1. University of Puerto Rico - Cayey
RISE Program
Biol. 3095 Seminar Scientific Literature and Bibliography
Seminar Reflection 2
Félix Vallés
Seminar 2. Mr. VíctorOcasio Alan Turing and the Machine/Science Writing and Critical Thinking
Seminar: September 26, 2013
David Hilbert’s Entscheidungsproblem, a challenge for finding an algorithm that takes as input a
mathematical statement and produces as output a statement that may be true or false. It had to
comply with formalization, completeness, consistency, conservation and decidability. Kurt Gödel stated
that a computable axiomatic system describing the arithmetic of natural numbers cannot be both
complete and consistent. Then Alan Turing purposed to settle Hilbert’s Entscheidungsproblem, by
incorporating basic math in machines. Turing gave rise to a Turing machine, a finite program that
deploys symbols on tape according to a table of rules. Every Turing machine was associated with a
function (partially computable). A function is computable if it is partially computable and halts for every
natural number. Turing finally concluded that Hilbert’s problem was impossible to accomplish since the
halting problem (whether the program decides to finish or continue running forever) is not decidable,
hence unsolvable Alan’s contribution was the participation in reading and breaking the German
navigational codes during the Second World War.