ζ(3)=∑n=1∞1n3=1+123+133+…zeta open paren 3 close paren equals sum from n equals 1 to infinity of the fraction with numerator 1 and denominator n cubed end-fraction equals 1 plus the fraction with numerator 1 and denominator 2 cubed end-fraction plus the fraction with numerator 1 and denominator 3 cubed end-fraction plus … It is approximately 1.2020569 . Significance: While even zeta values like have clear closed forms involving , no such "neat" form exists for
At a 1978 conference in Marseille, Apéry presented a proof that The "Miraculous" 1978 Proof cannot be written as
When asked where his complex formulas came from, he famously replied, "They grow in my garden". eventually verified his work
It appears in quantum electrodynamics , specifically relating to the anomalous magnetic moment of the electron. The "Miraculous" 1978 Proof he famously replied
cannot be written as a fraction—a claim that had eluded mathematicians for centuries.
Fellow mathematicians, including Henri Cohen and Alfred van der Poorten, eventually verified his work, confirming it as a genuine breakthrough. Apéry's constant (calculated with Twitter) - Numberphile