Martin Gardner (October 21, 1914 – May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was considered a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century. He was considered the dean of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
October 21, 1914|
Tulsa, Oklahoma, US
|Died||May 22, 2010
Norman, Oklahoma, US
|Alma mater||University of Chicago|
|Genre||Recreational mathematics, puzzles, close-up magic, annotated literary works, debunking|
|Literary movement||Scientific skepticism|
|Notable works||Fads and Fallacies in the Name of Science;
Mathematical Games (Scientific American column);
The Annotated Alice;
The Whys of a Philosophical Scrivener;
The Ambidextrous Universe
|Notable awards||Leroy P. Steele Prize for Mathematical Exposition (1987)
George Pólya Award (1999)
Gardner was best known for creating and sustaining interest in recreational mathematics—and by extension, mathematics in general—throughout the latter half of the 20th century, principally through his "Mathematical Games" columns, which appeared for twenty-five years in Scientific American, and his subsequent books collecting them.
Gardner was one of the foremost anti-pseudoscience polemicists of the 20th century. His book Fads and Fallacies in the Name of Science, published in 1957, became a classic and seminal work of the skeptical movement. In 1976 he joined with fellow skeptics to found CSICOP, an organization promoting scientific inquiry and the use of reason in examining extraordinary claims.
Youth and educationEdit
Gardner, son of a petroleum geologist, grew up in and around Tulsa, Oklahoma. His lifelong interest in puzzles started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles, Tricks and Conundrums. He attended the University of Chicago, where he earned his bachelor's degree in philosophy in 1936. Early jobs included reporter on the Tulsa Tribune, writer at the University of Chicago Office of Press Relations, and case worker in Chicago's Black Belt for the city's Relief Administration. During World War II, he served for four years in the U.S. Navy as a yeoman on board the destroyer escort USS Pope in the Atlantic. His ship was still in the Atlantic when the war came to an end with the surrender of Japan in August 1945.
In 1950 he wrote an article in the Antioch Review entitled "The Hermit Scientist". It was one of Gardner's earliest articles about junk science, and in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present.
In the late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine where for eight years he wrote features and stories for it and several other children's magazines. His paper-folding puzzles at that magazine led to his first work at Scientific American. For many decades, Gardner, his wife Charlotte, and their two sons, Jim and Tom, lived in Hastings-on-Hudson, New York, where he earned his living as a free-lance author, publishing books with several different publishers, and also publishing hundreds of magazine and newspaper articles. Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue. The year 1960 saw the original edition of his best-selling book ever, The Annotated Alice.
Retirement and deathEdit
In 1979, Gardner retired from Scientific American and he and his wife Charlotte moved to Hendersonville, North Carolina. Gardner never really retired as an author, but continued to write math articles, sending them to The Mathematical Intelligencer, Math Horizons, The College Mathematics Journal, and Scientific American. He also revised some of his older books such as Origami, Eleusis, and the Soma Cube. Charlotte died in 2000 and two years later Gardner returned to Norman, Oklahoma, where his son, James Gardner, was a professor of education at the University of Oklahoma. He died there on May 22, 2010. An autobiography — Undiluted Hocus-Pocus: The Autobiography of Martin Gardner — was published posthumously.
Martin Gardner had a major impact on mathematics in the second half of the 20th century. His column was called "Mathematical Games" but it was much more than that. His writing introduced many readers to real mathematics for the first time in their lives. The column lasted for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981. It was the original inspiration for many of them to become mathematicians or scientists themselves.
David Auerbach wrote, "A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century. His popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to the advent of the personal computer." Among the wide array of mathematicians, physicists, computer scientists, philosophers, magicians, artists, writers, and other influential thinkers who inspired and were in turn inspired by Gardner are John Horton Conway, Bill Gosper, Ron Rivest, Richard K. Guy, Piet Hein, Ronald Graham, Donald Knuth, Robert Nozick, Lee Sallows, Scott Kim, M. C. Escher, Douglas Hofstadter, Roger Penrose, Ian Stewart, Benoit Mandelbrot, Elwyn R. Berlekamp, Solomon W. Golomb, Raymond Smullyan, James Randi, Persi Diaconis, Penn & Teller, and Ray Hyman.
His admirers included such diverse people as W. H. Auden, Arthur C. Clarke, Carl Sagan, Isaac Asimov, Richard Dawkins, and Stephen Jay Gould. Salvador Dali once sought him out to discuss four-dimensional hypercubes. M. C. Escher wrote to Gardner in 1961 after reading The Annotated Alice and this led to Gardner introducing the previously unknown Escher's art to the world. His writing was both broad and deep. Noam Chomsky once wrote, "Martin Gardner's contribution to contemporary intellectual culture is unique—in its range, its insight, and understanding of hard questions that matter." Gardner repeatedly alerted the public (and other mathematicians) to recent discoveries in mathematics–recreational and otherwise. In addition to introducing many first-rate puzzles and topics like Conway's Game of Life, he was equally adept at writing captivating columns about traditional mathematical topics such as knot theory, Fibonacci numbers, Pascal's triangle, the Möbius strip, transfinite numbers, four-dimensional space, Zeno's paradoxes, Fermat's last theorem, and the four-color problem.
