Sunday, May 23, 2010

Deceased--Martin Gardner

Martin and Charlotte Gardner

Martin Gardner
October 21st, 1914 to May 22nd, 2010

"Math and science writer Martin Gardner dies at 95"

His "Mathematical Games" column ran in Scientific American magazine for 25 years.

May 23rd, 2010

Associated Press

NORMAN, Okla. —

Prolific mathematics and science writer Martin Gardner, known for popularizing recreational mathematics and debunking paranormal claims, died Saturday. He was 95.

Gardner died Saturday after a brief illness at Norman Regional Hospital, said his son James Gardner. He had been living at an assisted living facility in Norman.

Martin Gardner was born in 1914 in Tulsa, Okla., and earned a bachelor's degree in philosophy at the University of Chicago.

He became a freelance writer, and in the 1950s wrote features and stories for several children's magazines. His creation of paper-folding puzzles led to his publication in Scientific American magazine, where he wrote his "Mathematical Games" column for 25 years.

The column introduced the public to puzzles and concepts such as fractals and Chinese tangram puzzles, as well as the work of artist M.C. Escher.

Allyn Jackson, deputy editor of Notices, a journal of the American Mathematical Society, wrote in 2005 that Gardner "opened the eyes of the general public to the beauty and fascination of mathematics and inspired many to go on to make the subject their life's work."

Jackson said Gardner's "crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization."

The mathematics society awarded him its Steele Prize for Mathematical Exposition in 1987 for his work on math, particularly his Scientific American column.

"He was a renaissance man who built new ideas through words, numbers and puzzles," his son, a professor of special education at the University of Oklahoma, told The Associated Press.

Gardner also became known as a skeptic of the paranormal and wrote columns for Skeptical Inquirer magazine. He wrote works debunking public figures such as psychic Uri Geller, who gained fame for claiming to bend spoons with his mind.

Most recently he wrote a feature published in Skeptical Inquirer's March/April on Oprah Winfrey's New Age interests.

Former magician James Randi, now a writer and investigator of paranormal claims, paid tribute to Gardner on his website Saturday, calling his colleague and longtime friend "a very bright spot in my firmament."

He ended his Scientific American column in 1981 and retired to Hendersonville, N.C. Gardner continued to write, and in 2002 moved to Norman, where his son lives.

Gardner wrote more than 50 books.

Gardner was preceded in death by his wife, Charlotte. Besides James Gardner, he is survived by another son, Tom, of Asheville, N.C.

"Martin Gardner, Puzzler and Polymath, Dies at 95"


Douglas Martin

May 23rd, 2010

The New York Times

Martin Gardner, who teased brains with math puzzles in Scientific American for a quarter-century and who indulged his own restless curiosity by writing more than 70 books on topics as diverse as magic, philosophy and the nuances of Alice in Wonderland, died Saturday in Norman, Okla. He was 95.

He had been living in an assisted-living facility in Norman, his son James said in confirming the death.

Mr. Gardner also wrote fiction, poetry, literary and film criticism, as well as puzzle books. He was a leading voice in refuting pseudoscientific theories, from ESP to flying saucers. He was so prolific and wide-ranging in his interests that critics speculated that there just had to be more than one of him.

His mathematical writings intrigued a generation of mathematicians, but he never took a college math course. If it seemed the only thing this polymath could not do was play music on a saw, rest assured that he could, and quite well.

“Martin Gardner is one of the great intellects produced in this country in the 20th century,” said Douglas Hofstadter, the cognitive scientist.

W. H. Auden, Arthur C. Clarke, Jacob Bronowski, Stephen Jay Gould and Carl Sagan were admirers of Mr. Gardner. Vladimir Nabokov mentioned him in his novel “Ada” as “an invented philosopher.” An asteroid is named for him.

Mr. Gardner responded that his life was not all that interesting, really. “It’s lived mainly inside my brain,” he told The Charlotte Observer in 1993.

His was a clarifying intelligence: he said his talent was asking good questions and transmitting the answers clearly and crisply. In “Annotated Alice” (1960), Mr. Gardner literally rained on the parade of his hero, Lewis Carroll.

Carroll writes of a “golden afternoon” in the first line of “Alice’s Adventures in Wonderland,” a reference to an actual day rowing on the Thames. Mr. Gardner found that the day, July 4, 1862, was, in truth, “cool and rather wet.”

