early 1960's at Villa Serbelloni on Lake Como in Italy, where scientists were discussing progress in cracking the genetic code.
Almost immediately, Dr. Crick wrote, Dr. Thom informed him that some of his recent research was wrong -- that though supported experimentally, it did not comport with mathematical theory.
Dr. Crick was left with the impression that Dr. Thom did not understand how science worked: ''What he did understand he didn't like, and referred to it disparagingly as 'Anglo-Saxon.' ''
Dr. Bourguignon said a severe arterial inflammation made Dr. Thom's last years an agony for his family. With his circulation impaired, he underwent the amputation of a foot and lost his memory of all but the early years of his life.
Shown the cover of a newly produced compact disc inscribed with his life work, some 8,000 pages, he did not even recognize his own picture.
Dr. Thom is survived by his wife, Suzanne, and three children, Francoise, Elizabeth and Christian.Continue reading the main story