Alonzo Church: Mathematician. Philosopher. Computer Scientist?

1. Alonzo Church: Mathematician. Philosopher. Computer Scientist? Who is Alonzo Church? Alonzo Church was a man who was very important to the computer science world. Born in 1903, the son of a judge, Church attended Princeton. Church has made some huge impacts on the world of computer science. Funny thing: He had degrees in Mathematics and Philosophy. Church is best known for: Lambda (λ) Calculus, Church-Turing thesis, proving the negativity of the Entscheidungsproblem, Frege-Church ontology, and the Church-Rosser Theorem. Lambda (λ) Calculus λ Calculus is a system created by church that is in the world of mathematical logic and computer science for creating a computation by way of combining variables using abstraction. With his findings using λ Calculus, Church was able to negate David Hilbert’s Entscheidungsproblem, which asks for a procedure to determine the truth of arbitrary generalizations in a mathematical theory. For the case of Peano arithmetic including axioms, Church’s λ-Calculus disproved the theory. This is also known as Church’s Theorem. Through time computer scientists have come to an agreement that Church’s λ Calculus is indeed the very first computer programming language to exist. Within the language there lies typed and un-typed variants. The un-typed is said to be able to compute all mathematical functions. Today, λ Calculus has applications in several different areas: mathematics, philosophy, linguistics, and computer science. λ Calculus, along with Alan Turing’s Turing machine are important models in computation. Church-Turing Thesis The Church-Turing thesis says that any real-world computation can be written into an equivalent computation involving a Turing Machine. Church originally thesis says the real world computation can be done using lambda calculus which is equivalent to using recursive functions. This thesis also involves computation involving cellular automata, combinatory, register machines, and substitution systems. There are some conflicts with the thesis, some individuals say it can be proven and the other says it serves as a definition for computation. If there was such a machine that could answer the Turing Machine question then computer scientists would name it the oracle. The Church-Turing thesis has been extended to an ideas about processes in the biological world by Stephen Wolfram (Creator of Wolfram Alpha and Mathematica) in his principle of computational equivalence which says there are only a small amount of levels in computing power before a system becomes universal, like most natural and biological systems are natural. Church died in 1995 being a well decorated man in the math and computer science world. He earned a Ph.D. from Princeton University. His contributions to number theory and the theories of algorithms and computation laid a solid foundation to computer science

2. References Alonzo Church Biography. (n.d.). Retrieved February 2013, from http://www-history.mcs.st-andrews.ac.uk/Biographies/Church.html Barendregt, H. (2000, March). CSE. Retrieved February 2013, from Introduction to Lambda Calculus: ://www.cse.chalmers.se/research/group/logic/TypesSS05/Extra/geuvers.pdf Department, S. M. (2012, December 12). Stanford Encyclopedia of Philosohphy. Retrieved February 2013, from http://plato.stanford.edu/entries/lambda-calculus/