Mr. Gardner’s questions were often mathematical. What is special about the number 8,549,176,320? As Mr. Gardner explained in “The Incredible Dr. Matrix” (1976), the number is the 10 natural integers arranged in English alphabetical order.

The title of a book he published in 2000 was calculated to tweak religious fundamentalists — “Did Adam and Eve Have Navels?” — suggesting that the first man and woman had had umbilical cords. This time he gave no answer.

“Gardner has an old-fashioned, almost 19th-century, Oliver Wendell Holmes kind of American mind — self-educated, opinionated, cranky and utterly unafraid of embarrassment,” Adam Gopnik wrote in The New York Times Book Review in 1999.

Martin Gardner was born Oct. 21, 1914, in Tulsa, Okla., where his father, a petroleum geologist, started an oil company. As a boy he liked magic tricks, chess, science and collecting mechanical puzzles.

Unbeknownst to his mother at the time, he learned to read by looking at the words on the page as she read him L. Frank Baum’s Oz books. As an adult, he wrote a sequel to Baum’s “Wonderful Wizard of Oz” called “Visitors From Oz,” in which Dorothy encounters characters from the “Alice” books and Geraldo Rivera.

Mr. Gardner majored in philosophy at the University of Chicago, from which he graduated in 1936. In 1937 he returned to Oklahoma to be assistant oil editor of The Tulsa Tribune at $15 a week. Quickly bored, he returned to the University of Chicago, where he worked in press relations and moonlighted selling magic kits.

He joined the Navy and served on a destroyer. While doing night watch duty, he thought up crazy plots for stories, including “The Horse on the Escalator,” which he sold to Esquire magazine.

After a stint as editor of Humpty Dumpty, a children’s magazine, Mr. Gardner began a long relationship with Scientific American with an article in 1956 on hexaflexagons, strips of paper that can be folded in certain ways to reveal faces besides the two that were originally on the front and back. When the publisher suggested that he write a column about mathematical games, he jumped at the chance.

By his account, Mr. Gardner then rushed out to secondhand bookstores to find books about math puzzles, an approach he used for years to keep just ahead of his monthly deadline. “The number of puzzles I’ve invented you can count on your fingers,” he told The Times last year.

Dr. Hofstadter, who succeeded Mr. Gardner at Scientific American, said Mr. Gardner achieved elegant results by drawing on fields from logic to the philosophy of science to literature. He conveyed “the magical quality of mathematics,” Dr. Hofstadter said.

Mr. Gardner, who lived in Hastings-on-Hudson, N.Y., for most of the years he wrote for Scientific American, resigned from the magazine in 1981. Two years later he began a column in Skeptical Inquirer, “Notes of a Fringe Watcher,” which he continued to write until 2002. He had already begun beating this drum, debunking psuedoscience, in his book “Fads and Fallacies in the Name of Science.” He helped found the Committee for the Scientific Investigation of Claims of the Paranormal.

In The New York Review of Books in 1982, Stephen Jay Gould, the evolutionary biologist, called Mr. Gardner “the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.”

There was much more, including his annotated editions of “Casey at the Bat” and “The Night Before Christmas.” In his philosophical writing Mr. Gardner rejected speculative metaphysics because it could not be proved logically or empirically. He wrestled with religion in essays and in a novel that described his personal journey from fundamentalism, “The Flight of Peter Fromm” (1973). He ultimately found no reason to believe in anything religious except a human desire to avoid “deep-seated despair.” So, he said, he believed in God.

After retiring from Scientific American, Mr. Gardner lived for many years in Hendersonville, N.C. His wife, the former Charlotte Greenwald, died in 2000. Besides his son James, of Norman, he is survived by another son, Thomas, of Asheville, N.C., and three grandchildren. For all Mr. Gardner’s success in refuting those who take advantage of people’s gullibility, he sometimes could not help having fun with it himself. In one Scientific American column, he wrote that dwelling in pyramids could increase everything from intelligence to sexual prowess. In another he asked readers to remember the holiday that begins the month of April.

“I just play all the time,” he said in an interview with Skeptical Inquirer in 1998, “and am fortunate enough to get paid for it.”

