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Martin Gardner

Topic: Biography

 From HandWiki - Reading time: 31 min

Short description: American mathematics and science writer (1914–2010)
Martin Gardner
Martin Gardner.jpeg
BornTulsa, Oklahoma, U.S.
DiedMay 22, 2010(2010-05-22) (aged 95)
Norman, Oklahoma, U.S.
OccupationAuthor
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)
Spouse
Charlotte Greenwald (m. 1952)
Children2
Signature

Martin Gardner (October 21, 1914 – May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, 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 in 1999, MAGIC magazine named him as one of the "100 Most Influential 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]

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] is a 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]

He was a frequent contributor to The New York Review of Books.[20]

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,[21] 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.[22][23] His fascination with mathematics started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles, Tricks and Conundrums.[24][25]

He attended the University of Chicago where he studied history, literature and sciences under their intellectually-stimulating Great Books curriculum and earned his bachelor's degree in philosophy in 1936.[7] 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.[26] He attended graduate school for a year there, but he did not earn an advanced degree.[1]

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.[27] His paper-folding puzzles at that magazine led to his first work at Scientific American.[28] 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.[29]

In 1950, he wrote an article in the Antioch Review entitled "The Hermit Scientist".[30] 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. The year 1960 saw the original edition of the best-selling book of his career, The Annotated Alice.[31]

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.[32][33] 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".[29] 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.[34] 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.[35] It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:[36]

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 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.[29]

Gardner's son Jim once asked him what was his favorite puzzle, and Gardner answered almost immediately: "The monkey and the coconuts".[37] 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.[38]

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.[39] Over the next four decades fourteen more books followed.[23] Donald Knuth called them the canonical books.[40][41]

Retirement and death

In 1979, Gardner left Scientific American. He and his wife Charlotte moved to Hendersonville, North Carolina. He 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.[42] Charlotte died in 2000 and in 2004 Gardner returned to Oklahoma,[43] 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.[29]

Influence

His depth and clarity will illuminate our world for a long time.[44]

–Persi Diaconis

Martin Gardner had a major impact on mathematics in the second half of the 20th century.[45][46] His column ran for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981.[47][48] His writing inspired, directly or indirectly, many who would go on to careers in mathematics, science, and other related endeavors.[49][50][51][52][53][54]

Gardner's admirers included such diverse individuals 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.[55][56][33][57] Salvador Dalí once sought him out to discuss four-dimensional hypercubes.[58] 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."[59] Colm Mulcahy described him as "without doubt the best friend mathematics ever had."[60]

Gardner's column has been credited with introducing the public to works and problems that have become mainstays of popular mathematics including the secretary problem, Conway's Game of Life, the Mandelbrot set, Penrose tiles, public-key cryptosystems, and books such as A K Dewdney’s Planiverse and Douglas Hofstadter’s Gödel, Escher, Bach.[61][62][63] Gardner was instrumental in spreading the awareness and understanding of M. C. Escher’s work. Gardner wrote to 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.[60]

His writing was credited as both broad and deep.[64][65][66] 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."[56][67] 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 such as Penrose tiles[68] and Conway's Game of Life,[69] he was equally adept at writing 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.[59][70]

Gardner set a new high standard for writing about mathematics.[71][72][73][74][75] 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] John Horton Conway called him "the most learned man I have ever met."[55]

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.[1]

– AMS Notices

Gardner maintained an extensive network of experts and amateurs with whom he regularly exchanged information and ideas.[76] Doris Schattschneider would later term this circle of collaborators "Gardner's mathematical grapevine" or "MG2".[77][78]

Gardner's role as a hub of this network helped facilitate several introductions that led to further fruitful collaborations.[79] Mathematicians Conway, Berlekamp, and Guy, who met as a result of Gardner's influence, would go on to write Winning Ways for your Mathematical Plays, a foundational book in combinatorial game theory that Gardner championed.[80] Gardner also introduced Conway to Benoit Mandelbrot because he knew of their mutual interest in Penrose tiles.[32][81] Gardner's network was also responsible for introducing Doris Schattschneider and Marjorie Rice, who worked together to document the newly discovered pentagon tilings.[76][82]

Gardner credited his network with generating further material for his columns: "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."[77]

