The History of Mathematics
Into Modern Mathematics
What was the “Golden Age of Logic”?
Kurt Gödel’s work led to what is often described as the Golden Age of Logic. Spanning the years from about 1930 to the late 1970s, it was a time when there was a great deal of work done in mathematical logic. From the beginning, mathematicians broke into many camps, working on various phases of logic (for more information about logic, see “Foundations of Mathematics”), including:
Proof theory—In which the mathematical proofs started by Aristotle and continued by Boole (see above) were extensively studied, resulting in branches of this mathematics being applied to computing (including artificial intelligence).
Model theory—In which mathematicians investigated the connection between the truth in a mathematical structure and propositions about that structure.
Set theory—In which a breakthrough in 1963 showed that certain mathematical statements were undeterminable, a direct challenge to the major set theories of the time. This showed that Cantor’s Continuum Hypothesis (see above) is independent of the axioms of set theory, or that there are two mathematical possibilities: one that says the continuum hypothesis is true, one that says it is false.
Computability theory—In which mathematicians worked out the abstract theorems that would eventually help lead to computer technology. For example, English mathematician Alan Turing proved an abstract theorem that established the theoretical possibility of a single computing machine programmed to complete any computation. (For more information about Turing and computers, see below and “Math in Computing.”)