Charles Archibald Blake (November 24, 1906 - January 7, 1971), name officially changed to Archie Blake [1] was an American mathematician. He is well known for the Blake canonical form, a normal form for expressions in propositional logic. In order to compute the canonical form, he moreover introduced the concept of consensus, which was a precursor of the resolution principle, today a common technique in automated theorem proving.
In 1930, he became a member of the American Mathematical Society (AMS). [2] [3] He presented his canonical form at the AMS meeting at Columbia University on 29 Oct 1932. [4] In 1937, this work lead to a Ph.D. from the University of Chicago, supervised by Raymond Walter Barnard. [5]
He worked for the United States Coast and Geodetic Survey in Washington, D.C., from 1936 (or earlier) as a mathematician, [6] since 1938 as an Assistant Mathematician, [7] and since 1939 as an Associated Mathematician. [8] [9] In 1946, he was appointed a Senior Statistician in the Office of the Army Surgeon General, Washington, D.C. [10] He also worked for the Cornell Aeronautical Laboratory in Buffalo, New York. From there, he changed in 1954 to the Westinghouse Electric Corporation in Baltimore, Md., where he became an Advisory Engineer. [11] In 1956, he moved from Westinghouse to the Bendix Aviation Corporation, as a Systems Staff Mathematician. [12] In 1960, he became a Manager of the Analysis Section of Raytheon in Sudbury, Massachusetts. [13]
André Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the Bourbaki group, of which he was one of the principal founders.
Stephen Cole Kleene was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star, Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism.
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake in 1937, and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 and by Raymond J. Nelson in 1955. Also in 1955, Paul W. Abrahams and John G. Nordahl as well as Albert A. Mullin and Wayne G. Kellner proposed a decimal variant of the method.
Paul Richard Halmos was a Hungarian-born American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
Saunders Mac Lane, born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.
Emil Leon Post was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory.
Marshall Harvey Stone was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras.
Martin David Davis was an American mathematician and computer scientist who contributed to the fields of computability theory and mathematical logic. His work on Hilbert's tenth problem led to the MRDP theorem. He also advanced the Post–Turing model and co-developed the Davis–Putnam–Logemann–Loveland (DPLL) algorithm, which is foundational for Boolean satisfiability solvers.
Platon Sergeevich Poretsky was a noted Russian Imperial astronomer, mathematician, and logician.
In Boolean algebra, the consensus theorem or rule of consensus is the identity:
Vera Pless was an American mathematician who specialized in combinatorics and coding theory. She was professor emerita at the University of Illinois at Chicago.
Sylvain Edward Cappell, a Belgian American mathematician and former student of William Browder at Princeton University, is a topologist who has spent most of his career at the Courant Institute of Mathematical Sciences at NYU, where he is now the Silver Professor of Mathematics.
Zlil Sela is an Israeli mathematician working in the area of geometric group theory. He is a Professor of Mathematics at the Hebrew University of Jerusalem. Sela is known for the solution of the isomorphism problem for torsion-free word-hyperbolic groups and for the solution of the Tarski conjecture about equivalence of first-order theories of finitely generated non-abelian free groups.
Percy Alec Deift is a mathematician known for his work on spectral theory, integrable systems, random matrix theory and Riemann–Hilbert problems.
Jouko Antero Väänänen is a Finnish mathematical logician known for his contributions to set theory, model theory, logic and foundations of mathematics. He served as the vice-rector at the University of Helsinki, and a professor of mathematics at the University of Helsinki, as well as a professor of mathematical logic and foundations of mathematics at the University of Amsterdam. He completed his PhD at the University of Manchester under the supervision of Peter Aczel in 1977 with the PhD thesis entitled "Applications of set theory to generalized quantifiers". He was elected to the Finnish Academy of Science and Letters in 2002. He served as a member of the Senate of the University of Helsinki from 2004 to 2006 and the Treasurer of the European Mathematical Society from 2007 to 2014, as well as the Treasurer of the European Set Theory Society since 2012. Jouko Väänänen received the Magnus Ehrnrooth Foundation Prize in mathematics on April 29, 2024.
In Boolean logic, a formula for a Boolean function f is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of f.
In Boolean algebra, Poretsky's law of forms shows that the single Boolean equation is equivalent to if and only if , where represents exclusive or.
Philip Martin Whitman is an American mathematician who contributed to lattice theory, particularly the theory of free lattices.
Marion Elizabeth Stark was an American mathematician. She was one of the first women to receive a Ph.D. in mathematics.
Robert Henderson was a Canadian-American mathematician and actuary.
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