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.[83] Communication was often by postcard or telephone and Gardner kept meticulous notes of everything, typically on index cards.[84] Archives of some of his correspondence stored at Stanford University occupy some 63 linear feet of shelf space.[85] This correspondence led to columns about the rep-tiles and pentominos of Solomon W. Golomb; the space filling curves of Bill Gosper;[86] 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 Piet Hein and 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:[77][87][70][88][89][55][90][52][76]



Public key cryptography

These new ciphers are not absolutely unbreakable in the sense of the one-time pad. but in practice they are unbreakable in a much stronger sense than any cipher previously designed for widespread use. In principle these new ciphers can be broken. but only by computer programs that run for millions of years![91]

–Martin Gardner

In his August 1977 column, "A new kind of cipher that would take millions of years to break", Gardner described a new cryptographic system invented by Ron Rivest, Adi Shamir and Leonard Adleman.[92][93] The system, based on trapdoor functions, was known as RSA (after the three researchers) and has become a component of the majority of secure data transmission schemes.[87] Since RSA is a relatively slow algorithm it is not widely used to directly encrypt data.[94] More often, it is used to transmit shared keys for symmetric-key cryptography.[95]

Gardner identified the memorandum that his column was based on and invited readers to write to Rivest to request a copy of it.[91] Over seven thousand requests came pouring in, some of them from other countries. This caused significant consternation in the US defense agencies and possible legal problems for Gardner himself.[96] The National Security Agency (NSA) asked the RSA team to stop distributing the report and one letter to the IEEE suggested that disseminating such information might be violating the Arms Export Control Act and the International Traffic in Arms Regulations.[91] In the end the defense establishment could provide no legal basis for suppressing the new technology, and when a detailed paper about RSA was published in Communications of the ACM,[97] the NSA’s crypto monopoly was effectively terminated.[95]

Pseudoscience and skepticism

Martin Gardner is the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.[42]

– Stephen Jay Gould

Gardner was a critic of fringe science. His book Fads and Fallacies in the Name of Science (1952, revised 1957) launched the modern skeptical movement.[26] It debunked dubious movements and theories[98] 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.[99] He kept up running dialogues (both public and private) with many of them for decades.[26]

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."[100]

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). Intellectuals including 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.[101] These columns have been collected in five books starting with The New Age: Notes of a Fringe Watcher in 1988.[102]

Gardner was a 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.[103]

Martin Gardner continued to criticize junk science throughout his life. 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.[59] 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.[104]

Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century.[105] In 2010 he was posthumously honored with an award for his contributions in the skeptical field from the Independent Investigations Group.[106] 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",[107] and in 2011 it added Gardner to its Pantheon of Skeptics.[108]

Magic

Card magic, and magic in general, owe a far greater debt to Martin Gardner than most conjurors realize.[109]

–Stephen Minch

Martin Gardner held a lifelong fascination with magic and illusion that began when his father demonstrated a trick to him.[110] 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.[111] Gardner's first published writing (at the age of fifteen) was a magic trick in The Sphinx, the official magazine of the Society of American Magicians.[112] 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."[113][114] His first magic book for the general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field.[112] 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".[115]

Many of Gardner's lifelong friends were magicians.[116] 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.[70] Mathematics and magic were frequently intertwined in Gardner's work.[117] One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks.[111] 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.[118]

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.[119] 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.[112]

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.[120]

– Martin Gardner, 2008

Gardner was raised as a Methodist (his mother was very religious) but rejected established religion as an adult.[22] He considered himself a philosophical theist and a fideist.[120] 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."[121]

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.[122] 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.[123] 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.[124]

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.[122]

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 belonged to "a group of thinkers known as the 'mysterians'."[125] His philosophical views in general are described and defended in his book The Whys of a Philosophical Scrivener (1983, revised 1999).[126]

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.[127] The original book arose when Gardner found the Alice books "sort of frightening" when he was young, but found them fascinating as an adult.[128] 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.[129]

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,[130] and soon many other writers followed his lead.[131][132] 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.[116]

Novels and short stories

Gardner wrote two novels. He was a fan of the Oz books written by L. Frank Baum,[133] 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.[134]

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.[89] He took the title from a poem, a so-called grook, by his good friend Piet Hein,[135] which perfectly expresses Gardner's abiding sense of mystery and wonder about existence.[136]

