Martin Gardner

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.[4][5] He was also a leading authority on Lewis Carroll.[6] The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.[7] He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century.[8] He was considered the doyen of American puzzlers.[9] He was a prolific and versatile author, publishing more than 100 books.[10][11]

Martin Gardner
Born(1914-10-21)October 21, 1914
Tulsa, Oklahoma, U.S.
DiedMay 22, 2010(2010-05-22) (aged 95)
Norman, Oklahoma, U.S.
OccupationAuthor
NationalityUnited States
Alma materUniversity of Chicago
GenreRecreational mathematics, puzzles, close-up magic, annotated literary works, debunking
Literary movementScientific skepticism
Notable worksFads 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 awardsLeroy P. Steele Prize for Mathematical Exposition (1987)[1]
George Pólya Award (1999)[2][3]
Allendoerfer Award (1990)
Trevor Evans Award (1998)
Signature
Martin Gardner

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.[12][13] These appeared for twenty-five years in Scientific American, and his subsequent books collecting them.[14][15]

Gardner was one of the foremost anti-pseudoscience polemicists of the 20th century.[16] His 1957 book Fads and Fallacies in the Name of Science[17] became a classic and seminal work of the skeptical movement.[18] In 1976 he joined with fellow skeptics to found CSICOP, an organization promoting scientific inquiry and the use of reason in examining extraordinary claims.[19]

Biography
Gardner as a high school senior, 1932

Youth and education

Martin Gardner was born into a prosperous family in Tulsa, Oklahoma, to James Henry Gardner, a prominent petroleum geologist,[20] and his wife, Willie Wilkerson Spiers, a Montessori-trained teacher. His mother taught Martin to read before he started school, reading him The Wizard of Oz, and this began a lifelong interest in the Oz books of L. Frank Baum.[21][22] His fascination with puzzles started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles, Tricks and Conundrums.[23]

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.

After the war, Gardner returned to the University of Chicago.[24] He attended graduate school for a year there, but he did not earn an advanced degree.[1]

In 1950, he wrote an article in the Antioch Review entitled "The Hermit Scientist".[25] 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.

Early career

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.[26] His paper-folding puzzles at that magazine led to his first work at Scientific American.[27] 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 freelance author, publishing books with several different publishers, and also publishing hundreds of magazine and newspaper articles.[28] The year 1960 saw the original edition of the best-selling book of his career, The Annotated Alice.[29]

Retirement and death

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.[30] Charlotte died in 2000 and in 2004 Gardner returned to Oklahoma,[31] where his son, James Gardner, was a professor of education at the University of Oklahoma[1] in Norman. He died there on May 22, 2010.[4] An autobiography — Undiluted Hocus-Pocus: The Autobiography of Martin Gardner — was published posthumously.[28]

Influence
His depth and clarity will illuminate our world for a long time.[32]

–Persi Diaconis

Martin Gardner had a major impact on mathematics in the second half of the 20th century.[33][34] His column was called "Mathematical Games" but it was much more than that.[35][36][37] His writing introduced many readers to real mathematics for the first time in their lives.[38] 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.[39][40] It was the original inspiration for many of them to become mathematicians or scientists themselves.[41][42][43][44][45]

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."[46]

His admirers included such diverse people as W. H. Auden, Arthur C. Clarke, Carl Sagan, Isaac Asimov, Richard Dawkins, Stephen Jay Gould, and the entire French literary group known as the Oulipo.[47][48][49][50] Salvador Dalí once sought him out to discuss four-dimensional hypercubes.[51] Gardner wrote to M.C. Escher in 1961 to ask permission to use his Horseman tessellation in an upcoming column about H.S.M. Coxeter. Escher replied, saying that he knew Gardner as author of The Annotated Alice, which had been sent to Escher by Coxeter. The correspondence led to Gardner introducing the previously unknown Escher's art to the world.[52] His writing was both broad and deep.[53][54][55] 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."[48][56] Gardner repeatedly alerted the public (and other mathematicians) to recent discoveries in mathematics–recreational and otherwise.[57][58] In addition to introducing many first-rate puzzles and topics such as Penrose tiles[59] and Conway's Game of Life,[60] 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.[46][61]

Gardner set a new high standard for writing about mathematics.[62][63][64][65][66] 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."[1] And he was fearsomely bright.[67][68] John Horton Conway called him "the most learned man I have ever met."[47] Colm Mulcahy spoke for many when he said, "Gardner was without doubt the best friend mathematics ever had."[52][69][70][71][72]

Mathematical Games column
Further information: List of Martin Gardner Mathematical Games columns
I just play all the time and am fortunate enough to get paid for it.