Martin Gardner set a new high standard for writing about mathematics. In a 2004 interview he said, "I go up to calculus, and beyond that I don’t understand any of the papers that are being written. I consider that that was an advantage for the type of column I was doing because I had to understand what I was writing about, and that enabled me to write in such a way that an average reader could understand what I was saying. If you are writing popularly about math, I think it’s good not to know too much math." And he was fearsomely bright. John Horton Conway called him "the most learned man I have ever met." Colm Mulcahy said, "Gardner was without doubt the best friend mathematics ever had." Many people would agree with him.
Mathematical Games columnEdit
For over a quarter century Gardner wrote a monthly column on the subject of recreational mathematics for Scientific American. It all began with his free-standing article on hexaflexagons which ran in the December 1956 issue. Flexagons became a bit of a fad and soon people all over New York City were making them. Gerry Piel, the SA publisher at the time, asked Gardner, "Is there enough similar material to this to make a regular feature?" Gardner said he thought so. The January 1957 issue contained his first column, entitled "Mathematical Games". Almost 300 more columns were to follow.
The "Mathematical Games" column became the most popular feature of the magazine and was the first thing that many readers turned to. In September 1977 Scientific American acknowledged the prestige and popularity of Gardner's column by moving it from the back to the very front of the magazine. It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:
- Flexagons (Dec 1956)
- The Game of Hex (Jul 1957)
- The Soma cube (Sep 1958)
- Squaring the square (Nov 1958)
- The Three Prisoners problem (Oct 1959)
- Polyominoes (Nov 1960)
- The Paradox of the unexpected hanging (Mar 1963)
- Rep-tiles (May 1963)
- The Superellipse (Sep 1965)
- Pentominoes (Oct 1965)
- The mathematical art of M. C. Escher (Apr 1966)
- Fractals and the Koch snowflake curve (Mar 1967)
- Conway's Game of Life (Oct 1970)
- Nontransitive dice (Dec 1970)
- Newcomb's paradox (Jul 1973)
- Tangrams (Aug 1974)
- Penrose tilings (Jan 1977)
- Public-key cryptography (Aug 1977)
- Hofstadter's Godel, Escher, Bach (Jul 1979)
- The Monster group (Jun 1980)
Ironically, Gardner had problems learning calculus and never took a mathematics course after high school. While editing Humpty Dumpty's Magazine he constructed many paper folding puzzles, and this led to his interest in the flexagons invented by British mathematician Arthur H Stone. The subsequent article he wrote on hexaflexagons led directly to the column.
In the 1980s the "Mathematical Games" column began to appear only irregularly. Other authors began to share the column, and the June 1986 issue saw the final installment under that title. In 1981, on Gardner's retirement from Scientific American, the column was replaced by Douglas Hofstadter's "Metamagical Themas", a name that is an anagram of "Mathematical Games".
Virtually all of the games columns were collected in book form starting in 1959 with The Scientific American Book of Mathematical Puzzles & Diversions. Over the next four decades fourteen more books followed. Donald Knuth called them the canonical books.
Pseudoscience and skepticismEdit
Gardner was an uncompromising critic of fringe science. His book Fads and Fallacies in the Name of Science (1952, revised 1957) explored and debunked myriad dubious movements and theories including Fletcherism, food faddism, Dowsing Rods, Charles Fort, Rudolf Steiner, Dianetics, the Bates method for improving eyesight, Einstein deniers, the Flat Earth theory, the lost continents of Atlantis and Lemuria, Immanuel Velikovsky’s worlds in collision, the reincarnation of Bridey Murphy, Wilhelm Reich's orgone theory, the spontaneous generation of life, extra-sensory perception and psychokinesis, homeopathy, phrenology, palmistry, graphology, and numerology. This book and his subsequent efforts (Science: Good, Bad and Bogus, 1981; Order and Surprise, 1983, Gardner's Whys & Wherefores, 1989, etc.) earned him a wealth of detractors and antagonists in the fields of fringe science and New Age philosophy, with many of whom he kept up running dialogues (both public and private) for decades.
