Semi-Automated Mathematics

The fifth in a series of experiments in semi-automated mathematics is described. These experiments culminated in large complex computer programs which allow a mathematician to prove mathematical theorems on an man/machine basis. SAM V, the fifth program, is oriented primarily toward the development of efficient automatic techniques for handling some of the more basic processes of mathematical deduction, and toward the realization of efficient real-time interaction between man and machine through the use of cathode-ray tube displays. SAM V's most notable success is the solution of an open problem in lattice theory.