"Martin Gardner, 95, a journalist, provided in-depth analysis of Lewis Carroll's Cheshire Cat"


Emma Brown

May 23rd, 2010

Washington Post

Martin Gardner, 95, a journalist whose omnivorous curiosity gave rise to wide-ranging writings that popularized mathematics, explored theology and philosophy, debunked pseudoscience and provided in-depth analysis of Lewis Carroll's Cheshire Cat, died May 22 at a hospital in Norman, Okla.

His son, James Gardner, said the exact cause of death was not known.

A native of Tulsa, Okla., Mr. Gardner was writing stories and poems for a children's magazine in the 1950s when he submitted an article about hexaflexagons -- pieces of paper folded intricately to resemble, Mr. Gardner once said, "a budding flower" -- to Scientific American. Then-editor Dennis Flanagan was so taken with the piece that he hired Mr. Gardner to produce a regular column on recreational mathematics.

The resulting monthly feature, "Mathematical Games," ran from 1956 until 1981. It became one of Scientific American's most popular items, capturing the imagination of amateur and professional mathematicians and introducing a generation of young readers to the pleasures of problem-solving.

The sharp-witted column, packed with cultural references, humor and accessible logic puzzles instead of academic jargon, featured the mathematical concepts behind fractals, Chinese tangram puzzles, and the art of surrealist M.C. Escher. Widely read around the world, "Mathematical Games" made Mr. Gardner -- who never took a math class after high school -- the beloved grandfather of recreational mathematics and the inspiration for countless young people to consider careers in math and science.

"Beyond calculus, I am lost," he once told a reporter. "That was the secret of my column's success. It took me so long to understand what I was writing about that I knew how to write in a way most readers would understand."

"To Martin Gardner," three prominent mathematicians wrote in their dedication of a 1982 book of puzzles, " who brought more math to more millions than anyone else."

Math puzzles were just one part of the sprawling career Mr. Gardner built out of his efforts to examine the world.

In 1952, he published his first of more than 70 books, "Fads and Fallacies in the Name of Science." Deemed "unputdownable" by Washington Post critic Michael Dirda, the book heralded a lifelong passion for discrediting scientific fraud and quackery. With a mix of humor and calm logic, Mr. Gardner took on and exposed flat-earth theorists, flying saucers, the spoon-bending psychic Uri Geller and believers in extrasensory perception.

In 1976, he joined with Carl Sagan, Isaac Asimov and others in founding the Committee for the Scientific Evaluation of Claims of the Paranormal to encourage the rational investigation of everything from homeopathic remedies to fortune tellers. He later wrote a monthly column, "Notes of a Fringe Watcher," for the journal Skeptical Inquirer.

Following his own fascinations, he wrote books to explain scientific phenomena including Einstein's relativity theory ("Relativity for Millions," 1962) and oddities such as right- and left-handedness in mollusks and crystals and the bathtub vortex, in which water in a bathtub in the Northern hemisphere drains counterclockwise, while water in the Southern hemisphere drains clockwise ("The Ambidextrous Universe," 1964).

Mr. Gardner, a childhood fan of Frank L. Baum's Wizard of Oz books, used his inquisitiveness as a tool of literary criticism. In 1960, he published perhaps his most popular book, "The Annotated Alice," a line-by-line examination of the wordplay, satire and allusions in Carroll's "Alice's Adventures in Wonderland" and its sequel, "Through the Looking Glass."

Filling the margins of the original text with explanatory notes compressed essays, Mr. Gardner used physics, psychology, history and math to illuminate the classic tale, offering two possible origins for the phrase "grin like a Cheshire Cat" and digging up the weather ("cool and rather wet") on the day that Alice first heard the story of Wonderland.

The book "memorializes the meeting of two remarkable eccentric minds in a particular moment in intellectual history," wrote critic Adam Gopnik in the New York Times in 1999, upon the release of a new edition of the book. "Gardner has an old-fashioned, almost 19th-century, Oliver Wendell Holmes kind of American mind -- self-educated, opinionated, cranky and utterly unafraid of embarrassment."

Mr. Gardner went on to use a similar technique to annotate other classics, including Samuel Taylor Coleridge's ballad "The Rime of the Ancient Mariner" and E.L. Thayer's baseball poem "Casey at the Bat."