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.[137] The resulting journal, Word Ways, carried many of his articles—some of them posthumously—until publication ceased in 2020.[138] 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.[139]

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.[140] 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.[126]

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.[141] 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.[140]

Philosophy of mathematics

Gardner wrote on the philosophy of mathematics.[142] 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.[143] 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.[144]

Mathematics education

In the August 1998 edition of Scientific American, Gardner wrote his final piece for Scientific American titled, "A Quarter Century of Recreational Mathematics."[145] In it he said, "For 40 years I have done my best to convince educators that recreational math should be incorporated into the standard curriculum. It should be regularly introduced as a way to interest young students in the wonders of mathematics. So far, though, movement in this direction has been glacial." He recalls how as a young boy a math teacher had scolded him for working on a bit of recreation mathematics and laments at how wrongheaded this attitude is. He notes that the magazine Mathematics Teacher published by the National Council of Teachers of Mathematics, and specially dedicated to improving mathematics instruction for grades 8–14,[146] often has articles on recreational topics but that most teachers do not use them.[88]

Legacy and awards

The numerous awards Gardner received include:[147]

  • 1987 – Leroy P. Steele Prize for his many books and articles on mathematics
  • 1971 – L. Frank Baum Memorial Award from the International Wizard of Oz Club
  • 1980 – The main-belt asteroid 2587 Gardner discovered by Edward L. G. Bowell at Anderson Mesa Station is named after Martin Gardner.[148]
  • 1990 – Allendoerfer Award (along with Fan Chung & Ronald Graham) from The Mathematical Association of America (MAA)
  • 1994 – JPBM Communications Award from the Joint Policy Board for Mathematics
  • 1997 – became a Fellow (Class: Humanities and Arts, Section: Literature) of the American Academy of Arts and Sciences.
  • 1998 – Trevor Evans Award from the MAA[149]
  • 1999 – listed in the "100 Most Influential Magicians of the Twentieth Century" by Magic magazine.[150]
  • 2011 – Houdini Hall of Honor award (posthumous) from the Independent Investigations Group

The Mathematical Association 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.[151] The 2021 lecture Surprising discoveries of three amateur mathematicians: M.C. Escher, Marjorie Rice, and Rinus Roelofs was virtual and was given by Doris Schattschneider.[152]

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.[153] Gardner has an Erdös number of 1.[154]

Gathering 4 Gardner

Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations.[42] Moreover, his influence was so broad that many of his fans had little or no contact with each other.[155] 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.[55] 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.[156]

A second such get-together was held in 1996, again with Gardner in attendance. A video was made for the CBC Television program The Nature of Things with David Suzuki.[157] It featured Gardner along with many members of his circle and was called "Martin Gardner: Mathemagician" and broadcast on March 14, 1996. At this point Rogers and his friends decided 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, mathematical video maker Vi Hart, and Fields Medalist Manjul Bhargava.[42][158]

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.[159] The 2018 event was G4G13.[160]

Bibliography

In a publishing career spanning 80 years (1930–2010),[161] Gardner authored or edited over 100 books and countless articles, columns and reviews. A comprehensive bibliography of his works was published in 2023 by Dana Richards, with a foreword by Donald Knuth.[162]

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).

