 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 , shuffling symbols as simple as 0 and 1 , could imitate any conceivable 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 . 
 First , they proved that <a href='dey_it' title='1'><mark>there</mark></a> <a href='uninflect' title='2'><mark>were</mark></a> , in fact , <a href='uninflect' title='3'><mark>limits</mark></a> 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 , shuffling symbols as simple as 0 and 1 , could imitate any conceivable process of mathematical deduction . The key insight was the Turing machine — a simple theoretical construct <a href='null_relcl' title='4'><mark>that</mark></a>captured the essence of abstract symbol manipulation . This invention would inspire a handful of scientists to begin discussing the possibility of thinking machines . 
First , they proved that it was , in fact , limit to what mathematical logic could accomplish . But second ( and more important fir AI ) their work suggested that , within these limits , any form of mathematical reasoning could b mechanized . The Church @-@ Turing thesis implied that a mechanical device , shuffling symbols as simple as 0 and 1 , could imitate any conceivable process of mathematical deduction . The key insight was the Turing machine — a simple theoretical construct captured the essence of abstract symbol manipulation . This invention would inspire a handful of scientists to begin discussing the possibility of thinkin machines .