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This course explores the sociology of pure mathematics by delving into ancient Greek mathematical concepts, particularly Euclid's proof of the "Infinitude of Primes". The course aims to help students understand the historical context of pure mathematics and encourages a critical examination of modern mathematical claims. By analyzing Euclid's arguments, students will develop a computational mindset and gain insights into the differences between ancient and modern mathematical thinking. The course is designed for mathematics undergraduates and graduate students who are interested in foundational issues in mathematics and are open to questioning established mathematical beliefs.