In 1976 Gardner joined with fellow skeptics philosopher Paul Kurtz, psychologist Ray Hyman, sociologist Marcello Truzzi, and stage magician James Randi to found the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP). Luminaries such as astronomer Carl Sagan, author and biochemist Isaac Asimov, psychologist B. F. Skinner, and journalist Philip J. Klass later became fellows of CSICOP. From 1983 to 2002 he wrote a monthly column called "Notes of a Fringe Watcher" (originally "Notes of a Psi-Watcher") for Skeptical Inquirer, that organization's monthly magazine. These columns have been collected in five books starting with The New Age: Notes of a Fringe Watcher in 1988.
Gardner was a relentless critic of self-proclaimed Israeli psychic Uri Geller and wrote two satirical booklets about him in the 1970s using the pen name "Uriah Fuller" in which he explained how such purported psychics do their seemingly impossible feats such as mentally bending spoons and reading minds.
Martin Gardner continued to criticize junk science throughout his life–and he was fearless. His targets included not just safe subjects like astrology and UFO sightings, but topics such as chiropractic, vegetarianism, Madame Blavatsky, creationism, Scientology, the Laffer curve, Christian Science, and even the Hutchins-Adler Great Books Movement. The last thing he wrote in the spring of 2010 (a month before his death) was an article excoriating the 'dubious medical opinions and bogus science' of Oprah Winfrey—particularly her support for the thoroughly discredited theory that vaccinations cause autism; it went on to bemoan the 'needless deaths of children' that such notions are likely to cause.
Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century. In 2010 he was posthumously honored with an award recognizing his contributions in the skeptical field from the Independent Investigations Group. In 1982 the Committee for Skeptical Inquiry (CSICOP) awarded Gardner their highest award, In Praise of Reason Award for his "heroic efforts in defense of reason and the dignity of the skeptical attitude".
At a meeting of the executive council of the Committee for Skeptical Inquiry in Denver, Colorado in April 2011, Gardner was selected for inclusion in CSI's Pantheon of Skeptics. The Pantheon of Skeptics was created by CSI to remember the legacy of deceased fellows of CSI and their contributions to the cause of scientific skepticism.
Martin Gardner's father once showed him a magic trick when he was a little boy. Young Martin was fascinated to see physical laws seemingly violated and this led to a lifelong passion for magic and illusion. He wrote for a magic magazine in high school and worked in a department store demonstrating magic tricks while he was at the University of Chicago. The very first thing that Martin Gardner ever published (at the age of fifteen) was a magic trick in The Sphinx, the official magazine of the Society of American Magicians. He focused mainly on micromagic (table or close-up magic) and, from the 1930s on, published a significant number of original contributions to this secretive field. Magician Joe M. Turner said, The Encyclopedia of Impromptu Magic, which Gardner wrote in 1985, "is guaranteed to show up in any poll of magicians' favorite magic books." His first magic book for the general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field. He was well known for his innovative tapping and spelling effects, with and without playing cards, and was most proud of the effect he called the "Wink Change".
Many of Gardner's lifelong friends were magicians. These included William Simon who introduced Gardner to Charlotte Greenwald, whom he married in 1952, fellow CSICOP founder and pseudoscience fighter James Randi, Dai Vernon, Jerry Andrus, statistician Persi Diaconis, and polymath Raymond Smullyan. Diaconis and Smullyan like Gardner straddled the two worlds of mathematics and magic. Mathematics and magic were frequently intertwined in Gardner's work. One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks. Mathematical magic tricks were often featured in his "Mathematical Games" column–for example, his August 1962 column was titled "A variety of diverting tricks collected at a fictitious convention of magicians." From 1998 to 2002 he wrote a monthly column on magic tricks called "Trick of the Month" in The Physics Teacher, a journal published by the American Association of Physics Teachers.
In 1999 Magic magazine named Gardner one of the "100 Most Influential Magicians of the Twentieth Century". In 2005 he got a "Lifetime Achievement Award" from the Academy of Magical Arts. The last thing to be published during his lifetime (he had a lot of other stuff in the pipeline) was a magic trick in the May 2010 issue of Word Ways: The Journal of Recreational Linguistics.
Theism and religionEdit
Gardner believed in a personal God, in an afterlife, and in prayer, but rejected established religion. He considered himself a philosophical theist and a fideist. He had an abiding fascination with religious belief but was critical of organized religion. In his autobiography, he stated: "When many of my fans discovered that I believed in God and even hoped for an afterlife, they were shocked and dismayed... I do not mean the God of the Bible, especially the God of the Old Testament, or any other book that claims to be divinely inspired. For me God is a "Wholly Other" transcendent intelligence, impossible for us to understand. He or she is somehow responsible for our universe and capable of providing, how I have no inkling, an afterlife."
