Johann Friedrich Pfaff
Johann Friedrich Pfaff ( born December 22, 1765 in Stuttgart, † April 21, 1825 in Halle ( Saale) ) was a German mathematician and member of a dynasty of university professors (see below). He taught at the universities of Helmstedt and Halle, where he dealt primarily with analysis and partial differential equations.
- 2.1 Pfaff'sches problem
Life
Pfaff was the second oldest of twelve children of the Stuttgart Regional Finance Council Burkhard Friedrich Pfaff and his wife Maria Magdalena, née fire. Of his brothers were also two scientists: Christoph Heinrich Pfaff (1773-1852) and Wilhelm Andreas Pfaff ( 1774-1835 ).
He attended from 1774 to 1785, the High School Karl, a military school in the ducal Schloss Solitude in Stuttgart, where he graduated in 1785 legal studies. In addition, he made self-study in mathematics and was sent by Carl Eugen of Württemberg, ruler and founder of the school, on a multi-year educational journey. From 1785, he studied at the instigation of the Duke in Göttingen at Kästner and Lichtenberg Mathematics and Physics, 1787 went to Berlin to astronomer Bode and in the following year on an educational journey, among other things to Jena, Gotha, Prague and finally to Vienna. At the instigation of Lichtenberg, he was appointed in 1788 as professor of mathematics at the University of Helmstedt.
An historical service of the dedicated high school teacher was to have recognized the genius of the young Carl Friedrich Gauss; 1799 he was the expert of his dissertation and supported its request to obtain a PhD at the University of Helmstedt in absentia ( in absence). Other important students were Johann Christian Martin Bartels (1769-1836), Christian Ludwig Gerling (1788-1864) (1788-1864), Carl Brandan Mollweide (1774-1825) and the later Tubingen Jusprofessor Siegfried Heinrich Eduard von Schrader (1779-1860 ). As a developer of new talent to Pfaff also proved by a letter of recommendation to Göttingen for Alexander von Humboldt.
University Politically, Pfaff dedicated to the conservation of the University of Helmstedt as Braunschweigische State University. When she was still closed in 1810 because of french subversive activities during the Napoleonic Wars, Pfaff went to the University of Halle and just re-opened in 1812 by Prof. clique death also head of the local observatory. Both places at that time belonged to the kingdom of Westphalia established by Napoleon.
Also in Hall he was respected teacher, among other things August Ferdinand Möbius of (1790-1868), Johann August Grunert, Johann Joseph Beautiful and Karl Friedrich Wex.
Pfaff left extensive mathematical manuscripts, which are preserved in the University Library in Halle.
Relationship
Pfaff 1803 married his cousin Caroline Brand, daughter of the pastor Christoph fire. Christoph Brand was the brother of Johann Pfaff's mother and son of the church and chamber Council Gottfried fire. With Caroline Pfaff had joint sons Carl ( later historians ) and Ludwig.
His younger brother Christopher Henry was professor of chemistry in Kiel. His youngest brother, Johann Wilhelm Andreas was a professor of mathematics and astronomy at Dorpat, Würzburg and Erlangen. The sons of Johann Wilhelm Andreas turn were Professors Hans Ulrich Vitalis (mathematics ) and Friedrich (mineralogy ), his daughter was the writer Pauline Damayanti, the later the Liberal journalist Carl Ludwig Theodor Brater married and with him the daughter Agnes Sapper, also writer had.
Pfaff as a mathematician
Intensive Pfaff dealt with the theory of partial differential equations and in 1810 with the simplification of certain differential expressions ( " Pfaff cal problem " ), whose general solutions stated HGGraßmann ( 1809-77 ). The " Pfaffian forms " were part of the basic training in mathematical analysis and are still research topic. Pfaff's work was initially little used despite very positive review by Gauss note to Jacobi in 1827 highlighted its importance.
Other major works are mathematically in 1797 a Latin textbook on calculus in the spirit of Leonhard Euler, or the solution of a public task set for the largest a convex quadrilateral writable Ellipse (1810 ), which also dealt with Gauss and Mollweide.
Major publications are:
Pfaff'sches problem
In Helmstedt Pfaff published in 1788 work on a novel derivation of differentiation rules, in 1788 and later on the summation of certain series, and in 1793, following on from Euler, on the series expansion for integrals of certain powers.
Pfaff 1815 published his most important work, " Methodus generalis aequationes differentiarum particularum ... complete intigrandi ". It is the Pfaffian problem of integration of partial differential equations of the form with
Today it is called a Pfaffian form in n variables.
The first recognized only by Gauss as a significant method was in 1827 by Jacobi ( 1804-1851 ) further expanded. Pfaff had considered the case of an even number of variables, Jacobi was able to extend the method to an odd number of variables.