Peter Roth (mathematician)

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Peter Roth († April 1617 ) was an arithmetic master (Cossist) in Nuremberg .

Life

Peter Roth was the son of Heinrich Roth. It is known that he was imprisoned in 1590 for rebellion against the council, but then repented and apologized.

Little is known about Peter Roth. He married Maria Magdalena Herold, daughter of a gunmaker, on July 17, 1603, and was buried in Nuremberg on April 25, 1617.

A manuscript by Roth from 1599 at Columbia University has been preserved, in which the solutions (from chapter five) of the first German algebra book (Coss) by Christoph Rudolff are contained in the edition by Michael Stifel from 1554.

In his Arithmetica Philosophica he put forward the conjecture that polynomials of the nth degree have at most n roots. He presented the solution of cubic equations according to Gerolamo Cardano and treated sums of pyramid numbers and polygonal numbers according to Johannes Faulhaber (and believed that he had found the rules for them independently of Faulhaber). In the second part it contained all possible solutions to the 160 problems in Faulhaber's Arithmetic Cubicossischer Lustgarten (1604), which Faulhaber had actually written as an advertising pamphlet for his arts as a mathematician (the title alludes to the fact that he also used Cardano's methods of solving cubic equations mastered), so that Roth's publication, which he knew about to prepare from 1605, deeply angered him. As a mathematician who lived from the teaching of his arts, Faulhaber was not interested in the publication of solution formulas or the simplest possible representation (in his book 1604 he had only given the solutions, not the way). In the third part of his book, Roth presented new tasks as a challenge, especially to Faulhaber (who also later solved them). They lead to equations of the fourth through seventh degree. Roth was convinced of the solvability of the equations of the fourth and higher degree in radicals.

His book influenced the geometry book by René Descartes (1637) and his work on the decomposition of polynomials. It also increased Roth's reputation in other European countries. In 1626 Faulhaber reported that he was considered by many to be the most learned Arithmeticum Europae . After Faulhaber, Nicolaus Petri was the first to develop methods for the decomposition of polynomials, which Roth developed further.

The mathematics professor in Altdorf Daniel Schwenter (1585–1636) praised Roth for the construction of Latin squares (mathematical refreshment hours 1636). There appear to have been unpublished Roth manuscripts on geometry.

An arithmetic master Paul Roth (died 1628) mentioned in Nuremberg in 1619 (next to Sebastian Kurtz (1576-1659)) was probably his son.

Fonts

  • Arithmetica philosophica, or Schöne newe wolgegründte extremely artificial calculation of the Coss or Algebrae, Nuremberg: Johann Lantzenberger 1608, digitized, ETH library

literature

  • Ivo Schneider : Johannes Faulhaber, Birkhäuser 1993
  • Ivo Schneider: Peter Roth († April 1617). In: Rainer Gebhardt (Hrsg.): Arithmetic books and mathematical texts of the early modern times. Writings of the Adam-Ries-Bund Annaberg-Buchholz, Volume 11. Annaberg-Buchholz: Adam-Ries-Bund 1999, pp. 303-312
  • Kenneth Manders: Algebra in Roth, Faulhaber 1580-1635, and Descartes, Historia Mathematica, Volume 33, 2006, pp. 184-209, abstract at Science Direct

Web links

Individual evidence

  1. ↑ Sasaki, Descartes mathematical thought, Springer 2003, pp. 123f
  2. ^ Ivo Schneider, Johannes Faulhaber, p. 93
  3. ^ Ivo Schneider, Faulhaber, p. 107
personal data
SURNAME Roth, Peter
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH 16th Century
DATE OF DEATH April 1617
Place of death Nuremberg