In interviews, Mr. Gardner said that among his favorite books was "The Whys of a Philosophical Scrivener" (1983), a collection of essays about issues including faith, prayer, evil and immortality. Faith was also the subject of his 1973 semi-autobiographical novel, "The Flight of Peter Fromm," in which the title character and his atheist professor of divinity grapple for decades with questions about God.

"This is a brilliantly illuminating metaphysical novel that employs ideas as adversaries and translates them into human dilemmas," wrote a reviewer in the New York Times. "Can a novel whose action is essentially cerebral be exciting? Yes indeed -- if the novelist is as engaged by the history of ideas as is Gardner."

Martin Gardner was born Oct. 21, 1914, in Tulsa, where his father owned a small oil business. The younger Gardner grew up playing chess, practicing magic tricks and reading the Wizard of Oz series by Baum, which he later satirized in the novel "Visitors from Oz" (1999).

He entered the University of Chicago with a plan to eventually transfer to the California Institute of Technology and study physics. A devout Methodist who doubted the theory of evolution when he started college, his beliefs were shaken by courses he took in history, literature, biology and philosophy. "I quickly lost my entire faith in Christianity," he said in a 2005 interview.

He based "The Flight of Peter Fromm" on that crisis of faith. He ultimately believed in God but was unaffiliated with any church, preferring to call himself a philosophical theist. "I haven't been to church in ages," he said in 2007.

Mr. Gardner stayed at Chicago for four years, graduating in 1936 with a bachelor's degree in philosophy and a goal of becoming a writer. He worked for the now-defunct Tulsa Tribune and for the University of Chicago's press relations office before serving during World War II as a Navy yeoman aboard a destroyer escort.

After the war, he launched a freelance writing career with the publication in Esquire magazine of a story called "The Horse on the Escalator," a tragically comic tale about about a man who collected jokes about horses. Several years later, he found steady work in New York at Humpty Dumpty's Magazine. Each month for eight years, he wrote a short story and a poem offering moral advice, some of which were later collected in "Never Make Fun of a Turtle, My Son) (1969).

His wife, the former Charlotte Greenwald, died in 2000 after 48 years of marriage. In addition to his son James, of Norman, survivors include another son, Tom Gardner of Asheville, N.C.; and three grandchildren.

Over the years, Mr. Gardner earned a devoted following and respect from such diverse thinkers as the poet W.H. Auden, science-fiction writer Richard C. Clarke, evolutionary biologist Stephen Jay Gould and philosopher and political activist Noam Chomsky, who once wrote that "Martin Gardner's contribution to contemporary intellectual culture is unique -- in its range, its insight, and understanding of hard questions that matter."

The writer's admirers have gathered every two years since 1993 for a biannual conference called "Gathering for Gardner." Begun as a tribute, the invitation-only event features presentations by magicians, mathematicians and puzzle-lovers of every stripe.

"Many have tried to emulate him," mathematician Ronald Graham said of Mr. Gardner in 2009. "No one has succeeded."

"Profile: Martin Gardner, the Mathematical Gamester"

For 35 years, he wrote Scientific American's Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians


Philip Yam

May 22nd, 2010

Scientific American

Editor's note: In light of the recent death of Martin Gardner, we are republishing this profile from the December 1995 issue of Scientific American.

December 1995

Scientific American

The clerk at the Barnes and Noble bookstore in downtown Manhattan is not all that helpful. Having had limited success with smaller retailers, I am hoping that the computer can tell me which of Martin Gardner's 50 or so books are available in the store's massive inventory. Most of his books, of course, deal with recreational mathematics, the topic for which he is best known. But he has also penned works in literature, philosophy and fiction. I am looking specifically for The Whys of a Philosophical Scrivener, Gardner's essays that detail his approach to life. The clerk tells me to try the religion section, under "Christian friction." Is he kidding?

A scowl breaks across Gardner's otherwise amicable face after I relate the story. He is puzzled, too, but for a different reason. The book has nothing to do with that, Gardner insists. He makes it a point to describe himself as philosophical theist—in the tradition, he says, of Plato and Kant, among others. "I decided I couldn't call myself a Christian in any legitimate sense of the word, but I have retained a belief in a personal God," Gardner clarifies. "I admire the teachings of Jesus, but to me it's a little bit dishonest if you don't think Jesus was divine in some special way"—which Gardner does not.

