Henri Poincaré

Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath and in mathematics as "The Last Universalist" since he excelled in all fields of the discipline as it existed during his lifetime. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. 

In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system that laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology. Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations and was the first to present the Lorentz transformations in their modern symmetrical form. 

Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in formulating the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravities) emanating from a body and propagating at the speed of light as required by the Lorentz transformations.

The Poincaré group used in physics and mathematics was named after him. Early in the 20th century, he formulated the Poincaré conjecture that became, over time, one of the famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman. Poincaré was born into an influential French family on 29 April 1854 in the Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle.

His father, Léon Poincaré (1828–1892), was a professor of medicine at the University of Nancy. His younger sister Aline married the spiritual philosopher Émile Boutroux. Another notable member of Henri's family was his cousin, Raymond Poincaré, a fellow member of the Académie française, who was President of France from 1913 to 1920.

During his childhood, he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897). In 1862, Henri entered the Lycée in Nancy (now renamed the Lycée Henri-Poincaré [fr] in his honor, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée; during this time, he proved to be one of the top students in every topic he studied. 

He excelled in written composition. His mathematics teacher described him as a "monster of mathematics," and he won first prizes in the Concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best." However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. 

He graduated from the Lycée in 1871 with a baccalauréat in both letters and sciences. During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps. Poincaré entered the École Polytechnique as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice dune surface) in 1874. 

From November 1875 to June 1878, he studied at the École des Mines while continuing the study of mathematics in addition to the mining engineering syllabus. He received the degree of ordinary mining engineer in March 1879. As a graduate of the École des Mines, he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879, where 18 miners died. 

He carried out the official investigation into the accident in a characteristically thorough and humane way. At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. 

He faced the question of determining the integral of such equations and was the first person to study their general geometric properties. He realized that they could be used to model the behavior of multiple bodies in free motion within the Solar System. Poincaré graduated from the University of Paris in 1879.