– Martin Gardner, 1998

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.[73][49] 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".[28] Almost 300 more columns were to follow.[1]

The "Mathematical Games" column became the most popular feature of the magazine and was the first thing that many readers turned to.[74] 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.[75] It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:[76]

Solomon Golomb's Polyominoes were among the many recreational mathematics topics featured by Gardner in his column. The 35 hexominoes are depicted.

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. At a magic show in 1956 fellow magician Royal Vale Heath introduced Gardner to the intricately folded paper shapes known as flexagons and steered him to the four Princeton University professors who had invented and investigated their mathematical properties. The subsequent article Gardner wrote on hexaflexagons led directly to the column.[28]

Gardner's son Jim once asked him what was his favorite puzzle, and Gardner answered almost immediately: "The monkey and the coconuts".[77] It had been the subject of his April 1958 Games column and in 2001 he chose to make it the first chapter of his "best of" collection, The Colossal Book of Mathematics.[78]

In the 1980s "Mathematical Games" 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.[79] Over the next four decades fourteen more books followed.[22] Donald Knuth called them the canonical books.[80][81]

Martin Gardner's Mathematical Grapevine
He had carried on incredibly interesting exchanges with hundreds of mathematicians, as well as with artists and polymaths such as Maurits Escher and Piet Hein.[82]

– AMS Notices

There is a group of people who lie at the intersection of mathematics, philosophy, magic, and scientific skepticism who all knew and worked with Martin Gardner. They are united by a striking originality in their work and they sometimes owe much of their fame to being featured by Gardner in his column.[83][84] The fact that Gardner had an unerring eye for spotting and promoting such people is one of the reasons his column was so influential. Indeed, Gardner filled a role a little bit like the 17th century French polymath Marin Mersenne[85] in that he maintained this network and made these people aware of each other–and this led to further fruitful collaborations.[86] For example, if it were not for Gardner, mathematicians Conway, Berlekamp, and Guy probably would have never gotten together to write Winning Ways for your Mathematical Plays, a foundational book in combinatorial game theory.[87] Gardner also introduced Conway to Benoit Mandelbrot because he knew they both were interested in Penrose tiles.[73][88] If it were not for Gardner, Doris Schattschneider and Marjorie Rice would not have gotten together to document the newly discovered pentagon tilings.[89][90]

Late in his life Gardner once said, "When I first started the column, I was not in touch with any mathematicians, and gradually mathematicians who were creative in the field found out about the column and began corresponding with me. So my most interesting columns were columns based on the material I got from them, so I owe them a big debt of gratitude."[91] The games column was not just Gardner.[92] It was this group of people he collected, nurtured, and acted as a conduit for—a group that came to be known as "Martin Gardner’s mathematical grapevine."[91]

Gardner prepared each of his columns in a painstaking and scholarly fashion and conducted copious correspondence to be sure that everything was fact-checked for mathematical accuracy.[93] But this grapevine, with Gardner at the center, was also a rich source of ideas, mathematical and otherwise, with gossip flowing in many directions. Communications was often by postcard or telephone and Gardner kept meticulous notes of everything, typically on index cards.[94] Archives of just some of his correspondence stored at Stanford University occupy some 63 linear feet of shelf space.[95] This correspondence led to columns about the rep-tiles and pentominos of Solomon W. Golomb; the space filling curves of Bill Gosper;[96] the aperiodic tiles of Roger Penrose; the Game of Life invented by John H. Conway; the superellipse and the Soma cube of Piet Hein; the trapdoor functions of Diffie, Hellman, and Merkle; the flexagons of Stone, Tuckerman, Feynman, and Tukey; the geometrical delights in a book by H. S. M. Coxeter; the game of Hex invented by John Nash; Tutte's account of squaring the square; and many other topics.

