Carl Friedrich Hindenburg

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Infinitinomii dignitatum exponentis indeterminati historia leges ac formulae editio pluribus locis aucta et passim emendata , 1779

Carl Friedrich Hindenburg (born July 13, 1741 in Dresden , † March 17, 1808 in Leipzig ) was a German mathematician , professor of philosophy and physics .

Life

Hindenburg was the son of a Dresden wholesaler. He was tutored by a private tutor. In 1757 he went to the University of Leipzig and took courses in medicine , philosophy, physics, mathematics and aesthetics . In 1771 he completed his master's degree and was appointed private lecturer .

Even before his appointment as a private lecturer, Hindenburg published several writings in the field of philology in 1763 and 1769 . He made his first publications in the field of mathematics in 1776. Two years later he published his work on combinatorial mathematics . In the following years up to 1800 he published a number of mathematical writings. Hindenburg made a name for himself as the inventor of combinatorial analysis. This made him influential in Germany and found its way into many text and school books. The representatives of this school derived from a combinatorial way, for example, how the coefficients of the mth power (where m could also be fractional or negative) of an infinite series Q can be derived from the coefficients of Q. In their opinion, the subject of analysis was the symbolic transformation of finite or infinite strings, i.e. the investigation of the structure of formulas in their mutual dependence. This was in the tradition of algebraic analysis of the 18th century with its most important representative Leonhard Euler (formal manipulation of infinite series without considering questions of convergence) and was also called analysis of the finite in Germany . The main line of the further development of algebraic analysis passed through functions that can be represented by power series in the hands of Joseph-Louis Lagrange . In his use of combinatorics, Hindenburg also resorted to ideas from Gottfried Wilhelm Leibniz . His main work Infinitomii dignitatum appeared in 1779 and, according to the representatives of this school, the central content of analysis was in the combinatorial polynomial theorem found by Hindenburg . The underlying formula was already known to Leibniz (for integer m) and Euler, but unlike Hindenburg, it was written recursively. According to Jahnke, the reduction of analysis to computation in the finite that can be algorithmized using combinatorial principles (similar to constructive mathematics later ) also found approval among romantic intellectuals at the end of the 18th century, such as Novalis ( computing and thinking is one ), as Jahnke remarked first fractions in this picture when Siméon Denis Poisson discovered antinomies in infinite trigonometric series in 1811 (identities that were correct for integer exponents, but not for fractional numbers), which attracted a great deal of attention at the time and, for example, a motif of the work on convergence issues of infinite series by Niels Henrik Abel . The work of Augustin-Louis Cauchy then led to a paradigm shift in analysis, even if algebraic analysis in Germany continued for a while and only ended under the influence of Felix Klein and his teaching reform, who spoke of the misery of algebraic analysis in 1907 .

In 1781 Hindenburg was appointed associate professor of philosophy at the University of Leipzig. After the presentation of a doctoral thesis on water pumps , he was also appointed professor of physics in 1786, as which he then mainly worked for the next 20 years.

In 1797 he was elected a corresponding member of the Göttingen Academy of Sciences . In 1806 he was accepted as a foreign member of the Prussian Academy of Sciences . Since 1794 he was an honorary member of the Russian Academy of Sciences in Saint Petersburg .

Together with Daniel Bernoulli, he published the journal Leipziger Magazin zur pure and applied mathematics (Leipzig 1786–1789) and published the archive of pure and applied mathematics (Leipzig 1794–1801).

Fonts

  • Infinitomii dignitatum exponentis indeterminati historia leges ac formulae editio pluribus locis aucta et passim emendata, Göttingen 1779
  • Novi Systematis Permutationum Combinationum Ac Variationum Primae Lineae Et Logisticae Serierum Formulis Analytico-Combinatoriis Per Tabulas Exhibendae Conspectus Et Specimina ， Leipzig 1781
  • The polynomial theorem, the most important theorem of all analysis, Leipzig 1796

literature

Individual evidence

  1. ↑ Hans Niels Jahnke, Algebraische Analysis, in: D. Spalt, Rechnen mit dem Unendlichen, Springer 1990, p. 103
  2. ↑ See the presentation in Jahnke, Algebraische Analysis, 1990, pp. 104f. Hindenburg's presentation contained unclear points regarding the meaning of the equality of formula expressions, especially in the case of fractional exponents, which was taken up and further developed in the 1820s by Christoph Gudermann , Karl Weierstrass's teacher .
  3. ↑ Jahnke, Algebraische Analysis, 1990, p. 107
  4. ^ Jahnke, Algebraische Analysis, p. 121
  5. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 115.
  6. ^ Foreign members of the Russian Academy of Sciences since 1724. Carl Friedrich Hindenburg. Russian Academy of Sciences, accessed August 19, 2015 (Russian).

Web links

personal data
SURNAME Hindenburg, Carl Friedrich
BRIEF DESCRIPTION German mathematician, professor of philosophy and physics
DATE OF BIRTH July 13, 1741
PLACE OF BIRTH Dresden
DATE OF DEATH March 17, 1808
Place of death Leipzig