Theology and philosophy weigh heavily in our conversation, something I did not expect from a man who spent 25 years writing Scientific American' s "Mathematical Games" column and who, in the process, influenced untold numbers of minds. "I think my whole generation of mathematicians grew up reading Martin Gardner," comments Rudy Rucker, a writer and mathematician at San Jose State University. It is not uncommon to run into people who subscribed solely because of the mathematical gamester, a realization not lost on the magazine's caretakers when he resigned in 1981. "Here is the letter I have been dreading to receive from Martin Gardner," memoed then editor Dennis Flanagan to then publisher Gerard Piel. "I had a lot of books I wanted to write," Gardner explains of his decision. "I just didn't have time to do the column. I miss doing it because I met a lot of famous mathematicians through it."

In his living room in Hendersonville, N.C., near the Great Smoky Mountains at the Tennessee border, he rattles off several of these notables. Roger Penrose of the University of Oxford, now a best-selling author about consciousness and the brain, first became famous after Gardner reported Penrose's finding of tiles that can coat a plane without ever repeating the same pattern. John H. Conway of Princeton University saw his game-of-life computer program, a metaphor for evolution, flourish after appearing in the column. Most surprising to me, though, is Gardner's mention of the Dutch artist M. C. Escher, whose work he helped to publicize in 1961. He points to an original Escher print over my head, between the shelves of his wife's collection of antique metal doorstops. If he had known Escher would become famous, Gardner says, he would have bought more. "It's one of the rare pictures with color in it," he remarks. "It's based on Poincaré's model of the hyperbolic plane."

The 81-year-old Gardner seems more comfortable talking about others than about himself. Perhaps part of the reason is that he has no formal training in mathematics. In discussing his youth, he muses on religion and philosophy, topics to which we keep veering back. "When I grew up in Tulsa, it was called the oil capital of the word," he says. "Now it's known as the home of Oral Roberts. That's how far Tulsa has gone down the hill." He describes his father, a petroleum geologist, as a tolerant fellow who put up with his mother's Methodist devotion and Gardner's own early fanaticism. Influenced by a Sunday school teacher and a Seventh-Day Adventist, the young Gardner became convinced the second coming was near and that 666 was the number of the pope. "I grew up believing that the Bible was a revelation straight from God," he recounts. "It lasted about halfway through my years at the University of Chicago."

University life, however, slowly eroded his fundamentalist beliefs. "Certain authors have been a big influence on me," Gardner says and enumerates them. Besides Plato and Kant, there are G. K. Chesterton, William James, Charles S. Peirce, Miguel de Unamuno, Rudolf Carnap and H. G. Wells. From each, Gardner has culled a bit of wisdom. "From Chesterton I got a sense of mystery in the universe, why anything exists, " he expounds. "From Wells I took his tremendous interest in and respect for science." That's why he does not accept the virgin birth of Christ or a blood atonement for the sin of Adam and Eve, as he writes in the afterword of his semiautobiographical novel, The Flight of Peter Fromm. "I don't believe God interrupts natural laws or tinkers with the universe," he remarks. From James he derived his notion that belief in God is a matter of faith only. "I don't think there's any way to prove the existence of God logically."

Pondering existence for a living, however, was not his calling. "If you're a professional philosopher, there's no way to make any money except to teach. It has no use anywhere," Gardner offers. Instead he turned to writing, becoming assistant oil editor for the Tulsa Tribune and then returning to Chicago to assume a post in the university's press office. In 1941 he began a four-year stint on a destroyer escort (fittingly, the U.S.S. Pope ). After World War II, Gardner returned to Chicago, selling short stories to Esquire and taking more courses in philosophy under the GI bill.

Freelance writing is unstable, and Gardner found himself in New York City in the early 1950s, where he landed a regular job with the children's periodical Humpty Dumpty's Magazine, writing features and designing activities. "I did all the cutouts," he beams. But it was his lifelong interest in magic, still his main hobby, that led him to mathematical games. Every Saturday a group of conjurers would gather in a restaurant in lower Manhattan. "There would be 50 magicians or so, all doing magic tricks," Gardner reminisces. One of them intrigued him with a so-called hexaflexagon—a strip of paper folded into a hexagon, which turns inside out when two sides are pinched. Fascinated, Gardner drove to Princeton, where graduate students invented it. (A magician also played a pivotal role in another major step in Gardner's life: he introduced Gardner to his future wife, Charlotte.)

