{"id":"basel-problem","domain":"named-results","type":"Theorem","title":"Basel Problem","slug":"basel-problem","url":"/mathematics/named-results/basel-problem/","posed":"1650, Pietro Mengoli","proved":"1734, Leonhard Euler","summary":"Sum of reciprocal squares 1+1/4+1/9+... = pi^2/6. Connects pi to number theory. Special case zeta(2).","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Euler, L. (1741). De summis serierum reciprocarum. Commentarii academiae scientiarum Petropolitanae, 7, 123-134."},{"tier":1,"citation":"Ayoub, R. (1974). Euler and the zeta function. The American Mathematical Monthly, 81(10), 1067-1086."},{"tier":2,"citation":"van der Poorten, A. (1979). A proof that Euler missed. The Mathematical Intelligencer, 1(4), 195-203."},{"tier":3,"citation":"Dunham, W. (1999). Euler: The Master of Us All. MAA."}],"relationships":[{"type":"special_case_of","target":"riemann-hypothesis","label":"Riemann Hypothesis — ζ(2)"},{"type":"uses","target":"series-and-convergence","label":"Series & Convergence"},{"type":"uses","target":"complex-number","label":"Complex Number — residue theorem proof"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.1"}