Automated Theory Formation in Pure Mathematics by Simon Colton

in recent times, synthetic Intelligence researchers have principally targeted their efforts on fixing particular difficulties, with much less emphasis on 'the colossal photograph' - automating huge scale projects which require human-level intelligence to adopt. the topic of this publication, automatic thought formation in arithmetic, is one of these huge scale activity. automatic conception formation calls for the discovery of latest ideas, the calculating of examples, the making of conjectures and the proving of theorems. This ebook, representing 4 years of PhD paintings through Dr. Simon Colton demonstrates how conception formation might be computerized. construction on over twenty years of study into developing an automatic mathematician performed in Professor Alan Bundy's mathematical reasoning crew in Edinburgh, Dr. Colton has applied the HR procedure as an answer to the matter of forming theories via desktop. HR makes use of quite a few items of mathematical software program, together with computerized theorem provers, version turbines and databases, to construct a idea from the naked minimal of data - the axioms of a website. the most software of this paintings has been mathematical discovery, and HR has had many successes. specifically, it has invented 20 new forms of variety of enough curiosity to be permitted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed via many (human) mathematicians.