American mathematician who used computers to help find solutions to difficult classical problems in mathematics. Williams's first such solution, a number containing over 200,000 digits, solved Archimedes's 2,000-year-old "cattle of the sun" problem. This solution was completed in 1965. In another notable achievement, completed in 1985, Williams and his collaborators determined that the number consisting of a string of 1,031 consecutive ones is a prime number. This accomplishment showed the power of computers to help resolve lengthy mathematical problems.