Gardner described his own belief as philosophical theism inspired by the works of philosopher Miguel de Unamuno. While eschewing systematic religious doctrine, he retained a belief in God, asserting that this belief cannot be confirmed or disconfirmed by reason or science. At the same time, he was skeptical of claims that any god has communicated with human beings through spoken or telepathic revelation or through miracles in the natural world. Gardner has been quoted as saying that he regarded parapsychology and other research into the paranormal as tantamount to "tempting God" and seeking "signs and wonders". He stated that while he would expect tests on the efficacy of prayers to be negative, he would not rule out a priori the possibility that as yet unknown paranormal forces may allow prayers to influence the physical world.
Gardner wrote repeatedly about what public figures such as Robert Maynard Hutchins, Mortimer Adler, and William F. Buckley, Jr. believed and whether their beliefs were logically consistent. In some cases, he attacked prominent religious figures such as Mary Baker Eddy on the grounds that their claims are unsupportable. His semi-autobiographical novel The Flight of Peter Fromm depicts a traditionally Protestant Christian man struggling with his faith, examining 20th century scholarship and intellectual movements and ultimately rejecting Christianity while remaining a theist.
Gardner said that he suspected that the fundamental nature of human consciousness may not be knowable or discoverable, unless perhaps a physics more profound than ("underlying") quantum mechanics is some day developed. In this regard, he said, he was an adherent of the "New Mysterianism".
Gardner was considered a leading authority on Lewis Carroll. His annotated version of Alice's Adventures in Wonderland and Through the Looking Glass, explaining the many mathematical riddles, wordplay, and literary references found in the Alice books, was first published as The Annotated Alice (Clarkson Potter, 1960). Sequels were published with new annotations as More Annotated Alice (Random House, 1990), and finally as The Annotated Alice: The Definitive Edition (Norton, 1999), combining notes from the earlier editions and new material. The original book arose when Gardner found the Alice books "sort of frightening" when he was young, but found them fascinating as an adult. He felt that someone ought to annotate them, and suggested to a publisher that Bertrand Russell be asked; when the publisher was unable to get past Russell's secretary, Gardner was asked to take on the project himself.
In addition to the "Alice" books, Gardner produced annotated editions of G. K. Chesterton’s The Innocence Of Father Brown and The Man Who Was Thursday, as well as of celebrated poems including The Rime of the Ancient Mariner, Casey at the Bat, The Night Before Christmas, and The Hunting of the Snark; the last was also written by Lewis Carroll.
Novels and short storiesEdit
Gardner wrote several novels. He was a perennial fan of the Oz books written by L. Frank Baum, and in 1988 he published Visitors from Oz, based on the characters in Baum's various Oz books. Gardner was a founding member of the International Wizard of Oz Club, and winner of its 1971 L. Frank Baum Memorial Award.
His short stories were collected in The No-Sided Professor and Other Tales of Fantasy, Humor, Mystery, and Philosophy (1987).
At the age of 95 Gardner wrote Undiluted Hocus-Pocus: The Autobiography of Martin Gardner. He was living in a one-room apartment in Norman, Oklahoma and, as was his custom, wrote it on a typewriter and edited it using scissors and rubber cement. He took the title from a grook by his good friend Piet Hein, a grook which perfectly expresses Gardner's abiding sense of mystery and wonder about existence.
We glibly talk
of nature's laws
but do things have
a natural cause?
Black earth turned into
Gardner's interest in wordplay led him to conceive of a magazine on recreational linguistics. In 1967 he pitched the idea to Greenwood Periodicals and nominated Dmitri Borgmann as editor. The resulting journal, Word Ways, carried many articles from Gardner; as of 2013[update] it was still publishing his submissions posthumously. He also wrote a "Puzzle Tale" column for Asimov's Science Fiction magazine from 1977 to 1986. Gardner was a member of the all-male literary banqueting club, the Trap Door Spiders, which served as the basis of Isaac Asimov's fictional group of mystery solvers, the Black Widowers.
Gardner often used pen names. In 1952, while working for the children's magazine Humpty Dumpty, he contributed stories written by "Humpty Dumpty Jnr". For several years starting in 1953 he was a managing editor of Polly Pigtails, a magazine for young girls, and also wrote under that name. His Annotated Casey at the Bat (1967) included a parody of the poem, attributed to "Nitram Rendrag" (his name spelled backwards). Using the pen name "Uriah Fuller", he wrote two books attacking the alleged psychic Uri Geller. In later years, Gardner often wrote parodies of his favorite poems under the name "Armand T. Ringer", an anagram of his name. In 1983 somebody, called George Groth panned Gardner's book The Whys of a Philosophical Scrivener in the New York Review of Books. Only in the last line of the review was it revealed that George Groth was Martin Gardner himself.
