Deductive Reasoning in Propositional Logic Martin Davis (b 1928) is an American mathematician known for several important ideas and results in mathematics, logic, and computability theory Davis was an undergraduate student of Emil Post in New York and later completed his doctoral study under the supervision of Alonso Church at Princeton University in 1950 He is currently a Professor Emeritus at New York University One of Davis’ most important work, together with Hilari Putnam, led to the solution of Hilbert’s tenth problem, namely the proof of the algorithmic unsolvability of Diophantine equations That proof was eventually completed by the young Russian mathematician Yuri Matiyasevich in 1970, essentially using results by Davis, Putnam, and Julia Robinson In around 1960, Davis and Putnam invented the Davis–Putnam algorithm for checking the validity of a first-order logic formula (which only terminates on valid formulae), using a resolution-based decision procedure for propositional logic Later, their algorithm was improved to the Davis–Putnam–Logemann–Loveland (DPLL) algorithm which is still the basis for the currently most efficient complete SAT-solvers Davis is also known for inventing his models of Post-Turing machines Hilary Whitehall Putnam (31.07.1926 – 13.03.2016) is an American philosopher, mathematician, and computer scientist, a leading figure in analytic philosophy since the 1960s, especially in philosophy of mind, of language, of logic, of mathematics, and of science Putnam studied mathematics and philosophy at the University of Pennsylvania and received his PhD in philosophy at UCLA in 1951 for a dissertation on The Meaning of the Concept of Probability in Application to Finite Sequences, working with Reichenbach He then taught philosophy at Northwestern University, Princeton University, MIT and at Harvard University from 1965 until the end of his active academic career in 2000 Putnam is well known for his many influential works on theories of mind and meaning and, in particular, for his arguments in defence of scientific realism and objectivity of truth, knowledge, and mathematical reality Putnam also made important contributions to mathematics and logic In around 1960, he and Martin Davis developed the Davis–Putnam algorithm for solving the Boolean satisfiability problem Putnam also contributed to the eventual solution of Hilbert’s tenth problem 85