Paul Painlevé

Paul Painlevé. Photo from 1923

Paul Painlevé (born December 5, 1863 in Paris , † October 29, 1933 ibid) was a French mathematician and politician of the reform socialist Parti républicain-socialiste . In 1917 and 1925 he was Prime Minister of the Third French Republic for a few months each .

mathematics

Career

Painlevé studied from 1883 at the École normal supérieure mathematics and received his doctorate in 1887 after studying with Felix Klein and Hermann Amandus Schwarz at the University of Göttingen for a while. He was a professor at the University of Lille I , from 1892 he taught in Paris at the Sorbonne , the École polytechnique and later at the Collège de France and at the École normal supérieure. From 1900 he was an elected member of the Paris Academy of Sciences , whose president he became in 1918. In 1904 he gave a plenary lecture at the International Congress of Mathematicians in Heidelberg (Le Problem modern de l'intégration des equations différentielles).

Paul Painlevé at a young age

His mathematical work in the field of differential equations brought him into contact with their applications to the theory of flight and he became enthusiastic about the just developing aviation due to his passion for engineering . In 1908 he was Wilbur Wright's first aircraft passenger in France and in 1909 initiated the first university course on aeronautics .

In 1903 he was president of the Société Mathématique de France . In 1902 he became a Knight of the Legion of Honor .

Work

In simple cases, the solution of a differential equation can be expressed using elementary functions such as the trigonometric functions or the exponential function . Many special functions in mathematical physics are solutions to linear differential equations of the second order. Painlevé considered nonlinear differential equations of the second order with a special property now called the Painlevé property ( Painlevé equations ).

To define this property, the singularities of a solution are classified into fixed and movable singularities. A singularity is called mobile if it depends on the initial values ​​of the differential equation. For example, the differential equation has the solutions with the moving pole . A differential equation is now said to have the Painlevé property if the only moving singularities are poles. ${\displaystyle w'(z)=w(z)^{2}}$ ${\displaystyle w(z)=(z-a)^{-1}}$ ${\displaystyle a}$

The first order differential equations with the Painlevé property had been classified by Lazarus Fuchs and Henri Poincaré . Painlevé investigated this question for differential equations of form , where is rational. This led to a list of 50 equations, 44 of which, however, could be traced back to known equations. There remained 6 new equations, which are now called Painlevé's differential equations , their solutions as Painlevé's transcendentals . Painlevé's list was not entirely exhaustive, but Bertrand Gambier and Richard Fuchs completed it. Painlevé's transcendents are important in various areas of mathematical physics and are still the subject of intensive research today. ${\displaystyle w''(z)=R(z,w(z),w'(z))}$ ${\displaystyle R}$

In celestial mechanics he proved that in the three-body problem there are singularities of the collision type, but could not extend this to higher dimensions and assumed that singularities of the non-collision type exist for more than four bodies (as Hugo von Zeipel showed, then particles can escaping to infinity in finite time). The conjecture was proven for five and more bodies by Jeff Xia in the late 1980s .

In the 1920s, Painlevé was interested in the theory of gravity and the general theory of relativity , which had recently been introduced by Albert Einstein . Painlevé introduced a coordinate system for the Schwarzschild metric (a vacuum solution of Einstein's field equations ) in 1921 . This coordinate system clearly showed for the first time that the singularity of the Schwarzschild metric at the Schwarzschild radius (which represents the event horizon of a black hole ) is only a coordinate-dependent mathematical relic and does not represent a physical singularity . This was not generally accepted by physicists until about 1963, when the Kruskal-Szekeres coordinates introduced by Martin Kruskal and George Szekeres (and others) also showed it. The coordinates of Painlevé are also known as Gullstrand-Painlevé coordinates, after the simultaneous introduction by Allvar Gullstrand .

politics

He entered politics as a member of the French League for Human Rights in the wake of the Dreyfus Affair . In 1910 he was elected to the Chamber of Deputies for the first time for the moderate-left Parti républicain-socialiste , a foundation by Aristide Briand and Alexandre Millerand . In the same year he gave up his professorship to devote himself entirely to politics. He was particularly concerned with military issues and, as a specialist in the nascent military aviation, headed various state committees. After the beginning of the First World War , he became Minister for Public Education, Fine Arts and Defense Technology in the fifth cabinet of Aristide Briand (October 29, 1915 to December 12, 1916). In March 1917 he was appointed Minister of War under Alexandre Ribot . He was critical of the new French commander in chief Robert Nivelle and replaced him with Philippe Pétain after the failed Nivelle offensive and the severe mutinies in the French army in May 1917 . He appointed Ferdinand Foch Chief of Staff.

For the peace talks with the Austrian diplomat Nikolaus Revertera-Salandra in August 1917 in Freiburg , Switzerland , he commissioned Count Abel Armand, major in the intelligence department of the French General Staff, to offer Austria-Hungary unrealistic concessions (such as the annexation of Bavaria , Silesia and Poland ) in order to To win Austria for a separate peace . The state structure was to bear the name “Confédération Danubienne” under the Habsburg scepter. The negotiations failed because Revertera had no mandate to negotiate a separate peace, as Painlevé was trying to achieve.

