Foundations

In 1900. David Hilbert called onto mathematicians to work together toward the goal of putting the mathematics on the strong foundations. He called for a unyfing theory to be put as the foundation of all mathematics, the foundation from which the entirety of mathematics could be derived. Actually, he called at the problem of inconsistency and incompleteness; he wanted that math be put on solid grounds and showed sound, coherent and consistent, free of paradoxes.

The Hilber's remark was proveked by relativelly recent failures in math, the mostrecent of which was the paradoxes lurking in set theories. Before that, it was Euclidean geometry and the parallel postulate, which lead to the breakdown of Euclidean space in face of non-flat spaces, i.e. spherical and parabollic spaces.

However, later Goedel proved that Holbert's dream cannot be fullfilled, that a system sufficiently complex, such as math, is either incomplete or inconsistent.

Today, sets are still deemed by many as the most suitable theory to be at the foundation of math, although competitors are on the rise, of which the most prominent is category theory. The ZFC set theory is the one that most mathematicians consider as the math's foundation. In any case, sets are fundametal to math and they are way easier then categories for a first introduction to mathematics.