In his January 1960 Mathematical Games column, Gardner introduced the fictitious "Dr. Matrix" and wrote about him often over the next two decades. Dr. Matrix was not exactly a pen name, although Gardner did pretend that everything in these columns came from the fertile mind of the good doctor. Then in 1979 Dr. Matrix himself published an article in the quite respectable Two-Year College Mathematics Journal. It was called Martin Gardner: Defending the Honor of the Human Mind and contained a biography of Gardner and a history of his Mathematical Games column.
Philosophy of mathematicsEdit
Gardner was known for his sometimes controversial philosophy of mathematics. He wrote negative reviews of The Mathematical Experience by Philip J. Davis and Reuben Hersh and What Is Mathematics, Really? by Hersh, both of which were critical of aspects of mathematical Platonism, and the first of which was well received by the mathematical community. While Gardner was often perceived as a hard-core Platonist, his reviews demonstrated some formalist tendencies. Gardner maintained that his views are widespread among mathematicians, but Hersh has countered that in his experience as a professional mathematician and speaker, this is not the case.
Over the years Gardner held forth on many contemporary issues, arguing for his points of view in a wide range of fields, from general semantics to fuzzy logic to watching TV (he once wrote a negative review of Jerry Mander's book Four Arguments for the Elimination of Television). His philosophical views are described and defended in his book The Whys of a Philosophical Scrivener (1983, revised 1999).
Gathering 4 GardnerEdit
Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations. Moreover, his influence was so broad that many of his fans had little or no contact with each other. In 1993 this led Atlanta entrepreneur and puzzle collector Tom Rodgers to the idea of hosting a weekend gathering celebrating Gardner's contributions to recreational mathematics, rationality, magic, puzzles, literature, and philosophy. Although Gardner was famously shy, and would usually decline an honor if it required him to make a personal appearance, Rogers persuaded him to attend. It was called "Gathering 4 Gardner". A second such get-together was held in 1996, again with Gardner in attendance, and this led Rodgers and his friends to make the gathering a regular event. Participants range from long-time Gardner friends such as Conway, Elwyn Berlekamp, Ronald Graham, Donald Coxeter, and Richard Guy, to newcomers like mathematical artist Erik Demaine and mathematical video maker Vi Hart. The program consists of any topic which Gardner had ever written about. The event's name is frequently abbreviated to G4Gn with n being replaced by the number of the event. Thus the first gathering in 1993 was G4G1 and the 1996 event was G4G2. Since then it has been in even-numbered years, usually in the Atlanta area. Thus the 2016 event was G4G12.
- Jackson (2004)
- "MAA Writing Awards Presented" (PDF). Notices of the AMS. 47 (10): 1282. Nov 2000.
- Gardner, Martin (Jan 1999). "The Asymmetric Propeller" (PDF). The College Mathematics Journal. 30 (1): 18–22. doi:10.2307/2687198.
- Martin (2010)
- Singmaster, D. (2010) "Obituary: Martin Gardner (1914–2010)" Nature 465(7300), 884.
- Buffalo Public Library: The annotated Alice : Alice's adventures in wonderland & through the looking-glass: "Martin Gardner's groundbreaking work went on to sell over a million copies, establishing the modest math genius as one of our foremost Carroll scholars."
- Top 10 Martin Gardner Books, by Colm Mulcahy, Huffington Post Books, October 28, 2014
- Costello (1988): p.114.
- Maugh, Thomas H., II (26 May 2010). "Martin Gardner dies at 95; prolific mathematics columnist for Scientific American – Los Angeles Times". Los Angeles Times. Retrieved 2010-05-27.
- Martin (2010): "His mathematical writings intrigued a generation of mathematicians."
- Bellos (2010): "He became a kind of father figure to a generation of young mathematicians, who corresponded with him. Such was Gardner's influence between the late 1950s and 1980s that it would be hard to find a professional mathematician from those years who does not cite him as an inspiration."
- "Martin Gardner—Mathematician". Martin Gardner Home Site. Gathering 4 Gardner. 2014. Retrieved October 28, 2016.
- Originally published in 1952 as In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present
- Shermer, Michael (2001). The Borderlands of Science: Where Sense Meets Nonsense. Oxford University Press. p. 50. Retrieved May 20, 2016. "Fads and Fallacies in the Name of Science [is] still in print and arguably the skeptic classic of the past half-century."
- "About CSI - CSI". Committee for Skeptical Inquiry. Retrieved 2016-10-28.
- MacTutor History of Mathematics archive: Martin Gardner
- "Martin Gardner: Founder of the Modern Skeptical Movement » Wednesday, May 26th, 2010". Skeptic. Retrieved 2016-05-22.
- Gardner, Martin, "The Hermit Scientist", Antioch Review, Winter 1950–1951, pp. 447–457.
- Yam, Philip (December 1995). "Profile: Martin Gardner, the Mathematical Gamester". Scientific American. Retrieved May 22, 2010.
