Martin Gardner (October 21, 1914 – May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He is recognized as a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century. He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
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. These appeared for twenty-five years in Scientific American, and his subsequent books collecting them.
Gardner was one of the foremost anti-pseudoscience polemicists of the 20th century. His 1957 book Fads and Fallacies in the Name of Science became a classic and seminal work of the skeptical movement. In 1976 he joined with fellow skeptics to found CSICOP, an organization promoting scientific inquiry and the use of reason in examining extraordinary claims.
|Born||October 21, 1914|
Tulsa, Oklahoma, U.S.
|Died||May 22, 2010 (aged 95)|
Norman, Oklahoma, U.S.
|Alma mater||University of Chicago|
|Genre||Recreational mathematics, puzzles, close-up magic, annotated literary works, debunking|
|Literary movement||Scientific skepticism|
|Notable works||Fads and Fallacies in the Name of Science;|
Mathematical Games (Scientific American column);
The Annotated Alice;
The Whys of a Philosophical Scrivener;
The Ambidextrous Universe
|Notable awards||Leroy P. Steele Prize for Mathematical Exposition (1987)|
George Pólya Award (1999)
Gardner, son of a petroleum geologist father and an educator and artist mother, grew up in and around Tulsa, Oklahoma. His lifelong interest in puzzles started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles, Tricks and Conundrums. He attended the University of Chicago, where he earned his bachelor's degree in philosophy in 1936. Early jobs included reporter on the Tulsa Tribune, writer at the University of Chicago Office of Press Relations, and case worker in Chicago's Black Belt for the city's Relief Administration. During World War II, he served for four years in the U.S. Navy as a yeoman on board the destroyer escort USS Pope in the Atlantic. His ship was still in the Atlantic when the war came to an end with the surrender of Japan in August 1945.
In 1950 he wrote an article in the Antioch Review entitled "The Hermit Scientist". It was one of Gardner's earliest articles about junk science, and in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present.
In the late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine where for eight years he wrote features and stories for it and several other children's magazines. His paper-folding puzzles at that magazine led to his first work at Scientific American. For many decades, Gardner, his wife Charlotte, and their two sons, Jim and Tom, lived in Hastings-on-Hudson, New York, where he earned his living as a freelance author, publishing books with several different publishers, and also publishing hundreds of magazine and newspaper articles. Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue. The year 1960 saw the original edition of his best-selling book ever, The Annotated Alice. With this book Gardner virtually launched the entire mini-genre of "annotated" classics.
In 1979, Gardner retired from Scientific American and he and his wife Charlotte moved to Hendersonville, North Carolina. Gardner never really retired as an author, but continued to write math articles, sending them to The Mathematical Intelligencer, Math Horizons, The College Mathematics Journal, and Scientific American. He also revised some of his older books such as Origami, Eleusis, and the Soma Cube. Charlotte died in 2000 and two years later Gardner returned to Norman, Oklahoma, where his son, James Gardner, was a professor of education at the University of Oklahoma. He died there on May 22, 2010. An autobiography — Undiluted Hocus-Pocus: The Autobiography of Martin Gardner — was published posthumously.
Martin Gardner had a major impact on mathematics in the second half of the 20th century. His column was called "Mathematical Games" but it was much more than that. His writing introduced many readers to real mathematics for the first time in their lives. The column lasted for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981. It was the original inspiration for many of them to become mathematicians or scientists themselves.
David Auerbach wrote:
A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century. His popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to the advent of the personal computer.
Among the wide array of mathematicians, physicists, computer scientists, philosophers, magicians, artists, writers, and other influential thinkers who inspired and were in turn inspired by Gardner are John Horton Conway, Bill Gosper, Ron Rivest, Richard K. Guy, Piet Hein, Ronald Graham, Donald Knuth, Robert Nozick, Lee Sallows, Scott Kim, M. C. Escher, Douglas Hofstadter, Roger Penrose, Ian Stewart, David A. Klarner, Benoit Mandelbrot, Elwyn R. Berlekamp, Solomon W. Golomb, Raymond Smullyan, James Randi, Persi Diaconis, Penn & Teller, and Ray Hyman.
His admirers included such diverse people as W. H. Auden, Arthur C. Clarke, Carl Sagan, Isaac Asimov, Richard Dawkins, Stephen Jay Gould, and the entire French literary group known as the Oulipo. Salvador Dali once sought him out to discuss four-dimensional hypercubes. 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. His writing was both broad and deep. Noam Chomsky once wrote, "Martin Gardner's contribution to contemporary intellectual culture is unique—in its range, its insight, and understanding of hard questions that matter." Gardner repeatedly alerted the public (and other mathematicians) to recent discoveries in mathematics–recreational and otherwise. In addition to introducing many first-rate puzzles and topics such as Penrose tiles and Conway's Game of Life, he was equally adept at writing captivating columns about traditional mathematical topics such as knot theory, Fibonacci numbers, Pascal's triangle, the Möbius strip, transfinite numbers, four-dimensional space, Zeno's paradoxes, Fermat's last theorem, and the four-color problem.
