# 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. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/100-fundamentals/120-foundations-of-mathematics/foundations.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.