- Gardner, Martin; Berlekamp, Elwyn R.; Rodgers, Tom (1999). The mathemagician and pied puzzler: a collection in tribute to Martin Gardner. A K Peters, Ltd. ISBN 978-1-56881-075-1.
- Gardner, Martin (2013)
- Burstein (2011)
- Richards (2014)
- JPL Small-Body Database Browser 2587 Gardner (1980 OH)
- Princeton University Press: Reviews of Undiluted Hocus-Pocus
- Princeton University Press: Reviews of Undiluted Hocus-Pocus: "Martin Gardner occupies a special place in twentieth-century mathematics. More than any other single individual, he inspired a generation of young people to study math."–Barry Cipra
- Bellos (2010): He was not a mathematician – he never even took a maths class after high school—yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.
- Hofstadter (2010): The word games, with its lightweight flavor, did not even hint at the depth of the issues that the column dealt with.
- Richards (2014): Gardner’s columns seeded scores of new findings—far too many to list.
- Berlekamp (1982): Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy dedicated their book Winning Ways for your Mathematical Plays, saying "To Martin Gardner, who has brought more mathematics to more millions than anyone else."
- Hofstadter (2010): Many of today's most influential mathematicians and physicists, magicians and philosophers, writers and computer scientists, owe their direction to Martin Gardner. They may not even be aware of how big a role he played in their development.
- Mulcahy (Jan 2014): It’s been said that he had a million readers there at his peak.
- Malkevitch (2014): Martin Gardner's columns and books have been referenced by huge numbers of research papers that involve mathematics.
- Antonick (2014): Martin Gardner was well known for inspiring generations of students to become professional mathematicians.
- Antonick (2014): "Martin Gardner’s column in Scientific American was one of the two things that, above all others, convinced me I wanted to be a mathematician."–Ian Stewart
- Demaine (2008) p. ix: Many of today's mathematicians entered this field through Gardner's influence.
- Martin Gardner—Mathematician (official website): "Gardner will go down in history as one of the most significant mathematicians of all time."–Michael Aschbacher, editor of The Journal of Recreational Mathematics
- Auerbach (2013)
- Knuth (2011): Already when he began his monthly series in 1956 and 1957, he was corresponding with the likes of Claude Shannon, John Nash, John Milnor, and David Gale. Later he would receive mail from budding mathematicians John Conway, Persi Diaconis, Jeffrey Shallit, Ron Rivest, et al.
- Mulcahy (Oct 2014)
- Hofstadter (2010)
- Teller (2014)
- Mulcahy (2013)
- Brown (2010)
- The Economist (2010)
- Mulcahy (Jan 2014): The surrealist artist was intrigued by Martin’s writings on the 4-dimensional cube, or tesseract—-which had been a prominent feature of his own 1954 painting Crucifixion (Corpus Hypercubus).
- Mulcahy (Jan 2014)
- Mulcahy (Oct 2014): It went a lot further than puzzles—there was substance, depth and a fair share of mystery and wonder in the topics he wrote about.
- Mulcahy (Oct 2014): Penrose tiles are a good example of just how 'nontrivial' the consequences of his puzzle column could be. The materials scientist Dan Shechtman actually won a Nobel Prize in chemistry in 2011 'for the discovery of quasicrystals'—three-dimensional Penrose tiles—in some aluminium-manganese alloys.
- Hofstadter (2010): His approach and his ways of combining ideas are truly unique and truly creative, and, if I dare say so, what Martin Gardner has done is of far greater originality than work that has won many people Nobel Prizes.
- Malkevitch (2014): The range of wonderful problems, examples, and theorems that Gardner treated over the years is enormous. They include ideas from geometry, algebra, number theory, graph theory, topology, and knot theory, to name but a few.
- Bellos, Alex (2010): I discovered how good [the columns] really were, covering everything from public-key cryptography to superstring theory. He was the first to cover so many breakthroughs.
- Jackson (2004): His crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization.
- Lister (1995): Martin Gardner's supreme achievement was his ability to communicate difficult and often profound subjects with a few deft, but human strokes of his pen.
- Mirsky (2010): "His writing has been valued by generations of professional mathematicians."–Ian Stewart
- Teller (2014): "Gardner writes with authority and ease. You trust him to take you wherever he feels like going."
- Hofstadter (2010): Martin had a magical touch in writing about math.
- Princeton University Press: Reviews of Undiluted Hocus-Pocus: James Randi called him "a huge intellect."
- Martin (2010): "Martin Gardner is one of the great intellects produced in this country in the 20th century."–Douglas Hofstadter
- Malkevitch (2014): One of the greatest expositors of mathematics, for me perhaps the greatest, was Martin Gardner. Perhaps no one has done more to make the world aware of mathematics than Martin Gardner
- The Economist (2010): His gift, or rather one of them, was to explain mathematical concepts in ways that made sense to non-mathematicians. Many of them not only understood what he wrote but also became infected with his love of maths, of its beauty and of its capacity to give satisfaction.
