Gardner packed his commentary and footnotes on the text with insights into the hidden messages, allusions, word-games, private jokes, puns, parodies, mathematical riddles and assorted literary tricks encrypted in the tales, demonstrating that many of Carroll's jokes were in fact mathematical games.
"In the batty world of Carroll scholarship", declared one critic, "Martin Gardner is the undisputed king."
Not all academics shared this view. Although Gardner cited several important Freudian essays on the Alice canon, he always shrank from delving into the darker side of Carroll's psyche -- the author was obsessed with befriending young girls and photographing them in the nude. But Gardner was unstinting in his quest for other details. He was able to discover precise weather reports for Oxford on Friday July 4 1862, the day on which Carroll/Dodgson took the 10-year-old Alice Liddell and her sisters rowing on the Thames and entertained them with the story that became Alice's Adventures in Wonderland. While Carroll's prefatory chapter is headed "All in the Golden Afternoon", Gardner examined meteorological records that showed that the prevailing weather had been "cool and rather wet".
For half a century Gardner's book has never been out of print, selling more than a million copies in Britain and the United States. He published a sequel, More Annotated Alice, in 1990 and a definitive edition combining his notes from both volumes in 1999. He also produced The Annotated Snark (1962), The Annotated Ancient Mariner (1965) and The Annotated Innocence of Father Brown (1987), about GK Chesterton's fictional detective.
Although recognised as a self-taught scholar and enthusiastic Lewis Carroll fan, Gardner first became known for popularising recreational mathematics: the British mathematician Professor Richard Guy claimed Gardner brought more mathematics to more millions than anyone.
In his book of essays The Night Is Large (1997), Gardner organised his intellectual interests into seven categories: physical science, social science, pseudoscience, mathematics, the arts, philosophy and religion. "I give the impression of knowing far more than I do," he once admitted, "because I work hard on research, write glibly and keep extensive files of clippings on everything that interests me." Although at ease with the most abstract of concepts, his writing was always lucid, lively and vivid.
Martin Gardner was born on October 21 1914 in Tulsa, Oklahoma, the son of a geologist who started a small oil business and became a wildcatter. As a child Martin enjoyed magic tricks and playing chess. After graduating from high school in 1932, he earned a bachelor's degree in Philosophy at the University of Chicago, having also studied history, literature and the sciences under the intellectually-stimulating Great Books curriculum.
Although brought up a devout Methodist, he lost his Christian faith as a result of his wide reading, a transition he covered in a semi-autobiographical novel The Flight of Peter Fromm (1973).
In 1937 Gardner returned to Oklahoma, taking a reporter's job on the Tulsa Tribune, and after a spell in public relations back at the University of Chicago, in 1942 joined the US Naval Reserve as a yeoman in the destroyer escort USS Pope. On night watch, he dreamed up plots for stories, which he sold to Esquire magazine. After the war he became a freelance writer, and in the 1950s wrote features for Humpty Dumpty's Magazine and other children's periodicals.
In 1956 he sold an article to Scientific American magazine and followed this up with an essay about hexaflexagons -- hexagons made from strips of paper that show different faces when flexed in different ways. This so impressed the publisher that Gardner was invited to produce a regular column along similar lines. Since he had not studied mathematics after high school, Gardner plundered second-hand bookshops in Manhattan to find enough material to sustain his "Mathematical Games" column. In the event it ran for 25 years and earned Gardner the American Mathematical Society's prize for mathematical exposition.
His lack of scholarly expertise meant that instead of relying on academic jargon, Gardner packed his prose with cross-cultural references, jokes and anecdotes, giving the column the broadest-possible appeal. He introduced his readers to riddles, paradoxes, enigmas and even magic tricks, as well as concepts such as fractals and Chinese tangram puzzles, redefining the concept of "recreational mathematics".
Gardner also became known as a sceptic of the paranormal, and wrote works debunking public figures such as the psychic Uri Geller, who gained fame for claiming to bend spoons with his mind. In his first book Fads and Fallacies in the Name of Science (1952), Gardner exposed such quackery as flat-earth cults, alien abductions and a belief in UFOs. The book has since become a classic; the novelist Kingsley Amis, an early fan, regretted not stealing a copy when he had had the chance.
In 1976, with Carl Sagan, Isaac Asimov and others, Gardner co-founded the Committee for the Scientific Evaluation of Claims of the Paranormal, and wrote regularly for its magazine, the Skeptical Inquirer. Its most recent issue includes a feature he wrote on Oprah Winfrey's New Age interests.
In more than 70 books, Gardner produced lay guides to Einstein's Theory of Relativity; ambidexterity and physical symmetry; the bath plug vortex (the phenomenon by which bathwater in the northern hemisphere drains in an anticlockwise direction and clockwise in the southern hemisphere); and even the concept of God. He also published fiction, poetry and literary and film criticism as well as puzzle books.
In The Numerology of Dr Matrix (1967) Gardner investigated links between numerals and the occult, asking (for example) what is special about the number 8,549,176,320? (A: It is the 10 natural integers arranged in the order of the English alphabet.)
His many admirers instituted a regular convention of Gardner followers, known as "Gatherings for Gardner" (G4G), which attracted magicians, puzzle fans and mathematicians from all over the world.
Although Gardner attended these as guest of honour, as a matter of course he avoided conferences, meetings and parties, and despite his facility as a polymath never owned a computer or used email. He preferred to work standing up, and, while magic and conjuring tricks remained his principal hobby, was also an accomplished exponent of the musical saw.
Martin Gardner married, in 1952, Charlotte Greenwald, who predeceased him in 2000. Their two sons survive him.
25 May 2010 © Telegraph Group Limited 2010.