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 AMS Notices (2004)
  2. ↑ "MAA Writing Awards Presented". Notices of the AMS 47 (10): 1282. November 2000. https://www.ams.org/notices/200010/people.pdf. 
  3. ↑ Gardner, Martin (January 1999). "The Asymmetric Propeller". The College Mathematics Journal 30 (1): 18–22. doi:10.2307/2687198. https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020785.02p0455x.pdf. 
  4. ↑ 4.0 4.1 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. ↑ 7.0 7.1 Martin Gardner obituary Telegraph Media Group (2010)
  8. ↑ 8.0 8.1 Top 10 Martin Gardner Books , by Colm Mulcahy, Huffington Post Books, October 28, 2014
  9. ↑ Costello (1988): p. 114.
  10. ↑ England (2014): Even apart from mathematics and puzzles, Gardner'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". Gathering 4 Gardner. 2014. http://martin-gardner.org/MATHEMATICIAN.html. 
  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. https://archive.org/details/borderlandsofsci00mic_hoo. 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." 
  19. ↑ "About CSI". http://www.csicop.org/about/about_csi. 
  20. ↑ Reviews by and about Martin Gardner The New York Review of Books: 1973 to 1998
  21. ↑ James Gardner later became the 8th President of the American Association of Petroleum Geologists.
  22. ↑ 22.0 22.1 Martin Gardner Famous Scientists
  23. ↑ 23.0 23.1 England (2014)
  24. ↑ Suzuki (1996) at 17:20
  25. ↑ MacTutor
  26. ↑ 26.0 26.1 26.2 Shermer (1997)
  27. ↑ Yam, Philip (December 1995) Profile: Martin Gardner, the Mathematical Gamester (1914–2010) Scientific American
  28. ↑ 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. https://books.google.com/books?id=9GvNAjykUqQC&pg=PA3. 
  29. ↑ 29.0 29.1 29.2 29.3 Gardner, Martin (2013)
  30. ↑ Gardner, Martin, "The Hermit Scientist", Antioch Review, Winter 1950–1951, pp. 447–457.
  31. ↑ Burstein (2011)
  32. ↑ 32.0 32.1 Mulcahy (2014)
  33. ↑ 33.0 33.1 The Economist (2010)
  34. ↑ 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.
  35. ↑ Demaine (2008): p. 24
  36. ↑ 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.
  37. ↑ Antonick, Gary (2013). Martin Gardner’s The Monkey and the Coconuts in Numberplay The New York Times:, October 7, 2013
  38. ↑ Gardner, Martin The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001), W.W. Norton & Company; ISBN:0-393-02023-1
  39. ↑ Martin Gardner: Mathematical Games Collections by David Langford
  40. ↑ The New Martin Gardner Mathematical Library Cambridge University Press
  41. ↑ The Canon: The fifteen "Mathematical Games" books at martin-gardner.org
  42. ↑ 42.0 42.1 42.2 42.3 Richards (2014)
  43. ↑ Albers (2008)
  44. ↑ Princeton University Press: Reviews of Undiluted Hocus-Pocus
  45. ↑ 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
  46. ↑ 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.
  47. ↑ Mulcahy (2014): It's been said that he had a million readers there at his peak.
  48. ↑ Malkevitch (2014): Martin Gardner's columns and books have been referenced by huge numbers of research papers that involve mathematics.
  49. ↑ 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.
  50. ↑ 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.
  51. ↑ Antonick (2014): Martin Gardner was well known for inspiring generations of students to become professional mathematicians.
  52. ↑ 52.0 52.1 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
  53. ↑ Demaine (2008) p. ix: Many of today's mathematicians entered this field through Gardner's influence.
  54. ↑ Crease (2018): "As a columnist for Scientific American, Gardner inspired generations of physicists, mathematicians, philosophers, puzzle-makers, logicians, magicians and others, including me."
  55. ↑ 55.0 55.1 55.2 55.3 Mulcahy (2013)
  56. ↑ 56.0 56.1 Brown (2010)
  57. ↑ Dirda (2009)
  58. ↑ 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).
  59. ↑ 59.0 59.1 59.2 Auerbach (2013)
  60. ↑ 60.0 60.1 Mulcahy (2017)
  61. ↑ 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
  62. ↑ 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.
  63. ↑ 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.
  64. ↑ 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.
  65. ↑ 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.
