Paul Painlevé ( 5 December 1863 – 29 October 1933) was a French mathematician and statesman. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925. His entry into politics came in 1906 after a professorship at the Sorbonne that began in 1892.
His first term as prime minister lasted only nine weeks but dealt with weighty issues, such as the Russian Revolution, the American entry into the war, the failure of the Nivelle Offensive, quelling the French Army Mutinies and relations with the British.
In the 1920s as Minister of War he was a key figure in building the Maginot Line. In his second term as prime minister he dealt with the outbreak of rebellion in Syria’s Jabal Druze in July 1925 which had excited public and parliamentary anxiety over the general crisis of France’s empire.
Painlevé was born in Paris.
Brought up within a family of skilled artisans (his father was a draughtsman) Painlevé showed early promise across the range of elementary studies and was initially attracted by either an engineering or political career. However, he finally entered the École Normale Supérieure in 1883 to study mathematics, receiving his doctorate in 1887 following a period of study at Göttingen, Germany with Felix Klein and Hermann Amandus Schwarz.
Intending an academic career he became professor at Université de Lille, returning to Paris in 1892 to teach at the Sorbonne, École Polytechnique and later at the Collège de France and the École Normale Supérieure. He was elected a member of the Académie des Sciences in 1900.
He married Marguerite Petit de Villeneuve in 1901. Marguerite died during the birth of their son Jean Painlevé in the following year.
Painlevé’s mathematical work on differential equations led him to encounter their application to the theory of flight and, as ever, his broad interest in engineering topics fostered an enthusiasm for the emerging field of aviation. In 1908, he became Wilbur Wright’s first airplane passenger in France and in 1909 created the first university course in aeronautics.
Some differential equations can be solved using elementary algebraic operations that involve the trigonometric and exponential functions (sometimes called elementary functions). Many interesting special functions arise as solutions of linear second order ordinary differential equations.
Around the turn of the century, Painlevé, É. Picard, and B. Gambier showed that of the class of nonlinear second order ordinary differential equations with polynomial coefficients, those that possess a certain desirable technical property, shared by the linear equations (nowadays commonly referred to as the ‘Painlevé property’) can always be transformed into one of fifty canonical forms. Of these fifty equations, just six require ‘new’ transcendental functions for their solution.
These new transcendental functions, solving the remaining six equations, are called the Painlevé transcendents, and interest in them has revived recently due to their appearance in modern geometry, integrable systems and statistical mechanics.
In 1895 he gave a series of lectures at Stockholm University on differential equations, at the end stating the Painlevé conjecture about singularities of the n-body problem.
In the nineteen twenties, Painlevé briefly turned his attention to the new theory of gravitation, general relativity, which had recently been introduced by Albert Einstein. In 1921, Painlevé proposed the Gullstrand–Painlevé coordinates for the Schwarzschild metric. The modification in the coordinate system was the first to reveal clearly that the Schwarzschild radius is a mere coordinate singularity (with however, profound global significance: it represents the event horizon of a black hole).
This essential point was not generally appreciated by physicists until around 1963. In his diary, Harry Graf Kessler recorded that during a later visit to Berlin, Painlevé discussed pacifist international politics with Einstein, but there is no reference to discussions concerning the significance of the Schwarzschild radius.
Following Painlevé’s resignation, Briand formed a new government with Painlevé as Minister for War. Though Briand was defeated by Raymond Poincaré in 1926, Painlevé continued in office. Poincaré stabilised the franc with a return to the gold standard, but ultimately acceded power to Briand.
During his tenure as Minister of War, Painlevé was instrumental in the creation of the Maginot Line. This line of military fortifications along France’s Eastern border was largely designed by Painlevé, yet named for André Maginot, owing to Maginot’s championing of public support and funding.Painlevé remained in office as Minister for War until July 1929.
Though he was proposed for President of France in 1932, Painlevé withdrew before the election. He became Minister of Air later that year, making proposals for an international treaty to ban the manufacture of bomber aircraft and to establish an international air force to enforce global peace. On the fall of the government in January 1933, his political career ended.
Painlevé died in Paris in October of the same year. On 4 November, after a eulogy by Prime Minister Albert Sarraut, he was interred in the Panthéon.