<Tr> <Td> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in The Saint Petersburg Academy of Sciences . Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty - eight . Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties . The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem . </P> <P> The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series: </P>

Sum of inverse of squares of natural numbers
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