For Lu Zhou, teaching undergraduates also counted as a review of the fundamentals.
Under normal circumstances, he rarely spared any thought for things that seemed self-evident to him. Only at times like this could he temporarily set aside his research and consider why those self-evident things were self-evident in the first place.
"...Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in Analytic Number Theory. It is a hypothesis about the distribution of the zeros of the Riemann zeta function. But few people know why the Riemann Hypothesis was proposed in the first place."
"In fact, before the Riemann Hypothesis, there was an even broader proposition that countless scholars had studied for centuries: the pattern governing the distribution of prime numbers."
As he spoke, Lu Zhou wrote several numbers on the blackboard, then turned back to the students in the classroom.
"By the fundamental theorem of arithmetic, even middle school students know that every positive integer can be expressed as a product of prime factors. If we disregard the order of those prime factors, that expression is unique. Therefore, prime numbers are also the fundamental building blocks of positive integers."
"However, the distribution of prime numbers is nowhere near as easy to understand as their definition. One could even say that one of the most basic tasks of the entire field of Analytic Number Theory is to study the distribution of prime numbers."
Watching the students gradually become engaged, Lu Zhou knew that his class had already succeeded halfway.
Although the Riemann Hypothesis was an extremely complicated problem, understanding it was not actually as difficult as most people imagined. The truly difficult part was solving it...
After a brief pause, Lu Zhou continued.
"In Analytic Number Theory, people usually study the Prime-Counting Function,