Apery -

Roger Apéry was a French mathematician best known for the 1978 proof of the irrationality of the Riemann zeta function at 3, , now known as . Apéry’s Constant ( )

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

His presentation was disorganized and featured "unlikely assertions" that many attendees initially dismissed as a prank. Roger Apéry was a French mathematician best known

cannot be written as a fraction—a claim that had eluded mathematicians for centuries.

When asked where his complex formulas came from, he famously replied, "They grow in my garden". cannot be written as a fraction—a claim that

Apéry's constant is defined as the sum of the reciprocals of the positive cubes:

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 Apéry's constant (calculated with Twitter) - Numberphile At

At a 1978 conference in Marseille, Apéry presented a proof that