Martin Gardner set a new high standard for writing about mathematics. In a 2004 interview he said, "I go up to calculus, and beyond that I don't understand any of the papers that are being written. I consider that that was an advantage for the type of column I was doing because I had to understand what I was writing about, and that enabled me to write in such a way that an average reader could understand what I was saying. If you are writing popularly about math, I think it's good not to know too much math." And he was fearsomely bright. John Horton Conway called him "the most learned man I have ever met." Colm Mulcahy said, "Gardner was without doubt the best friend mathematics ever had." Many people would agree with him.
For over a quarter century Gardner wrote a monthly column on the subject of recreational mathematics for Scientific American. It all began with his free-standing article on hexaflexagons which ran in the December 1956 issue. Flexagons became a bit of a fad and soon people all over New York City were making them. Gerry Piel, the SA publisher at the time, asked Gardner, "Is there enough similar material to this to make a regular feature?" Gardner said he thought so. The January 1957 issue contained his first column, entitled "Mathematical Games". Almost 300 more columns were to follow.
The "Mathematical Games" column became the most popular feature of the magazine and was the first thing that many readers turned to. In September 1977 Scientific American acknowledged the prestige and popularity of Gardner's column by moving it from the back to the very front of the magazine. It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:
Ironically, Gardner had problems learning calculus and never took a mathematics course after high school. While editing Humpty Dumpty's Magazine he constructed many paper folding puzzles, and this led to his interest in the flexagons invented by British mathematician Arthur H Stone. The subsequent article he wrote on hexaflexagons led directly to the column.
Gardner's son Jim once asked him what was his favorite puzzle, and Gardner answered almost immediately: "The monkey and the coconuts". 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.
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. Over the next four decades fourteen more books followed. Donald Knuth called them the canonical books.
Gardner was an uncompromising critic of fringe science. His book Fads and Fallacies in the Name of Science (1952, revised 1957) debunked dubious movements and theories 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.) earned him a wealth of antagonists in fringe science and New Age philosophy; he kept up running dialogues (both public and private) with many of them for decades.
In 1976 Gardner joined with fellow skeptics philosopher Paul Kurtz, psychologist Ray Hyman, sociologist Marcello Truzzi, and stage magician James Randi to found the Committee for the Scientific Investigation of Claims of the Paranormal (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. These columns have been collected in five books starting with The New Age: Notes of a Fringe Watcher in 1988.
Gardner was a relentless critic of self-proclaimed Israeli psychic Uri Geller and wrote two satirical booklets about him in the 1970s using the pen name "Uriah Fuller" in which he explained how such purported psychics do their seemingly impossible feats such as mentally bending spoons and reading minds.
Martin Gardner continued to criticize pseudoscience throughout his life. His targets included astrology, UFO sightings, chiropractic, vegetarianism, Madame Blavatsky, creationism, Scientology, the Laffer curve, Christian Science, and the Hutchins-Adler Great Books Movement. The last thing he wrote in the spring of 2010 (a month before his death) was an article excoriating the "dubious medical opinions and bogus science" of Oprah Winfrey—particularly her support for the thoroughly discredited theory that vaccinations cause autism; it went on to bemoan the "needless deaths of children" that such notions are likely to cause.
Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century. In 2010 he was posthumously honored with an award for his contributions in the skeptical field from the Independent Investigations Group. 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", and in 2011 it added Gardner to its Pantheon of Skeptics.
Martin Gardner's father once showed him a magic trick when he was a little boy. Young Martin was fascinated to see physical laws seemingly violated and this led to a lifelong passion for magic and illusion. He wrote for a magic magazine in high school and worked in a department store demonstrating magic tricks while he was at the University of Chicago. The very first thing that Martin Gardner ever published (at the age of fifteen) was a magic trick in The Sphinx, the official magazine of the Society of American Magicians. He focused mainly on micromagic (table or close-up magic) and, from the 1930s on, published a significant number of original contributions to this secretive field. Magician Joe M. Turner said, The Encyclopedia of Impromptu Magic, which Gardner wrote in 1985, "is guaranteed to show up in any poll of magicians' favorite magic books." His first magic book for the general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field. He was well known for his innovative tapping and spelling effects, with and without playing cards, and was most proud of the effect he called the "Wink Change".
