Our Trip to Prime Number Theorem (2021)

The 1859 paper by Bernhard Riemann which introduced the zeta-function and linked it to the Prime Number distribution is only 9 pages and quite approachable. It inspired much of analytic number theory:

https://en.wikipedia.org/wiki/On_the_Number_of_Primes_Less_T...

It also contains his famous conjecture:

"One now finds indeed approximately this number of real roots within these limits, and it is very probable that all roots are real. Certainly one would wish for a stricter proof here; I have meanwhile temporarily put aside the search for this after some fleeting futile attempts, as it appears unnecessary for the next objective of my investigation"

Very good post! For an excellent introduction to the prime number theorem (and the Riemann Hypothesis), I recommend Prime Numbers and the Riemann Hypothesis, by Barry Mazur and William Stein. It is structured in small chapters, each illuminating one idea, and I find this fantastic.

As someone who has too many life obligations, but would love to do something similar one day, this was a nice read, thanks for sharing.

This looks like a very cool & fun experiment … there are many other subject matters on which this could be done …