The wide array of mathematicians, physicists, computer scientists, philosophers, magicians, artists, writers, and other influential thinkers who can be counted as part of Gardner's mathematical grapevine includes:[91][97][61][98][99][47][100][101][102][103]

Doris Schattschneider sometimes refers to this circle of collaborators as MG2..[104]

Gardner died in 2010 but the grapevine lives on, and is even adding new members from time to time. Many of the people in the Gardner circle continue to meet every two years at Gathering 4 Gardner (G4G) founded in 1993 by Berlekamp, Tom Rodgers, and other admirers of Martin Gardner.[105] A keynote speaker at G4G13 was Fields medalist Manjul Bhargava.[106]

Pseudoscience and skepticism
Martin Gardner is the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.[30]

– Stephen Jay Gould

Gardner was an uncompromising critic of fringe science. His book Fads and Fallacies in the Name of Science (1952, revised 1957) launched the modern skeptical movement.[24] It debunked dubious movements and theories[107] including Fletcherism, Lamarckism, 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.) provoked a lot of criticism from the advocates of alternative science and New Age philosophy;[108] he kept up running dialogues (both public and private) with many of them for decades.[24]

In a review of Science: Good, Bad and Bogus, Stephen Jay Gould called Gardner "The Quack Detector", a writer who "expunge[d] nonsense" and in so doing had "become a priceless national resource."[109]

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 (now called the Committee for Skeptical Inquiry). Luminaries such as astronomer Carl Sagan, author and biochemist Isaac Asimov, psychologist B. F. Skinner, and journalist Philip J. Klass became fellows of the program. 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.[110] These columns have been collected in five books starting with The New Age: Notes of a Fringe Watcher in 1988.[111]

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.[112]

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 the Hutchins-Adler Great Books Movement.[46] 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.[113]

Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century.[114] In 2010 he was posthumously honored with an award for his contributions in the skeptical field from the Independent Investigations Group.[115] In 1982 the Committee for Skeptical Inquiry awarded Gardner its In Praise of Reason Award for his "heroic efforts in defense of reason and the dignity of the skeptical attitude",[116] and in 2011 it added Gardner to its Pantheon of Skeptics.[117]

Magic
Card magic, and magic in general, owe a far greater debt to Martin Gardner than most conjurors realize.[118]

–Stephen Minch

Martin Gardner's father once showed him a magic trick when he was a little boy.[119] 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.[120] 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.[121] 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."[122][123] His first magic book for the general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field.[121] 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".[124]

Many of Gardner's lifelong friends were magicians.[125] These included William Simon who introduced Gardner to Charlotte Greenwald, whom he married in 1952, Dai Vernon, Jerry Andrus, statistician Persi Diaconis, and polymath Raymond Smullyan. Gardner considered fellow magician James Randi his closest friend. Diaconis and Smullyan like Gardner straddled the two worlds of mathematics and magic.[61] Mathematics and magic were frequently intertwined in Gardner's work.[126] One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks.[120] 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.[127]

In 1999 Magic magazine named Gardner one of the "100 Most Influential Magicians of the Twentieth Century".[8] In 2005 he received a 'Lifetime Achievement Fellowship' from the Academy of Magical Arts.[128] The last work to be published during his lifetime was a magic trick in the May 2010 issue of Word Ways: The Journal of Recreational Linguistics.[121]

Theism and religion
I am a philosophical theist. I believe in a personal God, and I believe in an afterlife, and I believe in prayer, but I don't believe in any established religion. This is called philosophical theism. ... Philosophical theism is entirely emotional. As Kant said, he destroyed pure reason to make room for faith.[129]