After Ribot's resignation due to the departure of the socialist SFIO from the all-party government, the Union sacrée , which had ruled France since the beginning of the First World War, Painlevé took over the post of Prime Minister for a few weeks in September 1917 in addition to heading the War Ministry . During his tenure, the Allied Conference in Rapallo fell , at which a joint high command was agreed in the form of the Allied Supreme War Council , in which Painlevé, who represented the French side in Rapallo, established Foch as the French representative. In the wake of the political upheaval caused by the heavy Italian defeat at Caporetto , Painlevé lost the support of the House of Representatives in November 1917 and resigned. He was succeeded by Georges Clemenceau .

In order to pool the forces of the left against the bloc national, which had ruled since 1919 , Painlevé announced the formation of a "Ligue de la République" in Avignon in 1921, which was founded shortly afterwards. Politicians who saw themselves as leftists , such as the socialists, the radical socialists or his own Républicain-socialistes, worked together more closely in the future and in the second ballot did not stand for another left if that made the election more promising.

Painlevé (center) with Prime Minister Poincaré and Foreign Minister Briand, 1925

This cooperation proved to be successful in the parliamentary elections of 1924: for the first time, under the radical socialist Édouard Herriot, the cartel des gauches , a coalition of left-wing parties with the SFIO, came to power. Painlevé again took a leading position and became President of the Chamber of Deputies. After the failure of the cartel in April 1925, he became prime minister of a centrist cabinet for a few months , which pursued a much more moderate policy than its predecessor: diplomatic relations with the Vatican were resumed, the project of a capital tax was dropped, and also in the dispute over it the separation of church and state in Alsace-Lorraine , which France had got back in 1918, Painlevé was indulgent. In doing so, he drew the wrath of the left for Herriot, who refused to support the austerity policy that Painlevé's Finance Minister Joseph Caillaux was trying to use to fight inflation . Painlevé reshuffled his cabinet on October 29, dismissed the unloved Caillaux and took over the finance ministry himself, but in vain: on November 22, 1925, he was overthrown in the Chamber of Deputies. In the following governments under Briand and Raymond Poincaré , Painlevé served again as Minister of War until 1929, and from December 1930 to January 1931 he was Minister of Aviation in the short-lived Théodore Steeg cabinet . At Poincaré's instigation, Painlevé developed the multicolore game of chance .

In February 1932 he tried to form a coalition government of his Républicain-socialistes and the Radical Socialists with the liberal Alliance démocratique . But because the latter insisted that the nationalist Fédération républicaine should also be involved, Painlevé returned the mandate to form a government to President Paul Doumer . In June 1932, Painlevé again took over the post of Minister of Aviation under Prime Minister Herriot. After Herriot had resigned in December 1932 in the dispute over the inter-allied war debts , he held this position in the successor cabinet to Joseph Paul-Boncour until January 1933. He died on October 29, 1933 in Paris.

Fonts

Books:

• Leçons sur la théorie analytique des equations différentielles, professées a Stockholm , Paris, 1897
• Leçons sur l'inégration des equations de la dynamique et applicantions , Paris 1894
• Leçons sur le frottement , Paris, 1895
• Leçons sur l'intégration des équations différentielles professées à Stockholm , Paris, 1897
• Cours de mécanique de l'École polytechnique , 2 volumes, Paris, 1920–1921
• The axiomes de la mécanique. Examen critique et note sur la propagation de la lumière , Paris, 1922
• with Charles Platrier: Cours de mécanique , Paris, 1929
• Leçons sur la résistance des fluides non visqueux , 2 volumes, Paris, 1930–1931
• Paroles et écrits de Paul Painlevé , Paris 1936 (published by the Society of Friends of Paul Painlevé, foreword by Paul Langevin , Jean Perrin )
• with Émile Borel : Theory and Practice of Aviation Technology, Library for Aviation and Aviation Technology, Volume 5, Berlin: W. Richard Carl Schmidt & Co., 1911 (Appendix and translation Artur Schöning, French original: L'Aviation, Paris: Felix Alcan 1910 , 2nd edition 1911)

Some essays:

• Sur les lignes singuliéres des fonctions analytiques , Annales de la Faculté des sciences de Toulouse 1888 (dissertation)
• Sur la transformation des fonctions harmoniques et les systémes triples de surfaces orthogonales, Travaux et mémoires de la Faculté de sciences de Lille, 1899, pp. 1-29
• Sur les equations différentielles du premier ordre, Annales scientifiques de l 'École normal supérieure, 3rd ser., Volume 8, 1891, pp. 9-58, 103-140, 201-226, 267-284, Volume 9, 1892, pp 9-30, 101-144, 283-308
• Mémoire sur la transformation des equations de la dynamique, Journal de mathématiques pures et appliquées, 4th ser., 1894, pp. 5-92
• Sur les mouvements et les trajectoires réels des systémes , Bulletin de la Société mathématique de France, Volume 22, 1894, pp. 136-184
• Sur les equations différentielles dont l'intégrale générale est uniforme , Bulletin de la Société mathématique de France, Volume 28, 1900, pp. 201-261
• Sur les equations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme , Acta mathematica, Volume 25, 1900, pp. 1-80

