For the mathematically inclined, Terence Tao's explanation provides an easier intuition of the relationship using real-variable methods: https://terrytao.wordpr

For the mathematically inclined, Terence Tao's explanation provides an easier intuition of the relationship using real-variable methods: https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/ https://terrytao.wordpress.com/2010/04/10/the-euler-maclauri...