The Music of the Primes
After the complex and fascinating reading of What We Cannot Know by Marcus du
Sautoy, I read The Music of the Primes (La música de los números primos).
On this occasion, he explores prime numbers and the mathematical research that was done on them.
These are some of the stories covered in the book:
- Euclid. Demonstration of infinite prime numbers.
- University of Göttingen.
- Gauss. Instead of predicting what the prime numbers might be, he wondered how
many prime numbers there are. Notice a pattern – as numbers increase, the
number of prime numbers decreases.
- Riemann hypothesis. Using the zeta function he constructs a mathematical
landscape where he connects the distribution of prime numbers with geometry.
Are all zeros on the same line?
- University of Cambridge.
- Hardy. Demonstration of infinite zeros on the line.
- Ramanujan. Created a formula to calculate prime numbers with a tiny margin of error.
- Turing. Built a machine to demonstrate that Riemann’s hypothesis is false.
- Computer. So far, all calculations show that Riemann’s hypothesis was correct and all zeros are
on the same line.
- Princeton Institute for Advanced Studies.
- Montgomery - Dyson. Behaviour of atoms corresponds to the behaviour of prime
- RSA. Factorization of prime numbers.