William Rowan Hamilton (usually designated by his initials W.R.) is perhaps the most famous Irish scientist to have ever lived. He is perhaps best known for developing the concept of a Hamilton circuit and the related concept of a Hamilton path, a vital part of graph theory. His discoveries, mostly in the realm of mathematics, continue to influence and shape the realms of mathematics, game theory, and computer science even today.
Hamilton was born in 1805 in Dublin, Ireland. His father was a successful lawyer and his mother came from a family noted for a high level of intelligence, so it was no surprise that young William was a child prodigy. By the age of three he was an excellent reader and had mastered advanced arithmetic. Due to his obvious brilliance, the family sent him to live with his uncle James, a noted linguist, so by the time he was ten he knew English, Latin, Greek, Hebrew, Italian, and French, and was actively studying Chinese, Japanese, Korean, Sanskrit, Persian, and Arabic.
By the time he was 17, his interest had moved to mathematics; he was interested in calculus and mathematical astronomy and was quite adept at both. He also showed profound interest in Laplace transforms and optics. Having been privately tutored all of his life, William finally went to school at Trinity College in Dublin at age eighteen. Before he even received a degree there, he won the position of Royal Astronomer of Ireland, beating out several famous astronomers for the position; it was a clear indication of the respect others had for his intelligence. He would hold this post until his death.
He moved into the Dunsink Observatory near Dublin at age 22, where he would work and live for the remainder of his life. He would spend that life devoted to a wide variety of research topics, ranging from optics to abstract algebra to dynamics. Later in his career, he invented the concept of a quaternion, an interesting and useful algebraic object. Hamilton thought a noncommutative algebra of triples (i.e., his quaternion) would be the key to all of mathematical physics and spent the rest of his life largely studying them. He was also responsible for developing the Hamiltonian formalism, which have become part of the bedrock of virtually all branches of physics (thanks to redbaker for informing me of the importance of the Hamiltonian formalism.) He also published several games of varying degrees of success.
His personal life was a shambles, as he married and divorced three times and spent the last twenty years of his life as a recluse, scarcely leaving the Dunsink Observatory where he lived and worked. He died from gout in 1865, leaving behind reams of papers containing unpublished research. Mixed in with these papers were a large number of dinner places, many containing the remains of desiccated pork and mutton chops. A somewhat sad end to the life of a brilliant man.
His greatest contribution to modern science is that of the Hamilton circuit, which is used today in approximate and partial solutions to the the traveling salesman problem and other such problems. It is a fundamental part of the field of graph theory, a major branch of computer science.