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Faulhaber's Academia Algebrae

Sums of odd powers

Johann Faulhaber (1580–1635) was a founder of a school for engineers who loved numbers. This love is evident in his 1631 work Academia Algebrae. In this treatise, Faulhaber developed and published formulas for sums for integers up to the 17th power, though without revealing their derivation.

Faulhaber's Academia Algebrae

Faulhaber’s work would later influence astronomer Johannes Kepler (1571–1630) and mathematician René Descartes (1596–1650). The general formula for summing powers of integers is now known as Faulhaber's formula.

Artifact dimensions

6.2 in. × 7.7 in.

Artifact origin

Augsburg, Germany

Current artifact location

Rare Book & Manuscript Library, Butler Library, Columbia University in the City of New York

Catalog number

SMITH 512 1631 F27


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Computational Explanation

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Other Resources

Additional Reading

  • Faulhaber, J. Academia Algebrae. Ulm, Germany: Johann Remelins, 1631.
  • Knuth, D. "Johann Faulhaber and the Sums of Powers." Mathematics of Computation, Vol. 61, pp. 277–294, 1993.
  • Smith, D. A Source Book in Mathematics. Mineola, NY: Dover, pp. 85–90, 1959.