  66. ↑ 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.
  67. ↑ MacTutor: Gardner has produced a number of mathematical papers, written with leading mathematicians.
  68. ↑ 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.
  69. ↑ 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
  70. ↑ 70.0 70.1 70.2 Hofstadter (2010)
  71. ↑ AMS Notices (2004): "His crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization." —Allyn Jackson.
  72. ↑ 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.
  73. ↑ Mirsky (2010): "His writing has been valued by generations of professional mathematicians."–Ian Stewart
  74. ↑ Teller (2014): "Gardner writes with authority and ease. You trust him to take you wherever he feels like going."
  75. ↑ Hofstadter (2010): Martin had a magical touch in writing about math.
  76. ↑ 76.0 76.1 76.2 Peterson (2014)
  77. ↑ 77.0 77.1 77.2 Case (2014)
  78. ↑ David A. Klarner, editor (1981), "In Praise of Amateurs" in The Mathematical Gardner, Weber & Schmidt, 1981.
  79. ↑ Propp (2015): "Before there were search engines, the intellectual world relied on human hubs to serve as repositories of knowledge and connectors of people with common interests who otherwise would not have known one another. Martin Gardner was such a connector. His column was the best mathematical watering hole of its day, and behind the scenes he served as a tireless mathematical match-maker. Gardner was a hub par excellence."
  80. ↑ 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.
  81. ↑ Gardner (2013) page 144: Conway had been making new discoveries about Penrose tiling, and Mandelbrot was interested because Penrose tiling patterns are fractals.
  82. ↑ Cole, K. C. (March 11, 1998), "Beating the Pros to the Punch", Los Angeles Times, http://articles.latimes.com/1998/mar/11/news/mn-27706 .
  83. ↑ AMS Notices (2011)
  84. ↑ BBC News (2014): His secret was a fantastic card index system of his own, going back to the 1930s, stored in shoe boxes.
  85. ↑ Stanford University Archives: Gardner (Martin) Papers Online Archive of California
  86. ↑ Discrete Geometry, Combinatorics and Graph Theory : Revised selected papers; Jin Akiyama, William Y.C. Chen, Mikio Kano
  87. ↑ 87.0 87.1 BBC News (2014)
  88. ↑ 88.0 88.1 Gardner (1998)
  89. ↑ 89.0 89.1 Teller (2014)
  90. ↑ The Math Factor Podcast Website John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.
  91. ↑ 91.0 91.1 91.2 The Tensions Around The RSA Method by Bill Buchanan, medium.com, Jan 9, 2022
  92. ↑ Robinson, Sara (June 2003). "Still Guarding Secrets after Years of Attacks, RSA Earns Accolades for its Founders". SIAM News 36 (5). http://www.msri.org/people/members/sara/articles/rsa.pdf. 
  93. ↑ Public Key Cryptography History Living Internet
  94. ↑ RSA Cryptography: History And Uses Telsy Communications
  95. ↑ 95.0 95.1 "The Day Cryptography Changed Forever" by Steven Ellis, medium.com, Jan 6, 2020
  96. ↑ BBC News (2014): "He also broke the story of the invention of RSA cryptography — the now standard way in which confidential data such as passwords, bank information, and the like, are secured in digital transmission—getting into trouble with the US government in the process."
  97. ↑ R. L. Rivest, A. Shamir, L. Adleman "A method for obtaining digital signatures and public-key cryptosystems" Communications of the ACM, Vol. 21, No. 2, Feb. 1978.
  98. ↑ 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"
  99. ↑ 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.
  100. ↑ 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.
  101. ↑ Articles by Martin Gardner: 115 Results Skeptical Inquirer
  102. ↑ Prometheus Books The New Age: Notes of a Fringe-Watcher by Martin Gardner
  103. ↑ Confessions of a psychic : the secret notebooks of Uriah Fuller University Of Wisconsin–Madison Library
  104. ↑ Oprah Winfrey: Bright (but Gullible) Billionaire Skeptical Inquirer, March/April 2010
  105. ↑ Skeptical Inquirer Magazine Names the Ten Outstanding Skeptics of the Century
  106. ↑ About the IIG Awards Independent Investigations Group
  107. ↑ "CSICOP Council in Atlanta: Police Psychics, Local Groups". The Skeptical Inquirer 7 (3): 13. 1983. 
  108. ↑ The Pantheon of Skeptics Committee for Skeptical Inquiry
  109. ↑ Martin Gardner's Magic Influence at martin-gardner.org