Having sold a piece on logic machines to Scientific American a few years prior (which, incidentally, included a cardboard cutout), he approached the magazine with an article on flexagons. "Gerry Piel called me in and asked, 'Is there enough material similar to this to make a regular column?' I said I thought there was, and he said to turn one in," Gardner recalls. It was a bit of a snow job: Gardner did not even own a mathematics book at the time. "I rushed around New York and bought as many books on recreational math as I could," he states. Gardner officially began his new career in the January 1957 issue; the rubric "Mathematical Games" was chosen by the magazine. "By coincidence, they're my initials," Gardner observes. "I always had a private interest in math without any formal training. I just sort of became a self-taught mathematician. If you look at those columns in chronological order, you will see they started out on a much more elementary level than the later columns."

Gardner's timing was perfect. Only a few outlets for recreational mathematicians existed at the time. "A lot of creative mathematicians were making discoveries, but the work was considered too trivial by professional math journals to publish. So I had the pleasure of picking up this stuff." Perhaps more important to the success of the column was his nonmathematical background. "His references were so wonderfully cross-cultural and broad," Rucker states. "He talked about experimental literature, about cranks, about philosophers—relating mathematics to the most exciting things around." He was also able to form a network of associates who passed on ideas. "Martin was very good at giving attribution," says mathematician Ronald L. Graham of AT&T Bell Laboratories. "That inspired people to work on problems."

Gardner has a natural penchant for fun and games. In an April Fools' piece, he claimed Einstein's theory of relativity was disproved and that Leonardo da Vinci invented the flush toilet. At the suggestion of a friend, he harshly panned his own Whys book in a review written under the pseudonym George Groth. "I heard that people read the review and didn't buy the book on my recommendation," Gardner comments.

Although his home seems to display order and formality, Gardner's playfulness is everywhere. Optical illusions abound, including an inside-out face mask illuminated from below that appears holographic, eerily seeming to track a viewer's motions. He demonstrates several magic tricks with rubber bands, at one point rummaging through a closet to extract a fake, blood-dripping severed arm through which he wiggles his own fingers. This Wonderland feeling is appropriate, for Gardner is an expert on Lewis Carroll. His best-seller is The Annotated Alice, in which he shows that Carroll encoded messages, chess moves and caricatures of people he knew. In Los Angeles recently, wealthy electronics store owner John Fry inaugurated a new outlet containing 15- foot statues of the Alice characters—and Gardner was the honored guest.

After nearly 40 years of presenting math, Gardner says the biggest transformation in the field has been the entrance of the computer. "It's changed the character of all mathematics, especially combinatorial math, where problems are impossible to solve by hand. A good example is the four-color map problem, which was finally solved by a computer." The theorem states that at least four hues are needed to paint all planar maps so that no adjacent regions are the same color. Chaos theory, fractals and factoring of prime numbers are a few other examples.

Gardner himself does not own a computer (or, for that matter, a fax or answering machine). He once did—and got hooked playing chess on it. "Then one day I was doing the dishes with my wife, and I looked down and saw the pattern of the chessboard on the surface of the water," he recalls. The retinal retention lasted about a week, during which he gave his computer to one of his two sons. "I'm a scissors-and-rubber-cement man," Gardner says, although he feels he ought to get another computer despite the lasting impression his first one left.

Retirement does not find Gardner at rest. He writes for the Skeptical Inquirer, although he is planning to switch to topics that are not outright shams, such as Freud's dream theory and false memories evoked by therapists. And there is time for games. During my visit, an editor called to say that his firm wants to publish Gardner's manuscript on Lewis Carroll's mathematical puzzles. Gardner describes a recent problem he received from Japan, which dealt with an ant crawling on an extended cube. A mathematician phones to inquire whether Gardner heard anything about a rumor of a new result in Penrose tiling. And every afternoon at 4:30, he and Charlotte investigate fluid dynamics by mixing vodka martinis. For Gardner, the game is the life.

Martin Gardner [Wikipedia]

The Annotated Alice: The Definitive Edition


Lewis Carroll

Martin Gardner [Editor, Introduction]

ISBN-10: 0393048470

ISBN-13: 978-0393048476

Martin Gardner -a tribute

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