Short answers, pulled from the story.
Jules Henri Poincaré was born on the 29th of April 1854 in the Cité Ducale neighborhood of Nancy. His early years were marked by a severe illness that left him with diphtheria and poor eyesight for much of his childhood.
Henri Poincaré introduced concepts such as homotopy, homology, Betti numbers, and the fundamental group when he published his first article on topology in 1894. These ideas remain central to modern geometry and transformed how mathematicians understood spaces of any dimension.
Henri Poincaré made groundbreaking contributions to the three-body problem by revealing unpredictable behavior within deterministic systems even though he did not solve the original question. His analysis showed that simple rules could produce complex chaotic outcomes over time and laid the foundation for modern chaos theory.
Critics noted that the committee favored experimental achievements over theoretical breakthroughs which prevented Henri Poincaré from winning the award between 1904 and 1912. Prominent figures including Marie Curie and Hendrik Lorentz had nominated him yet no single discovery stood out enough to justify the honor.
Henri Poincaré wrote to Hendrik Lorentz in 1905 pointing out errors in transformations and proposing corrections that ensured all Maxwell's equations remained invariant. He introduced what is now called the relativistic velocity-addition law and demonstrated that these transformations formed a mathematical group before Albert Einstein published his own version of special relativity.