Riemann’s famous 1859 article “On the Number of Primes Less Than a Given Quantity” is one of the most influential works in the history of mathematics, particularly in the field of number theory.

In this paper, Bernhard Riemann explores the distribution of prime numbers—a topic that had puzzled mathematicians for centuries. His groundbreaking approach connects the distribution of primes to the properties of the Zeta function, a complex function initially studied in the context of analytic number theory.

The article’s significance lies not only in its immediate impact on number theory but also in the way it set the stage for future developments in mathematics. Riemann’s techniques and ideas continue to influence modern research.

In this first lesson, we provide a detailed explanation of the initial pages, all the way up to the claim of the famous Riemann Hypothesis.