- Jackson (2004): He 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.
- Knuth (2011): Indeed, more people have probably learned more good mathematical ideas from Martin Gardner than from any other person in the history of the world.
- Hofstadter (2010): There were thousands of such people spread all around the world—mathematicians, physicists, philosophers, computer scientists, and on and on—who thought of Martin Gardner's column not as merely a feature of that great magazine Scientific American, but as its very heart and soul.
- Demaine (2008): p. 24
- Institute for Research in Computer Science: University Paris-Diderot: Hex & Rex & T-Rex & C-Hex Piet Hein discovered HEX in 1942, but it was only when Martin Gardner wrote about HEX in Scientific American in 1957 that it became widely known.
- Adamatzky, A. (Ed.) (2010). Game of Life Cellular Automata ebook, ISBN 1849962170. pp. 15-16, Conway came to New York to meet with Gardner [and] could not believe the amount of interest Gardner’s columns on the game of Life had generated.
- Martin Gardner: Mathematical Games Collections by David Langford
- The New Martin Gardner Mathematical Library Cambridge University Press
- The Canon: The fifteen "Mathematical Games" books at martin-gardner.org
- Regis, Ed (June 4, 2000). "There's One Born Every Minute (author)". New York Times. Retrieved May 20, 2016. Nobody who read it will soon forget its stellar roll call of mid-20th-century cranks and crackpots.
- "CSI | Articles by Martin Gardner". Csicop.org. Retrieved 2010-09-01.
- Prometheus Books The New Age: Notes of a Fringe-Watcher by Martin Gardner
- "Linkapedia Visualarts Discover more about Uriah Fuller". linkapedia-visualarts.com.
- Oprah Winfrey: Bright (but Gullible) Billionaire Skeptical Inquirer, March/April 2010
- Skeptical Inquirer Magazine Names the Ten Outstanding Skeptics of the Century
- "About the IIG Awards". Iigwest.com. Retrieved 2012-04-14.
- "CSICOP Council in Atlanta: Police Psychics, Local Groups". The Skeptical Inquirer. 7 (3): 13. 1983.
- "The Pantheon of Skeptics". CSI. Committee for Skeptical Inquiry. Archived from the original on 31 January 2017. Retrieved 30 April 2017.
- Martin Gardner's Magic Influence at martin-gardner.org
- Costello (1988) p. 115: His father had taught him his first trick, the "Knife and Paper" trick, a bit of legerdemain involving a butter knife with bits of paper on it.
- Bellos (2010)
- Gathering 4 Gardner (2014)
- Demaine (2008) p. 12
- Reviews of Martin Gardner's Impromptu The Miracle Factory
- Demaine (2008): pp. 4-5
- Lister (1995)
- from Dover Publications: Mathematics, Magic and Mystery "As a rule, we simply accept these tricks and 'magic' without recognizing that they are really demonstrations of strict laws based on probability, sets, number theory, topology, and other branches of mathematics."
- The Dover Math and Science Newsletter May 16, 2011
- Happy 101st Birthday, Martin Gardner by Gabrielle Beacken, Princeton University Press, October 21, 2015
- Carpenter, Alexander (2008), "Martin Gardner on Philosophical Theism, Adventists and Price" Interview, 17 October 2008, Spectrum.
- Gardner (2013) p. 191
- Groth (1983)
- French, Chris (2010-05-25). "Martin Gardner: 1914-2010". The Guardian. ISSN 0261-3077. Retrieved 2017-01-31.
- The Whys of a Philosophical Scrivener by Martin Gardner, Quill, 1983, pp. 238–239
- Frazier, Kendrick. "A Mind at Play: An Interview with Martin Gardner". Skeptical Inquirer. Retrieved 29 January 2016.
- Jan Susina. Conversation with Martin Gardner: Annotator of Wonderland. The Five Owls. Jan./Feb. 2000. 62–64.
- Alice Still Lives Here by Michael Sims, Nashville Scene, July 06, 2000
- MacTutor History of Mathematics archive: Martin Gardner: My mother read The Wizard of Oz to me when I was a little boy, and I looked over her shoulder as she read it. I learned how to read that way.
- Brown (2010): 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.
- Grooks by Piet Hein
- Eckler, A. Ross (2010). "Look back"""""!". Word Ways: The Journal of Recreational Linguistics. 43 (3): 167–168.
- Don Albers' interview of Gardner, Part 4: The Trap Door Spiders
- Top 10 Martin Gardner Alter Egos at martin-gardner.org
- "Gardner's Whys" in The Night is Large, chapter 40, pp. 481–87.