He also contributed to the book by Émile Borel, Sur les fonctions de variables réelles et les développements en série de polynomes (Paris, 1905, pp. 101–147) and Pierre Boutroux , Leçons sur les fonctionsdéfinies par les équations différentielles du premier ordre (Paris, 1908, pp. 141-187).

literature

• Lucienne Félix: Painlevé, Paul . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 10 : SG Navashin - W. Piso . Charles Scribner's Sons, New York 1974, p. 274-276 .
• Anne-Laure Anizan: Paul Painlevé: Science et politique de la Belle Epoque aux années trente, PU Rennes 2012

Web links

• Literature by and about Paul Painlevé in the catalog of the German National Library
• Newspaper article about Paul Painlevé in the 20th century press kit of the ZBW - Leibniz Information Center for Economics .
• John J. O'Connor, Edmund F. Robertson :  Paul Painlevé. In: MacTutor History of Mathematics archive .
• Painleve "Ordinary Differential Equations - Existence of Solutions", Encyclopedia of Mathematical Sciences, 1900
• CV and portrait (French) on the website of the French National Assembly

Individual evidence

1. ^ Paul Painlevé La mécanique classique et la théorie de la relativité , CR Acad. Sci. (Paris), Volume 173, 1921, pp. 677-680. on-line
2. ↑ Allvar Gullstrand General solution of the static one-body problem in Einstein's theory of gravity , Arkiv. Mat. Astron. Fys. 16 (8), 1-15 (1922)
3. ^ Painlevé, Paul . In: dtv lexicon on history and politics in the 20th century , ed. v. Carola Stern , Thilo Vogelsang , Erhard Klöss and Albert Graff, dtv, Munich 1974, vol. 3, p. 604.
4. ^ Painlevé, Paul . In: dtv lexicon on history and politics in the 20th century , ed. v. Carola Stern, Thilo Vogelsang, Erhard Klöss and Albert Graff, dtv, Munich 1974, vol. 3, p. 604.
5. ↑ Wolfgang Steglich : The peace attempts of the warring powers in the summer and autumn of 1917. Source-critical investigations, files and interrogation protocols . Verlag Steiner, Stuttgart 1984, ISBN 3-515-02455-7 , p. 46 (No. 3) and p. 52f. (No. 9); and André Scherer, Jacques Grunewald: L'Allemagne et les problemèmes de la paix pendant la première guerre mondiale. Documents extraits des archives de l'Office allemand des Affaires étrangères. 4 volumes (German original documents), Paris 1962/1978, ISBN 2-85944-010-0 , Volume 2, p. 378 ff. (No. 231).
6. ↑ Wolfgang Steglich: The peace attempts of the warring powers in the summer and autumn of 1917. Source-critical investigations, files and interrogation protocols . Verlag Steiner, Stuttgart 1984, ISBN 3-515-02455-7 , p. 65 (No. 21).
7. ^ Daniela Neri-Ultsch: Socialists and Radicaux - a difficult alliance . Oldenbourg, Munich 2005, p. 78.
8. ^ Jean-Jacques Becker and Serge Berstein: Victoires et frustrations 1914–1929 (= Nouvelle histoire de la France contemporaine , vol. 12), Editions du Seuil, Paris 1990, p. 269 f.
9. ↑ Philipp Heyde: The end of the reparations. Germany, France and the Youngplan . Schöningh, Paderborn 1998, p. 390 f.
10. ^ Painlevé, Paul . In: dtv lexicon on history and politics in the 20th century , ed. v. Carola Stern, Thilo Vogelsang, Erhard Klöss and Albert Graff, dtv, Munich 1974, vol. 3, p. 604.

predecessor	Office	successor
Alexandre Ribot Edouard Herriot	Prime Minister of France September 12, 1917 - November 16, 1917 April 17, 1925–28. November 1925	Georges Clemenceau Aristide Briand
Lucien Lacaze Charles Nollet Édouard Daladier Louis Guillaumat	Minister of War of France March 20, 1917 - November 16, 1917 April 17, 1925–29. October 1925 November 28, 1925 - June 23, 1926 July 19, 1926–3. November 1929	Georges Clemenceau Édouard Daladier Louis Guillaumat André Maginot
Raoul Péret	President of the French National Assembly June 9, 1924–22. April 1925	Edouard Herriot
Albert Sarraut	Minister of Education of France October 29, 1915-12. December 1916	René Viviani