Person: Faulhaber, Johann
Johann Faulhaber was a German Cossist or early algebraist. He is important for his work explaining the recently invented logarithms.
Mathematical Profile (Excerpt):
- Among the scientists with whom Faulhaber collaborated were Kepler and van Ceulen.
- Faulhaber was a 'Cossist', an early algebraist.
- Faulhaber's most major contribution, however, was in studying sums of powers of integers.
- In 1631 Faulhaber published Academia Algebra Ⓣ(Academy of Algebra) in Augsburg.
- Faulhaber states that such polynomials in NNN exist for all kkk, but gave no proof.
- It is not known how much Jacobi was influenced by Faulhaber's work, but we do know that Jacobi owned Academia Algebra since his copy of it is now in the University of Cambridge.
- Faulhaber did not discover the Bernoulli numbers but Jacob Bernoulli refers to Faulhaber in Ars Conjectandi Ⓣ(The art of conjecturing) published in Basel in 1713, eight years after Jacob Bernoulli died, where the Bernoulli numbers (so named by De Moivre) appear.
- Faulhaber gave formulae for mmm-fold sums of powers defined as follows.
- One cannot help thinking that nobody has ever checked these numbers since Faulhaber himself wrote them down, until today.
Born 5 May 1580, Ulm, Germany. Died 1635, Ulm, Germany.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive