Background

Christian Kramp was born on July 8, 1760, in Strasbourg, France. His father, Jean-Michel, was a teacher at the Gymnasium in Strasbourg.

Education

Brought up speaking French and German, Kramp studied medicine at the University of Strasbourg. He was also a disciple of the German philosopher and mathematician K. F. Hindenburg.

Career

Kramp practiced in several Rhineland cities that were contained in the region annexed to France in 1795. Turning to education, Kramp taught mathematics, chemistry, and experimental physics at the École Centrale of the department of the Ruhr in Cologne. Following Napoleon’s reorganization of the educational system, whereby the Écoles Centrales were replaced by lycées and faculties of law, letters, medicine, and science were created, Kramp, around 1809, became professor of mathematics and dean of the Faculty of Science of Strasbourg.

In 1783, the year the Montgolfier brothers made the first balloon ascension, Kramp published in Strasbourg an account of aerostatics in which he treated the subject historically, physically, and mathematically. He wrote a supplement to this work in 1786. In 1793 he published a study on crystallography and, in Strasbourg, a memoir on double refraction.

Kramp published a medical work in Latin in 1786 and another, a treatise on fevers, in German in 1794. His critique of practical medicine appeared in Leipzig in 1795. Moreover, in 1812 he published a rather mediocre study on the application of algebraic analysis to the phenomenon of the circulation of the blood. He corresponded with Bessel on astronomy and made several calculations of eclipses and occultations in the years before 1820; his most important astronomical work, however, is the Analyse des réfractions astrono-miques et terrestres (1798), which was very favorably received by the Institut de France. He wrote several elementary treatises in pure mathematics, as well as numerous memoirs, and the Éléments d'arithmétique universelle (1808). Kramp also contributed to the various journals that K. F. Hindenburg edited.

Achievements

• Christian Kramp went down in history as a noted physician and mathematician, best known for his work on factorials. He was the first to use the notation "n!" in his work Elements d'arithmétique universelle. He may also be considered to be one of the representatives of the combinatorial school, which played an important role in German mathematics.
  
  Kramp's function, a scaled complex error function, was named after him; it is better known today as the Faddeeva function.

Works

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• book

  • Éléments de géométrie 1806
  • Geschichte Der Aerostatik, Historisch, Physisch Und Mathematisch Ausgeführt, Volume 1 1784
  • Geschichte Der Aerostatik, Historisch, Physisch Und Mathematisch Ausgefuhrt, Volume 2 1784
  • Geschichte Der Aerostatik, Historisch, Physisch Und Mathematisch Ausgeführt, Volume 3 1786
  • Kristallographie Des Mineralreichs 1793
  • Elemens D'Arithmetique 1801
  • De vi vitali arteriarum diatribe. Addita nova de febrium indole generali conjectura 1786

Views

In the Analyse des réfractions astronomiques Kramp attempted to solve the problem of refraction by the simplifying assumption that the elasticity of air is proportional to its density. He also presented a rather extensive numerical table of the transcendental function which is so important in the calculus of probabilities, and which sometimes is called Kramp’s transcendental. In this same work he considered products of which the factors are in arithmetic progression. He called these products “facultés analytiques,” but he ultimately adopted the designation “factorials,” proposed by his fellow countryman Arbogast.

Although Kramp was not aware of it, his ideas were in agreement with those of Stirling (1730) and especially those of Vandermond. The notation nl for the product of the first n numbers, however, was his own. Like Bessel, Legendre, and Gauss, Kramp extended the notion of factorial to non-whole number arguments, and in 1812 he published a numerical table that he sent to Bessel. In his Arithmétique universelle Kramp developed a method that synthesizes the fundamental principles of the calculus of variations as stated by Arbogast with the basic procedures of combinatorial analysis. He thus strove to create an intimate union of differential calculus and ordinary algebra, as had Lagrange in his last works.

Membership

A corresponding member of the Berlin Academy since 1812, Kramp was elected a corresponding member of the geometry section of the Academy of Sciences of Paris at the end of 1817.

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  Corresponding member

  Berlin Academy , Germany

  1812 - 1826

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  Corresponding member

  Academy of Sciences of Paris , France

  1817 - 1826

Connections

It is not known whether Kramp was married or not.

Father:

Jean-Michel Kramp

teacher:

K. F. Hindenburg

References

• Dictionary of Scientific Biography, Volume 7
  1973