Martin Davis (mathematician)

“Davis became one of the earliest computer programmers when he began programming on the ORDVAC computer at the University of Illinois in the early 1950s. His book Computability and Unsolvability ... first appeared in 1958 and has become a classic in theoretical computer science.”

“The analysis of algorithmic process that emerged from the work of Gödel, Church, Turing, and Post has been of great importance not only for theoretical investigations but also for practice, by providing an expansive framework for computer science. The discussion of computation-like processes that transcend the limits imposed by the Church–Turing thesis can likewise be framed either in terms of theory or of practice.”

“Nonstandard analysis is a technique rather a subject. Aside from theorems that tell us that nonstandard notions are equivalent to corresponding standard notions, all the results we obtain can be proved by standard methods. Therefore, the subject can only be claimed to be of importance insofar as it leads to simpler, more accessible expositions, or (more important) to mathematical discoveries.”

“A partially computable function may be thought of as one for which we possess an algorithm which enables us to compute its value for elements of its domain, but which will have us computing forever in attempting to obtain a functional value for an element not in its domain, without ever assuring us that no value is forthcoming. In other words, when an answer is forthcoming, the algorithm provides it; when no answer is forthcoming, the algorithm has one spend an infinite amount of time in a vain search for an answer.”