““In the chapter on prime numbers, I mentioned Bernhard Riemann's 1859 paper 'On the Number of Primes Less than a Given Magnitude'. In it he found a method of calculating how many primes there are below any given number. This would give mathematicians an amazing insight into the distribution and nature of prime numbers. The only problem was that he couldn't prove that this method definitely worked. He did, however, prove that if an apparent alignment in the zeta function was real, then the prime counting method was real. Then he failed to prove that too.””
![“The rule for working out prime numbers is very simple, but no one has ever worked out a simple formula for telling you whether a very big number is a prime number or what the next one will be. […] Prime numbers is what is left when you have taken all the patterns away. I think prime numbers are…” quote by Mark Haddon](https://sms4smile.com/quotes/img-quotes/b7f/mark-haddon-1056_life_the-rule-for-working-out-prime-numbers-i_2825727.jpg)
![“Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.” quote by Lucio Russo](https://sms4smile.com/quotes/img-quotes/66c/lucio-russo-43521_analysis_euclid-manages-to-obtain-a-rigorous-proo_2943863.jpg)
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
