 First , they proved that there were , in fact , limits to what mathematical logic could accomplish . But second ( and more important for AI ) their work suggested that , within these limits , any form of mathematical reasoning could be mechanized . The Church @-@ Turing thesis implied that a mechanical device , <unk> symbols as simple as 0 and 1 , could imitate any <unk> process of mathematical deduction . The key insight was the Turing machine — a simple theoretical construct that captured the essence of abstract symbol manipulation . This invention would inspire a handful of scientists to begin discussing the possibility of thinking machines . 
