The Basel problem is a problem in mathematical analysis, with relevance to number theory, concerning an infinite sum of inverse squares. Pietro Mengoli first posed it in 1650, and Leonhard Euler solved it in 1734, reading his solution to the Saint Petersburg Academy of Sciences on 5 December 1735. The problem had resisted the leading mathematicians of the time, so Euler's solution brought him immediate fame at the age of twenty eight, and he went on to generalize it considerably, work that Bernhard Riemann took up more than a century later in his 1859 paper on the distribution of prime numbers.
Facts
StatementThe sum of the infinite series of reciprocals of the squares of the natural numbers equals pi squared divided by six. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Basel Problem (Wikipedia)
Sources
1. Basel Problem (Wikipedia)
Wikimedia Foundationlead paragraph, problem definition sentence
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
lead paragraph, Euler announcement sentence
Euler found the exact sum to be pi-squared over six and announced this discovery in 1735 (rendered from the article's LaTeX display formula {\pi^2}/{6}, not literal running prose).
- In Branch: Analysis, Lead sentence
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