Allen Newell and Herbert A. Simon who used what John McCarthy calls an "approximation"[2] in 1958 wrote that alpha–beta "appears to have been reinvented a number of times".[3] Arthur Samuel had an early version and Richards, Hart, Levine and/or Edwards invented alpha–beta independently in the United States.[4] McCarthy proposed similar ideas during the Dartmouth Conference in 1956 and suggested it to a group of his students including Alan Kotok at MIT in 1961.[5] Alexander Brudno independently conceived the alpha–beta algorithm, publishing his results in 1963.[6] Donald Knuth and Ronald W. Moore refined the algorithm in 1975[7][8] and Judea Pearl proved its optimality in 1982.[9]