Explore the logical weaknesses in modern pure mathematics through a Socratic lens in this 52-minute video lecture. Delve into historical problems surrounding the continuum, analysis, and set theory, while examining their relevance in the context of computational thinking. Confront a challenging "limit conundrum" based on the Collatz conjecture to test your understanding of limits. Investigate topics such as Greek mathematical perspectives, decimal arithmetic, real numbers, infinite decimals, and the fundamental conjecture of algebra. Critically analyze modern set theory and its implications for the foundations of mathematics.