– Martin Gardner, 2008

Gardner was raised as a Methodist (his mother was very religious) but rejected established religion as an adult.[21] He considered himself a philosophical theist and a fideist.[129] He believed in a personal God, in an afterlife, and prayer, but rejected established religion. Nevertheless, he had abiding fascination with religious belief. 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."[130]

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.[131] 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.[132] 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.[133]

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.[131]

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".[134]

Annotated works

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.[135] The original book arose when Gardner found the Alice books "sort of frightening" when he was young, but found them fascinating as an adult.[136] 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.[137]

There had long been annotated books written by scholars for other scholars, but Gardner was the first to write such a work for the general public,[138] and soon many other writers followed his lead.[139][140] Gardner himself went on to produce 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.[125]

Novels and short stories

Gardner wrote two novels. He was a perennial fan of the Oz books written by L. Frank Baum,[141] 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 other novel was The Flight of Peter Fromm (1973), which reflected his lifelong fascination with religious belief and the problem of faith.[142]

His short stories were collected in The No-Sided Professor and Other Tales of Fantasy, Humor, Mystery, and Philosophy (1987).[1]

Autobiography

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.[99] He took the title from a poem, a so-called grook, by his good friend Piet Hein,[143] which perfectly expresses Gardner's abiding sense of mystery and wonder about existence.[144]

We glibly talk
 of nature's laws
but do things have
 a natural cause?

Black earth turned into
 yellow crocus
is undiluted
 hocus-pocus.

Word play

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.[145] The resulting journal, Word Ways, carried many of his articles; as of 2013 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.[146]

Pen names

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.[147] In 1983 one 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.[148]

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.[149] 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. It would be a further decade before Martin published an article in such a mathematics journal under his own name.[147]

Philosophy of mathematics

Gardner was known for his sometimes controversial philosophy of mathematics.[150] 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.[151]

Other views

Over the years Gardner held forth on many contemporary issues, arguing for his points of view in 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).[152] He was a frequent contributor to The New York Review of Books.[153] His philosophical views are described and defended in his book The Whys of a Philosophical Scrivener (1983, revised 1999).[148]

Legacy and awards

The numerous awards Gardner received include:[154]

The Mathematical Associating of America has established a Martin Gardner Lecture to be given each year on the last day of MAA MathFest, the summer meeting of the MAA. The first annual lecture, Recreational Mathematics and Computer Science: Martin Gardner's Influence on Research, was given by Erik Demaine of the Massachusetts Institute of Technology on Saturday, August 3, 2019, at MathFest in Cincinnati.[158]

There are eight bricks honoring Gardner in the Paul R. Halmos Commemorative Walk, installed by The Mathematical Association of America (MAA) at their Conference Center in Washington, D.C.[159] Gardner has an Erdös number of 1.[160]

Gathering 4 Gardner
Main article: Gathering 4 Gardner

Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations.[30] Moreover, his influence was so broad that many of his fans had little or no contact with each other.[161] 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.[47] 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 the first such "Gathering 4 Gardner" (G4G), held in Atlanta in January 1993.[162]

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, bi-annual event. Participants over the years have ranged from long-time Gardner friends such as John Horton Conway, Elwyn Berlekamp, Ronald Graham, Donald Coxeter, and Richard K. Guy, to newcomers like mathematician and mathematical artist Erik Demaine and mathematical video maker Vi Hart.[30]

The program at the "G4G" meetings presents topics which Gardner had written about. The first gathering in 1993 was G4G1 and the 1996 event was G4G2. Since then it has been in even-numbered years, so far always in Atlanta.[163] The 2018 event was G4G13.[164]

Bibliography
Main article: Martin Gardner bibliography

In a publishing career spanning 80 years (1930-2010),[165] Gardner authored or edited over 100 books and countless articles, columns and reviews.

All Gardner's works were non-fiction except for two novels — The Flight of Peter Fromm (1973) and Visitors from Oz (1998) — and two collections of short pieces — The Magic Numbers of Dr. Matrix (1967, 1985) and The No-Sided Professor (1987).