  110. ↑ 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.
  111. ↑ 111.0 111.1 Bellos (2010)
  112. ↑ 112.0 112.1 112.2 Gathering 4 Gardner (2014)
  113. ↑ Demaine (2008) p. 12
  114. ↑ Reviews of Martin Gardner's Impromptu The Miracle Factory
  115. ↑ Demaine (2008): pp. 4–5
  116. ↑ 116.0 116.1 Lister (1995)
  117. ↑ 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."
  118. ↑ The Dover Math and Science Newsletter May 16, 2011
  119. ↑ "Hall of Fame". http://www.magiccastle.com/hall_of_fame/. 
  120. ↑ 120.0 120.1 Carpenter, Alexander (17 October 2008). "Interview: Martin Gardner on Philosophical Theism, Adventists and Price". http://www.spectrummagazine.org/node/1091. 
  121. ↑ Gardner (2013) p. 191
  122. ↑ 122.0 122.1 Groth (1983)
  123. ↑ Martin Gardner: 1914–2010: Chris French mourns the passing of Martin Gardner, The Guardian , May 25, 2010
  124. ↑ The Whys of a Philosophical Scrivener by Martin Gardner, Quill, 1983, pp. 238–239
  125. ↑ "A Mind at Play: An Interview with Martin Gardner" by Kendrick Frazier, Skeptical Inquirer Volume 22.2, March/April 1998
  126. ↑ 126.0 126.1 "Gardner's Whys" in The Night is Large, chapter 40, pp. 481–87.
  127. ↑ Dirda (2009): With this book Gardner virtually launched the entire mini-genre of annotated classics.
  128. ↑ Jan Susina. Conversation with Martin Gardner: Annotator of Wonderland. The Five Owls. Jan./Feb. 2000. 62–64.
  129. ↑ Alice Still Lives Here[yes|permanent dead link|dead link}}] by Michael Sims, Nashville Scene, July 06, 2000
  130. ↑ Richards (2018)
  131. ↑ Kindley (2015): Just as importantly, though, The Annotated Alice gave rise to a new popular genre.
  132. ↑ Richards (2018): The look and feel was entirely due to Martin Gardner.
  133. ↑ 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.
  134. ↑ 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.
  135. ↑ Grooks by Piet Hein
  136. ↑ Undiluted Hocus-Pocus, Princeton University Press, 2013, ISBN:978-0691159911, Reviewed by Andy Magid
  137. ↑ Eckler, A. Ross (2010) "Look Back!" Word Ways: Vol 43: Issue 3, Article 6
  138. ↑ Farrell, Jeremiah (November 2020). "More Word Ways?". Word Ways 53 (3): 4. https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=5950&context=wordways. Retrieved 19 September 2020. 
  139. ↑ Don Albers' interview of Gardner, Part 4: The Trap Door Spiders
  140. ↑ 140.0 140.1 Top 10 Martin Gardner Alter Egos at martin-gardner.org
  141. ↑ 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.
  142. ↑ Skeptic Martin Gardner Dies by Loren Coleman, CryptoZoo News, May 23, 2010
  143. ↑ Is Mathematics for Real? by Martin Gardner, The New York Review, Aug 13, 1981
  144. ↑ Hersh, Reuben (31 October 1997). "Re: Martin Gardner book review". Foundations of Mathematics mailing list. http://www.cs.nyu.edu/pipermail/fom/1997-November/000128.html. 
  145. ↑ A Quarter Century of Recreational Mathematics, by Martin Gardner Scientific American blog on May 29, 2010
  146. ↑ Mathematics Teacher website National Council of Mathematics Teachers
  147. ↑ Martin Gardner's Awards
  148. ↑ JPL Small-Body Database Browser 2587 Gardner (1980 OH)
  149. ↑ The Mathematical Association of America's Trevor Evans Awards
  150. ↑ Magic magazine, Jun 1999, page 60
  151. ↑ MAA MathFest 2019 Invited Addresses
  152. ↑ Doris Schattschneider MAA: 2021 Martin Gardner Lecturer
  153. ↑ Brick Installation Honors Martin Gardner MAA New release
  154. ↑ John Conway Reminiscences about Dr. Matrix and Bourbaki by Dana Richards & Collm Mulcahy, Scientific American, October 1, 2014
  155. ↑ 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
  156. ↑ Robert P. Crease, Gathering for Gardner , The Wall Street Journal , p. W11, 2 April 2010
  157. ↑ Suzuki (1996)
  158. ↑ Gathering 4 Gardner's G4G13 Presents "Poetry, Drumming, and Mathematics" with Professor Manjul Bhargava The Atlanta Journal-Constitution, April 15, 2018
  159. ↑ Crease (2018)
  160. ↑ G4G13 Information gathering4gardner.org
  161. ↑ Gardner's first publication at age 16 was a magic trick in the periodical The Sphinx.
  162. ↑ The Bibliography of Martin Gardner Dana Richards (editor), Donald E. Knuth (foreword), June, 2023, Pub: Stanford Center for the Study of Language and Information, ISBN:1684000327

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