- Matrix, Irving Joshua (1979). Martin Gardner: Defending the Honor of the Human Mind, The Two-Year College Mathematics Journal, Vol. 10, No. 4 (Sep., 1979), pp. 227-232.
- It would be a further decade before Martin published an article in such a mathematics journal under his own name.
- Skeptic Martin Gardner Dies by Loren Coleman, CryptoZoo News, May 23, 2010
- Hersh, Reuben (31 October 1997). "Re: Martin Gardner book review". Foundations of Mathematics mailing list. Retrieved 22 May 2010.
- Science, good, bad, and bogus – Martin Gardner – Google Books. Books.google.com.au. Retrieved 2012-04-14.
- Robert P. Crease, Gathering for Gardner, The Wall Street Journal, p. W11, 2 April 2010
- About G4G gathering4gardner.org
- Antonick, Gary (2014). Ignited by Martin Gardner, Ian Stewart Continues to Illuminate The New York Times, October 27, 2014
- Auerbach, David (2013). A Delville of a Tolkar: Martin Gardner’s “Undiluted Hocus-Pocus” Los Angeles Review of Books, November 4, 2013
- Bellos, Alex (2010). Martin Gardner obituary The Guardian, May 27, 2010
- Berlekamp, Elwyn R (2014). The Mathematical Legacy of Martin Gardner Society for Industrial and Applied Mathematics (SIAM), September 2, 2014
- Berlekamp, Elwyn R., John H. Conway, and Richard K. Guy (1982). Winning Ways for your Mathematical Plays Academic Press, ISBN 0120911507.
- Brown, Emma (2010). Martin Gardner, prolific math and science writer, dies at 95 The Washington Post, May 24, 2010
- Burstein, Mark, ed. (2011). A Bouquet for the Gardner: Martin Gardner Remembered. New York: The Lewis Carroll Society of North America. ISBN 978-0-930326-17-3.
- Costello, Matthew J. (1988). The Greatest Puzzles of All Time New York: Prentice Hall Press, ISBN 0133649369
- Demaine (2008). Edited by Erik D. Demaine, Martin L. Demaine, Tom Rodgers. A lifetime of puzzles : a collection of puzzles in honor of Martin Gardner's 90th birthday A K Peters: Wellesley, MA, ISBN 1568812450
- Gardner, Martin (2013). Undiluted Hocus-Pocus: The Autobiography of Martin Gardner Princeton University Press, ISBN 0691159912.
- The Economist (2010). Martin Gardner obituary Jun 3rd 2010
- Gardner, Martin (2016) The Recreational Mathematics of Piet Hein Piet Hein Website
- Gathering 4 Gardner (2014). Martin Gardner—Magician
- Groth, George (1983). Review of Gardner’s Game with God The New York Review of Books, December 8, 1983
- Hofstadter, Douglas (2010). Martin Gardner: A Major Shaping Force in My Life Scientific American, May 24, 2010
- Jackson, Allyn (2004). Interview with Martin Gardner Notices of the AMS, Vol. 52, No. 6, June/July 2005, pp. 602–611
- Knuth, Donald E. (2011). Memories of Martin Gardner Notices of the AMS, Vol. 58, No. 3, March 2011, p. 420
- Lister, David (1995). Martin Gardner and Paperfolding British Origami Society, February 15, 1995.
- O'Connor, John J.; Robertson, Edmund F., "Martin Gardner", MacTutor History of Mathematics archive, University of St Andrews.
- Malkevitch, Joseph (2014). Magical Mathematics - A Tribute to Martin Gardner American Mathematical Society, March 2014
- Martin, Douglas (2010). Martin Gardner, Puzzler and Polymath, Dies at 95 The New York Times, May 23, 2010
- Martin Gardner—Mathematician (official website)
- Mulcahy, Colm (Jan 2014). Martin Gardner — The Best Friend Mathematics Ever Had The Huffington Post, January 23, 2014
- Mirsky, Steve (May 2010). Scholars and Others Pay Tribute to Mathematical Games Columnist Martin Gardner Scientific American, May 24, 2010
- Mulcahy, Colm (Oct 2014). Martin Gardner, puzzle master extraordinaire BBC News Magazine, October 21, 2014
- Mulcahy, Colm (2013). Celebrations of Mind Honor Math’s Best Friend, Martin Gardner Scientific American, October 29, 2013
- Princeton University Press Reviews of Undiluted Hocus-Pocus: The Autobiography of Martin Gardner
- Richards, Dana (2014). Math Games of Martin Gardner Still Spur Innovation by Dana Richards & Colm Mulcahy, Scientific American, October 1, 2014
- Teller (2014). ‘Undiluted Hocus-Pocus,’ by Martin Gardner The New York Times: Sunday Book Review, January 3, 2014