Review of Feasible Computations and Provable Complexity Properties by Juris Hartmanis

Abstract

"It may only be a slight exaggeration to claim that in the 1930s we started to understand what is and is not effectively computable and that in the 1970s we started to understand what is and is not practically or feasibly computable. There is no doubt that the results about what can and cannot be effectively computed or formalized in mathematics have had a profound influence on mathematics, and, even more broadly, they have influenced our view of our scientific methods. We believe that the results about what can and cannot be practically computed will also have a major influence on computer science, mathematics, and even though more slowly, will affect other research areas and influence how we think about scientific theories." - Juris Hartmanis (from the Introduction)