 In the 20th century , the study of mathematical logic provided the essential breakthrough that made artificial intelligence seem plausible . The foundations had been set by such works as <unk> 's The Laws of Thought and <unk> 's <unk> . Building on <unk> 's system , Russell and Whitehead presented a formal treatment of the foundations of mathematics in their masterpiece , the <unk> <unk> in 1913 . Inspired by Russell 's success , David <unk> challenged mathematicians of the 1920s and 30s to answer this fundamental question : " can all of mathematical reasoning be formalized ? " His question was answered by <unk> 's incompleteness proof , Turing 's machine and Church 's <unk> <unk> . Their answer was surprising in two ways . 
