TITLE: Mathematical definition of `intelligence' (and consequences) AUTHOR: Warren D. Smith DATE: May 2006 ABSTRACT: In {\S}9 we propose an abstract mathematical definition of, and practical way to measure, ``intelligence.'' Before that is much motivating discussion and arguments why it is a good definition, and after it we deduce several important consequences -- fundamental theorems about intelligence. The most important (theorem 5 of {\S}12) is our construction of an algorithm that implements an ``asymptotically uniformly competitive intelligence'' (UACI). Although our definition of intelligence initially seems ``multidimensional'' -- two entities would seem capable of being relatively more or less intelligent independently in each of an infinite number of ``dimensions'' of intelligence -- the UACI is an intelligent entity that is simultaneously as intelligent as any other entity (asymptotically) in every dimension simultaneously. This in a considerable sense makes intelligence ``one dimensional'' again and presumably explains why ``IQ'' is a useful quantity. Unfortunately the obvious UACI implementations are useless for practical purposes because of enormous constants of inefficiency. There are many obvious and non-obvious ways to try to get more practicality and efficiency, and it is entirely unclear how far and fast that can be pushed ({\S}15 & 22). In {\S}16-20 we examine the four most important bodies of experimental facts about human intelligence and find that all four are \emph{predicted} by the hypothesis that human intelligence works similarly to our mathematical construction of a UACI: (1) the Spearman positive correlation and $g$ principles (which we shall see are less supported by evidence than is generally claimed, but probably still roughly correct), (2) the findings of Jean Piaget and successors about the time-development of human intelligence, (3) forgetfulness, and (4) time-consumption behavior. To a large extent this all is a rediscovery of recent work by Marcus Hutter; we survey that in {\S}24. Although we believe our definition of ``intelligence'' largely demystifies that concept, it is more mysterious what a ``consciousness'' is -- although we propose a tentative definition which if correct would trivialize that issue. Finally, to further the development and sanity of AI, we recommend that an annual intelligence contest be held. We explain how to do that in {\S}23; both humans and computers could enter the contest.