References
  1. AMS Notices (2004)
  2. "MAA Writing Awards Presented" (PDF). Notices of the AMS. 47 (10): 1282. Nov 2000. Archived (PDF) from the original on 2014-07-12.
  3. Gardner, Martin (Jan 1999). "The Asymmetric Propeller" (PDF). The College Mathematics Journal. 30 (1): 18–22. doi:10.2307/2687198. JSTOR 2687198. Archived (PDF) from the original on 2014-03-04.
  4. Martin (2010)
  5. Singmaster, D. (2010) "Obituary: Martin Gardner (1914–2010)" Nature 465(7300), 884.
  6. Kindley (2015): When it comes to explanations of Carroll’s books, no one has yet improved on the work of Gardner.
  7. Buffalo Public Library: The annotated Alice : Alice's adventures in wonderland & through the looking-glass Archived 2016-06-24 at the Wayback Machine: "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."
  8. Top 10 Martin Gardner Books Archived 2016-03-25 at the Wayback Machine, by Colm Mulcahy, Huffington Post Books, October 28, 2014
  9. Costello (1988): p.114.
  10. England (2014): Even apart from mathematics and puzzles, Gar dner's output was staggering.
  11. "Martin Gardner dies at 95; prolific mathematics columnist for Scientific American" by Thomas H. Maugh, Los Angeles Times, May 26, 2010
  12. AMS Notices (2011): "Martin Gardner was a gem. There is absolutely no question that he, more than anyone else in the world, was responsible for turning people of all ages on to the pleasures of mathematical recreations." —Ronald L. Graham
  13. Case 2014: Gardner is credited with the rebirth of recreational mathematics in the U.S.
  14. Martin (2010): "His mathematical writings intrigued a generation of mathematicians."
  15. 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."
  16. "Martin Gardner—Mathematician". Martin Gardner Home Site. Gathering 4 Gardner. 2014. Archived from the original on November 18, 2016. Retrieved October 28, 2016.
  17. Originally published in 1952 as In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present
  18. 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. "Fads and Fallacies in the Name of Science [is] still in print and arguably the skeptic classic of the past half-century."
  19. "About CSI - CSI". Committee for Skeptical Inquiry. Archived from the original on 2016-11-12. Retrieved 2016-10-28.
  20. James Gardner later became the 8th President of the American Association of Petroleum Geologists.
  21. Martin Gardner Famous Scientists
  22. England (2014)
  23. MacTutor
  24. Shermer (1997)
  25. Gardner, Martin, "The Hermit Scientist", Antioch Review, Winter 1950–1951, pp. 447–457.
  26. Yam, Philip (December 1995) Profile: Martin Gardner, the Mathematical Gamester (1914-2010) Archived 2018-05-11 at the Wayback Machine Scientific American
  27. 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.
  28. Gardner, Martin (2013)
  29. Burstein (2011)
  30. Richards (2014)
  31. Albers (2008)
  32. Princeton University Press: Reviews of Undiluted Hocus-Pocus
  33. 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 Arthur Cipra
  34. 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.
  35. Hofstadter (2010): The word games, with its lightweight flavor, did not even hint at the depth of the issues that the column dealt with.
  36. Richards (2014): Gardner's columns seeded scores of new findings—far too many to list.
  37. 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."
  38. 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.
  39. Mulcahy (2014): It's been said that he had a million readers there at his peak.
  40. Malkevitch (2014): Martin Gardner's columns and books have been referenced by huge numbers of research papers that involve mathematics.
  41. Bhargava (2018): Eventually, when I was around 12 years old, through my puzzle explorations I of course also had the good fortune of discovering the works of Martin Gardner. They inspired me a huge amount, and gave me something far more enjoyable to do than go to math class! I also read other recreational mathematics and puzzle books, such as those of Raymond Smullyan, and all of these works definitely had a great influence on me as a playing and playful mathematician.
  42. Antonick (2014): Martin Gardner was well known for inspiring generations of students to become professional mathematicians.
