Logicism

During the foundations crises of mathematics in XIX, logicism was born as an attempt to base all of math in logic. This movement was lead by Gottlob Frege, Bertrand Russell and other logicians. The idea was to start with basic logical assertions and gradually build the system that could prove the whole of math, thereby reducing mathematics to logic. Principia Mathematica was Russel's and Whitehead's monumental effort to pull this off. The work started enthusiastically, but amounting problems slowed it down drastically, lead to unsatisfactory solutions and prolonged the publishing by years. Eventually it was published, and although it was recognized as a paramount work, it failed to meet its goal, bringing frustrations to its authors instead of fame.

Being tremendously voluminous and dry read, Principia wasn't particularly well received even by its niche target audience, save for one young reader who couldn't put it down. This prompted the inception of the classic Russel's joke about a published author meeting an admirer of his work: "So, you're the one!". The one was an Austrian academic Kurt Gödel that was at the time chasing a subject for his graduation thesis when he stumbled over a copy of Principia somebody was using as a doorstop. Right then and there Gödel would find inspiration for his paper that would soon ruin it for everybody.

Logicism was slowly waning anyway, but it finally ceased, taking the hope of math being built on a strong foundation along with it, when it became known that such an attempt is impossible, as proved by the Gödel's incompleteness theorems.

Despite the negative nature of the incompleteness theorems, Gödel's completeness theorem, another application of mathematics to logic, showed how close logicism came to being true. The completeness theorem showed that every rigorously defined mathematical theory may be described precisely by a first-order logic (FOL).