Perhaps one of the greatest contributors to mathematics in the 20th century, Kurt Gödel made famous by the incompleteness theorem, which stated that within any axiomatic mathematical system there are things that cannot be proved or disproved on the basis of the axioms within that system, therefore was not able to be complete or consistent. His proof made him on even grounds with one of the greatest logicians, Aristotle.

Kurt Gödel was born on April, 28, 1906, in Austria-Hungary (Czech Republic now). Where, he was living in a newly formed country of Czechoslovakia because of World War I in 1918. Later, he was accepted into the University of Vienna, where he earned his doctorate in mathematics in 1929 and joined its staff the following year. During the early 1900s, Vienna was considered intellectually dominant in the world and earned the title of Vienna Circle, a gathering of scientists, mathematicians, and philosophers who believed in logical positivism, or a naturalistic, empiricist, and antimetaphysical view. Gödel was introduced to the group by his mentor, Hans Hahn. He held views of Platonism, theism, and mind-body dualism, which the Vienna Circle felt a bit contempt towards. Moreover, Gödel was subjected to paranoia, a mental instability, which he gained as a child and grew as he aged.

“Über die Vollständigkeit des Logikkalküls” (On the completeness of the Calculus of Logic), or the completeness theorem was published abridged in 1930, Gödel proved one of the most important local results of his time. It established that classical first-order logic, or predicate calculus is complete in the sense that all of the first-order logical truths can be proved in standard first-order proof systems. “It stated that no consistent system of axioms whose theorems can be listed by an “effective procedure” is capable of proving all facts about natural numbers,” as described by “The Exploratorium.”

Moreover, a year later he published the incompleteness theorem, (also the...

Kurt Gödel was born on April, 28, 1906, in Austria-Hungary (Czech Republic now). Where, he was living in a newly formed country of Czechoslovakia because of World War I in 1918. Later, he was accepted into the University of Vienna, where he earned his doctorate in mathematics in 1929 and joined its staff the following year. During the early 1900s, Vienna was considered intellectually dominant in the world and earned the title of Vienna Circle, a gathering of scientists, mathematicians, and philosophers who believed in logical positivism, or a naturalistic, empiricist, and antimetaphysical view. Gödel was introduced to the group by his mentor, Hans Hahn. He held views of Platonism, theism, and mind-body dualism, which the Vienna Circle felt a bit contempt towards. Moreover, Gödel was subjected to paranoia, a mental instability, which he gained as a child and grew as he aged.

“Über die Vollständigkeit des Logikkalküls” (On the completeness of the Calculus of Logic), or the completeness theorem was published abridged in 1930, Gödel proved one of the most important local results of his time. It established that classical first-order logic, or predicate calculus is complete in the sense that all of the first-order logical truths can be proved in standard first-order proof systems. “It stated that no consistent system of axioms whose theorems can be listed by an “effective procedure” is capable of proving all facts about natural numbers,” as described by “The Exploratorium.”

Moreover, a year later he published the incompleteness theorem, (also the...