  43. 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
  44. Demaine (2008) p. ix: Many of today's mathematicians entered this field through Gardner's influence.
  45. Crease (2018): "As a columnist for Scientific American, Gardner inspired generations of physicists, mathematicians, philosophers, puzzle-makers, logicians, magicians and others, including me."
  46. Auerbach (2013)
  47. Mulcahy (2013)
  48. Brown (2010)
  49. The Economist (2010)
  50. Dirda (2009)
  51. Mulcahy (2017): 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).
  52. Mulcahy (2017)
  53. BBC News (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.
  54. BBC News (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.
  55. 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.
  56. MacTutor: Gardner has produced a number of mathematical papers, written with leading mathematicians.
  57. 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.
  58. 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.
  59. Kullman (1997): Martin Gardner, in his "Mathematical Games" column in Scientific American presented "for the first time" a description of the Penrose tiles, including many of Conway's results concerning them.
  60. MAA FOCUS (2010): "Another milestone was in late 1970, when Martin’s column introduced the world to John Horton Conway’s Game of Life"–John Derbyshire
  61. Hofstadter (2010)
  62. AMS Notices (2004): "His crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization." —Allyn Jackson.
  63. 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.
  64. Mirsky (2010): "His writing has been valued by generations of professional mathematicians."–Ian Stewart
  65. Teller (2014): "Gardner writes with authority and ease. You trust him to take you wherever he feels like going."
  66. Hofstadter (2010): Martin had a magical touch in writing about math.
  67. Princeton University Press: Reviews of Undiluted Hocus-Pocus: James Randi called him "a huge intellect."
  68. Martin (2010): "Martin Gardner is one of the great intellects produced in this country in the 20th century."–Douglas Hofstadter
  69. 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
  70. 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.
  71. AMS Notices (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." —Allyn Jackson
  72. AMS Notices (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." – Donald Knuth
  73. Mulcahy (2014)
  74. 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.
  75. Demaine (2008): p. 24
  76. 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.
  77. Antonick, Gary (2013). Martin Gardner’s The Monkey and the Coconuts in Numberplay The New York Times:, October 7, 2013
  78. Gardner, Martin The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001), W.W. Norton & Company; ISBN 0-393-02023-1
  79. Martin Gardner: Mathematical Games Collections Archived 2016-06-29 at the Wayback Machine by David Langford
  80. The New Martin Gardner Mathematical Library Archived 2016-12-26 at the Wayback Machine Cambridge University Press
  81. The Canon: The fifteen "Mathematical Games" books at martin-gardner.org Archived 2015-02-16 at the Wayback Machine
  82. AMS Notices (2004)
  83. MAA FOCUS (2010): Many things took off after Martin covered them: the Game of Googol (Feb 1960), the art of M. C. Escher (Apr 1966), Conway’s Game of Life (Oct 1970), Mandelbrot’s fractals, Penrose tilings (Jan 1977), public-key cryptosystems (Aug 1977), Douglas Hofstadter’s Gödel, Escher, Bach (Jul 1979), and A K Dewdney’s Planiverse (Jul 1980).
  84. 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.
  85. Grosslight, Justin (2013). "Small Skills, Big Networks: Marin Mersenne as Mathematical Intelligencer". History of Science. 51 (3): 337–374. Bibcode:2013HisSc..51..337G. doi:10.1177/007327531305100304. S2CID 143320489.
  86. AMS Notices (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." –Donald Knuth
