Vladimir Voevodsky, formerly a gifted but restless student who flunked out of college out of boredom before emerging as one of the most brilliant and revolutionary mathematicians of his generation, died on Sept. 30 at his home in Princeton, N.J. He was 51.

Nadia Shalaby, his former wife, said he was found dead in his home by friends, whom she had called when she had not heard from him. They then called the police. He had been ill and had apparently collapsed, she said. [The cause was not immediately known, but Dr. Shalaby said on Oct. 11 that it was found to have been an aneurysm.]

Dr. Voevodsky was renowned for founding entirely new fields of mathematics and creating groundbreaking new tools for computers to confirm the accuracy of proofs. In 2002, he was awarded the Fields Medal, which recognizes brilliance and promise in mathematicians under 40.

He was “one of the giants of our time,” Thomas Hales, a mathematician at the University of Pittsburgh, said in an interview. Dr. Voevodsky, he said, transformed every field he touched. In his work using computers, for example, he upended mathematical thinking to such a degree that he changed the meaning of the equals sign.