Department of Computer Science University of Western Ontario PART 1 In their book Mathematics and Logic Kac and Ulam (1971) comment: "The point of view as it has evolved through centuries is that one need not know what things are as long as one knows what statements about them one is allowed to make. Hilbert's famous Grundlagen der Geometrie begins with the sentence: 'Let there be three kinds of objects; the objects of the first kind shall be called "points", those of the second kind "lines", and those of third "planes". That is all, except that there follows a list of initial statements (axioms) that involve the words "point', "line" and "plane", and from which other statements involving those undefined words can now be deduced by logic alone. This permits geometry to be taught to a blind man and even to a computer!" Leaving aside the attitude implicit in Kac & Ulam's use of the word'even' in the phrase even to a computer', it has become clear that programs to prove theorems in ...

In E. W. Elcock and D. Michie (Eds.), Machine intelligence 8. New York: Wiley, 11-29.

... the technique of heuristic programmingis under detailed investigation as a means to the end of applying largescaledigital computers to the solution of a difficult class of problems currentlyconsidered to be beyond their capabilities; namely those problemsthat seem to require the agent of human intelligence and ingenuity fortheir solution. It is difficult to characterize such problems further, except,perhaps, to remark rather vaguely that they generally involve complexdecision processes in a potentially infinite and uncontrollable environment.If, however, we should restrict the universe of problems to those thatamount to the discovery of a proof for a theorem in some well-definedformal system, then the distinguishing characteristics of those problems ofspecial interest to us are brought clearly into focus.Proceedings of an International Conference on Information Processing. Paris:UNESCO House, 273-282.