  87. Berlekamp (2014): Partly because of what I had read about them in Martin Gardner’s columns, I was appropriately awestruck in the 1960s when I first met Sol Golomb and then Richard Guy, each of whom had a large influence on my subsequent work. In 1969 Richard introduced me to John Horton Conway, and the three of us immediately began collaborating on a book that eventually became Winning Ways for Your Mathematical Plays. In the 1970s, I joined Conway in some of his many visits to Gardner’s home on Euclid Avenue, in Hastings-on-Hudson, New York. Gardner soon became an enthusiastic advocate of our book project, and he previewed various snippets of it in his Scientific American columns.
  88. Gardner (2013) page 144: Conway had been making new discoveries about Penrose tiling, and Mandelbrot was interested because Penrose tiling patterns are fractals.
  89. Peterson (2014): Rice sent her discoveries to Gardner, and Gardner’s mathematical grapevine—an extensive network of experts and amateurs with whom Gardner regularly exchanged information and checked out ideas—helped spread the word. Schattschneider was one of those who received news of Rice’s findings and, as time went on, began to correspond directly with Rice to follow her progress and provide advice and pertinent references.
  90. Cole, K. C. (March 11, 1998), "Beating the Pros to the Punch", Los Angeles Times.
  91. Case (2014)
  92. Malkevitch (2014): Gardner drew on a large number of mathematicians over the years for ideas and inspirations for his columns.
  93. AMS Notices (2011)
  94. BBC News (2014): His secret was a fantastic card index system of his own, going back to the 1930s, stored in shoe boxes.
  95. Stanford University Archives: Gardner (Martin) Papers Online Archive of California
  96. Discrete Geometry, Combinatorics and Graph Theory : Revised selected papers; Jin Akiyama, William Y.C. Chen, Mikio Kano
  97. BBC News (2014)
  98. Gardner (2010)
  99. Teller (2014)
  100. The Math Factor Podcast Website John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.
  101. Scott Kim, Puzzle Master: His Scientific American column Mathematical Games, which ran for 25 years, inspired my own career as a puzzle designer.
  102. 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
  103. Peterson (2014)
  104. David A. Klarner, editor (1981), "In Praise of Amateurs" in The Mathematical Gardner, Weber & Schmidt, 1981.
  105. Elwyn Berlekamp Tribute Gathering 4 Gardner on April 17, 2019
  106. Bhargava (2018): Eventually, when I was around 12 years old, through my puzzle explorations I of course also had the good fortune of discovering the works of Martin Gardner. They inspired me a huge amount, and gave me something far more enjoyable to do than go to math class!
  107. There's One Born Every Minute review by Ed Regis, The New York Times, June 4, 2000; "Martin Gardner's 1957 book Fads and Fallacies in the Name of Science is the classic put-down of pseudoscience. Nobody who read it will soon forget its stellar roll call of mid-20th-century cranks and crackpots"
  108. Friedel (2018): This book and his subsequent efforts earned him a wealth of detractors and antagonists in the fields of “fringe science” and New Age philosophy.
  109. Gould (1982): In this climate, beleaguered rationalism needs its skilled debaters—writers who can combine wit, penetrating analysis, sharp prose, and sweet reason into an expansive view that expunges nonsense without stifling innovation, and that presents the excitement and humanity of science in a positive way. ... For more than thirty years, Martin Gardner has played this largely thankless role with tireless efficiency. He is more than a mere individual fighting a set of personal battles; he has become a priceless national resource.
  110. Articles by Martin Gardner: 115 Results Skeptical Inquirer
  111. Prometheus Books The New Age: Notes of a Fringe-Watcher by Martin Gardner
  112. "Linkapedia Visualarts Discover more about Uriah Fuller". linkapedia-visualarts.com.
  113. Oprah Winfrey: Bright (but Gullible) Billionaire Archived 2016-05-01 at the Wayback Machine Skeptical Inquirer, March/April 2010
  114. Skeptical Inquirer Magazine Names the Ten Outstanding Skeptics of the Century
  115. About the IIG Awards Independent Investigations Group
  116. "CSICOP Council in Atlanta: Police Psychics, Local Groups". The Skeptical Inquirer. 7 (3): 13. 1983.
  117. The Pantheon of Skeptics Committee for Skeptical Inquiry
  118. Martin Gardner's Magic Influence Archived 2016-05-21 at the Wayback Machine at martin-gardner.org
