Basel problem

proper noun

The question as to the value of ∑ₙ₌₁ ᪲1/(n²), the sum of the reciprocals of the squares of the positive integers.

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Meanings

proper noun
  1. mathematicsThe question as to the value of ∑ₙ₌₁ ᪲1/(n²), the sum of the reciprocals of the squares of the positive integers.

    Solving the Basel problem was one of the early triumphs of L. Euler (1707–1783)... .

    2005, Rajendra Bhatia, Fourier Series, Mathematical Association of America, →ISBN, section 3.10, page 75
    2 more examples

    As noted, some of Euler's contemporaries, while accepting his answer to the Basel Problem, wondered about the validity of the argument that got him there.

    1999, William Dunham, Euler: The Master of Us All, Mathematical Association of America, →ISBN, page 55

    And so ends one of Euler's most famous papers. We see that Euler actually solves the Basel problem three times and that he does much more.

    2007, Charles Edward Sandifer, The Early Mathematics of Leonhard Euler, Mathematical Association of America, →ISBN, page 165

Origin

Named after Basel, the home town of Euler and of the Bernoulli family who unsuccessfully attacked the problem.

Full word history & related roots →
Cite this entry
APA

Basel problem. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/Basel%20problem

MLA

“Basel problem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Basel%20problem. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “Basel problem,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/Basel%20problem.

Source: Basel problem on Wiktionary, CC BY-SA 4.0.