LNAI 7788 - Automated Reasoning and Mathematics

This article presents examples of the monumental contributions of Bill McCune to mathematics, logic, computer science, and especially automated reasoning. The examples are presented in the form of short stories and recollections of the author during his long association with Bill. In addition to Bill’s accomplishments as a researcher, the author provides personal memories giving glimpses into Bill’s complex personality and his generosity as a collaborator. 1 Perspective and Genesis Perhaps you have wondered what would result if you had the opportunity to spend thousands of hours with a great mind. For more than two decades, I had that opportunity as I shared research time with my esteemed colleague William (Bill) McCune. We shared many ideas, conjectures, and, yes, guesses. Each of us had two main goals. The first goal was to formulate enhancements for an automated reasoning program, enhancements that would substantially add to its power. The second goal was to employ the program in a way that would contribute to various areas of mathematics and logic. From the viewpoint of making contributions to mathematics and logic, Bill and I had a marvelous automated assistant; indeed, in 1988, if memory serves, he designed and implemented the automated reasoning program called OTTER. (We did have access to a program designed at Argonne before OTTER was produced.) In but four months, even though Bill was also involved in research of different aspects, he wrote more than 30,000 lines of code, producing a program that, from then until now, has exhibited the smallest number of bugs. Yes, his effort was and is monumental; indeed, when you obtain a conclusion, a set of conclusions, a proof, you can assume with almost total certainty that all is in order. Also important is the robustness of OTTER, permitting you to have it search for desired objects for weeks, if needed, without stopping. In this article, I shall tell a number of short stories that provide ample evidence of Bill’s inventive mind, his accurate insights, and his impeccable professionalism. His successes in the context of enhancements have played a key role in much of what has occurred in the past ten years. As I shall highlight here, Bill answered (with one of his programs) open questions in areas that include group theory, lattice theory, Boolean algebra, combinatory logic, and—so impressive—Robbins algebra; for various open questions, see Chapter 7 of [14]. This work was supported by the U.S. Department of Energy, under Contract DEAC02-06CH11357. M.P. Bonacina and M.E. Stickel (Eds.): McCune Festschrift, LNAI 7788, pp. 1–14, 2013. c © Springer-Verlag Berlin Heidelberg 2013