  119. 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.
  120. Bellos (2010)
  121. Gathering 4 Gardner (2014)
  122. Demaine (2008) p. 12
  123. Reviews of Martin Gardner's Impromptu Archived 2017-03-21 at the Wayback Machine The Miracle Factory
  124. Demaine (2008): pp. 4-5
  125. Lister (1995)
  126. from Dover Publications: Mathematics, Magic and Mystery Archived 2016-05-06 at the Wayback Machine "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."
  127. The Dover Math and Science Newsletter Archived 2015-05-03 at the Wayback Machine May 16, 2011
  128. "Hall of Fame". The Academy of Magical Arts. Archived from the original on 2016-11-20. Retrieved 2017-12-24.
  129. Carpenter, Alexander (17 October 2008). "Interview: Martin Gardner on Philosophical Theism, Adventists and Price". Spectrum. Archived from the original on July 13, 2016. Retrieved December 21, 2019.
  130. Gardner (2013) p. 191
  131. Groth (1983)
  132. Martin Gardner: 1914-2010: Chris French mourns the passing of Martin Gardner, The Guardian, May 25, 2010
  133. The Whys of a Philosophical Scrivener by Martin Gardner, Quill, 1983, pp. 238–239
  134. "A Mind at Play: An Interview with Martin Gardner" by Kendrick Frazier, Skeptical Inquirer Volume 22.2, March/April 1998
  135. Dirda (2009): With this book Gardner virtually launched the entire mini-genre of annotated classics.
  136. Jan Susina. Conversation with Martin Gardner: Annotator of Wonderland. The Five Owls. Jan./Feb. 2000. 62–64.
  137. Alice Still Lives Here by Michael Sims, Nashville Scene, July 06, 2000
  138. Richards (2018)
  139. Kindley (2015): Just as importantly, though, The Annotated Alice gave rise to a new popular genre.
  140. Richards (2018): The look and feel was entirely due to Martin Gardner.
  141. MacTutor: 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.
  142. 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.
  143. Grooks by Piet Hein Archived 2014-10-10 at the Wayback Machine
  144. Undiluted Hocus-Pocus, Princeton University Press, 2013, ISBN 978-0691159911, Reviewed by Andy Magid
  145. Eckler, A. Ross (2010) "Look Back!" Word Ways: Vol 43: Issue 3, Article 6
  146. Don Albers' interview of Gardner, Part 4: The Trap Door Spiders Archived 2008-11-19 at the Wayback Machine
  147. Top 10 Martin Gardner Alter Egos Archived 2017-03-17 at the Wayback Machine at martin-gardner.org
  148. "Gardner's Whys" in The Night is Large, chapter 40, pp. 481–87.
  149. 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.
  150. Skeptic Martin Gardner Dies Archived 2015-10-02 at the Wayback Machine by Loren Coleman, CryptoZoo News, May 23, 2010
  151. Hersh, Reuben (31 October 1997). "Re: Martin Gardner book review". Foundations of Mathematics mailing list. Retrieved 22 May 2010.
  152. Gardner, Martin (1981). Science, good, bad, and bogus – Martin Gardner – Google Books. ISBN 9780879751449. Retrieved 2012-04-14.
  153. Reviews by and about Martin Gardner The New York Review of Books: 1973 to 1998
  154. Martin Gardner's Awards Archived 2016-03-18 at the Wayback Machine
  155. JPL Small-Body Database Browser Archived 2018-07-06 at the Wayback Machine 2587 Gardner (1980 OH)
  156. The Mathematical Association of America's Trevor Evans Awards Archived 2017-05-16 at the Wayback Machine
  157. Magic magazine, Jun 1999, page 60
  158. MAA MathFest 2019 Invited Addresses
  159. Brick Installation Honors Martin Gardner Archived 2017-06-28 at the Wayback Machine MAA New release
  160. John Conway Reminiscences about Dr. Matrix and Bourbaki by Dana Richards & Collm Mulcahy, Scientific American, October 1, 2014
  161. MAA FOCUS (2010): "His heritage goes beyond essays and books; he left a community of magicians, mathematicians, and wits carrying things forward and delighting in it all."–Peter Renz
  162. Robert P. Crease, Gathering for Gardner Archived 2018-03-28 at the Wayback Machine, The Wall Street Journal, p. W11, 2 April 2010
  163. Crease (2018)
  164. G4G13 Information Archived 2018-05-20 at the Wayback Machine gathering4gardner.org
  165. Gardner's first publication at age 16 was a magic trick in the periodical The Sphinx.

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