A Mathematician's Apology

by G. H. Hardy
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Last Updated on May 7, 2015, by eNotes Editorial. Word Count: 1084

Niels Henrik Abel
Niels Henrik Abel was a Norwegian mathematician (1802–1829) known for the tremendous amount of brilliant work he completed in his brief, twentysix- year life.

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Francis Herbert Bradley
Metaphysician and philosopher F. H. Bradley (1846–1924) is most noted for his Appearance and Reality (1893), which was considered an important philosophical discussion of contemporary metaphysical thought at the time of its publication. He was also known by the influence his writing had on author T. S. Eliot.

Albert Einstein
German-born physicist Albert Einstein (1879– 1955) is considered one of the most brilliant men who ever lived. His theory of relativity, which he introduced in 1915, was revolutionary. It related matter with energy and displaced Newtonian mechanics as the cornerstone of physics by introducing the concept of space-time. In 1921, he received the Nobel Prize. A Jewish pacifist, Einstein immigrated to the United States shortly after Hitler came to power.

Euclid of Alexandria, Egypt (approximately 325–265 B.C.), is the most prominent mathematician of antiquity, best known for his treatise on mathematics titled The Elements. Euclid taught in Alexandria, but little else is known of his life. However, the timelessness of The Elements has made Euclid the leading mathematics teachers of all time.

John Burdon Sanderson Haldane
British geneticist, biologist, and writer John Burdon Sanderson (J. B. S.) Haldane (1892–1964) was one of the most influential scientists of the early twentieth century and was well known for his left-leaning politics. His numerous works include Callinicus: A Defense of Chemical Warfare (1925). Disillusioned with the state of Marxism after World War II, he eventually moved to India, where he continued to conduct scientific research.

Lancelot Hogben
Educated at Trinity College, Cambridge, Lancelot Hogben (1895–1975) is best known for his book Mathematics for the Million, which is considered a classic in its field. In the book, Hogben covers the entire spectrum of applied mathematics from simple math to advanced calculus. The work received positive reviews from the likes of H. G. Wells and Albert Einstein, though it achieved prominence due to the harsh criticism it received from G. H. Hardy.

Alfred Edward Houseman
British poet Alfred Edward (A. E.) Houseman (1859–1936) was known for the argument made in his 1933 lecture ‘‘The Name and Nature of Poetry’’ that poetry should appeal more to emotions than to intellect. He published several collections, including Last Poems (1922). His final collection, More Poems, was published shortly after his death in 1936.

Dr. Samuel Johnson
The leading literary scholar and critic of his time, Dr. Samuel Johnson (1709–1784) was equally celebrated for his brilliant and witty conversation. The work that firmly established Johnson’s reputation was his Dictionary of the English Language (1755), the first comprehensive lexicographical work on English ever undertaken.

John Edensor Littlewood
For thirty-five years, John Edensor Littlewood (1885–1977) collaborated with G. H. Hardy, working on the theory of series, the Riemann zeta function, inequalities, and the theory of functions. The collaboration led to a series of papers, Partito numerorum, using the Hardy-Littlewood-Ramanujan analytical method. Among his many awards, Littlewood was elected a fellow of the Royal Society in 1915 and received the Royal Medal of the society in 1929. He received the Sylvester Medal of the society in 1943.

Sir Isaac Newton
Sir Isaac Newton (1642–1727) was one of history’s most influential and famous scientists. His work as a mathematician, physicist, and astronomer brought him world renown. Newton rings, Newton’s law, and the MKS unit of pressure (the Newton) are named after him.

Greek philosopher and mathematician Pythagoras (c. 580–400 B.C.) lived most of his life in Crotona, in southern Italy. His doctrines ‘‘Kosmos,’’ ‘‘Metempsychosis,’’ and the ‘‘Music of the Spheres’’ are well known. The famous Pythagorean theorem, concerning right-angled triangles, holds that the square of the hypotenuse (i.e., the long line opposite the right angle) is equal to the sum of the squares of the other two sides. This idea was current for many centuries beforehand, but Pythagoras was the first to prove it to be true.

Srinivasa Ramanujan
Srinivasa Ramanujan (1887–1920) was a celebrated Indian mathematician. He is well known for his contributions to the analytical theory of numbers, elliptic functions, continued fractions, and infinite series. Despite a lack of formal higher education and a life of ill health and severe poverty, Ramanujan proved to be a preeminent mathematical genius of his time. In 1913, he sent a paper to G. H. Hardy, who immediately saw his genius and arranged to have him take a position at Trinity College, Cambridge, where for the next four years the two men collaborated on what are considered to be five of the most remarkable papers in their field. In 1918, an impressive list of mathematicians proposed his name for election as a fellow to the prestigious Royal Society of London, a rare honor that was immediately bestowed upon him. Even after his death at the young age of thirty-two, his notes continued to be a subject of research and a source of further mathematical theorems, formulas, and solutions.

Bertrand Arthur Williams Russell
Bertrand Arthur Williams Russell (1872–1970) is considered one of the founders of analytic philosophy. In 1900, following his education at Trinity College, Cambridge, Russell became acquainted with the work of Italian mathematician Giuseppe Peano. Peano’s work inspired him to write The Principles of Mathematics (1903), which he subsequently expanded in collaboration with Alfred North Whitehead into the three volumes of Principia Mathematica (1910–1913). Russell’s many essays, often in the form of short reflections or observations on moral or psychological topics, are written in a terse, vivid, and provocative style. Russell was also well known for his pacifist views, which cost him his job at Cambridge during World War I and also brought him a six-month jail sentence. His greatest literary achievement was A History of Western Philosophy (1945).

Charles Percy Snow
Charles Percy (C. P.) Snow (1905–1980) led a varied career that included scientific and civil service work, but he is best known as the author of the serialized fictional work entitled Strangers and Brothers (1940). His schooling was in chemistry and physics, and during World War II he served as director of technical personnel for Britain’s Ministry of Labour. In 1957, he was knighted, and in 1964 he was named baron for his services to the Ministry of Labour. His 1959 Rede Lecture on ‘‘The Two Cultures and the Scientific Revolution,’’ lamenting the increasing gulf between ‘‘literary intellectuals’’ and ‘‘scientists,’’ provoked widespread and heated debate. In addition to his work in the sciences, Snow was the author of much short fiction published by London’s Sunday Times, and over the course of his lifetime he published more than a dozen novels.

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