Many of Gardner's lifelong friends were magicians. These included William Simon who introduced Gardner to Charlotte Greenwald, whom he married in 1952, fellow CSICOP founder and pseudoscience fighter James Randi, Dai Vernon, Jerry Andrus, statistician Persi Diaconis, and polymath Raymond Smullyan. Diaconis and Smullyan like Gardner straddled the two worlds of mathematics and magic. Mathematics and magic were frequently intertwined in Gardner's work. One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks. Mathematical magic tricks were often featured in his "Mathematical Games" column–for example, his August 1962 column was titled "A variety of diverting tricks collected at a fictitious convention of magicians." From 1998 to 2002 he wrote a monthly column on magic tricks called "Trick of the Month" in The Physics Teacher, a journal published by the American Association of Physics Teachers.
In 1999 Magic magazine named Gardner one of the "100 Most Influential Magicians of the Twentieth Century". In 2005 he received a 'Lifetime Achievement Fellowship' from the Academy of Magical Arts. 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.
Gardner believed in a personal God, in an afterlife, and in prayer, but rejected established religion. He considered himself a philosophical theist and a fideist. He had an abiding fascination with religious belief but was critical of organized religion. In his autobiography, he stated: "When many of my fans discovered that I believed in God and even hoped for an afterlife, they were shocked and dismayed ... I do not mean the God of the Bible, especially the God of the Old Testament, or any other book that claims to be divinely inspired. For me God is a "Wholly Other" transcendent intelligence, impossible for us to understand. He or she is somehow responsible for our universe and capable of providing, how I have no inkling, an afterlife."
Gardner described his own belief as philosophical theism inspired by the works of philosopher Miguel de Unamuno. While eschewing systematic religious doctrine, he retained a belief in God, asserting that this belief cannot be confirmed or disconfirmed by reason or science. At the same time, he was skeptical of claims that any god has communicated with human beings through spoken or telepathic revelation or through miracles in the natural world. Gardner has been quoted as saying that he regarded parapsychology and other research into the paranormal as tantamount to "tempting God" and seeking "signs and wonders". He stated that while he would expect tests on the efficacy of prayers to be negative, he would not rule out a priori the possibility that as yet unknown paranormal forces may allow prayers to influence the physical world.
Gardner wrote repeatedly about what public figures such as Robert Maynard Hutchins, Mortimer Adler, and William F. Buckley, Jr. believed and whether their beliefs were logically consistent. In some cases, he attacked prominent religious figures such as Mary Baker Eddy on the grounds that their claims are unsupportable. His semi-autobiographical novel The Flight of Peter Fromm depicts a traditionally Protestant Christian man struggling with his faith, examining 20th century scholarship and intellectual movements and ultimately rejecting Christianity while remaining a theist.
Gardner said that he suspected that the fundamental nature of human consciousness may not be knowable or discoverable, unless perhaps a physics more profound than ("underlying") quantum mechanics is some day developed. In this regard, he said, he was an adherent of the "New Mysterianism".
Gardner was considered a leading authority on Lewis Carroll. His annotated version of Alice's Adventures in Wonderland and Through the Looking Glass, explaining the many mathematical riddles, wordplay, and literary references found in the Alice books, was first published as The Annotated Alice (Clarkson Potter, 1960). Sequels were published with new annotations as More Annotated Alice (Random House, 1990), and finally as The Annotated Alice: The Definitive Edition (Norton, 1999), combining notes from the earlier editions and new material. The original book arose when Gardner found the Alice books "sort of frightening" when he was young, but found them fascinating as an adult. He felt that someone ought to annotate them, and suggested to a publisher that Bertrand Russell be asked; when the publisher was unable to get past Russell's secretary, Gardner was asked to take on the project himself.
In addition to the "Alice" books, Gardner produced annotated editions of G. K. Chesterton's The Innocence Of Father Brown and The Man Who Was Thursday, as well as of celebrated poems including The Rime of the Ancient Mariner, Casey at the Bat, The Night Before Christmas, and The Hunting of the Snark; the last was also written by Lewis Carroll.
Gardner wrote two novels. He was a perennial fan of the Oz books written by L. Frank Baum, and in 1988 he published Visitors from Oz, based on the characters in Baum's various Oz books. Gardner was a founding member of the International Wizard of Oz Club, and winner of its 1971 L. Frank Baum Memorial Award. His other novel was The Flight of Peter Fromm (1973), which reflected his lifelong fascination with religious belief and the problem of faith.
His short stories were collected in The No-Sided Professor and Other Tales of Fantasy, Humor, Mystery, and Philosophy (1987).
At the age of 95 Gardner wrote Undiluted Hocus-Pocus: The Autobiography of Martin Gardner. He was living in a one-room apartment in Norman, Oklahoma and, as was his custom, wrote it on a typewriter and edited it using scissors and rubber cement. He took the title from a grook by his good friend Piet Hein, a grook which perfectly expresses Gardner's abiding sense of mystery and wonder about existence.
We glibly talk
of nature's laws
but do things have
a natural cause?
Black earth turned into
Gardner's interest in wordplay led him to conceive of a magazine on recreational linguistics. In 1967 he pitched the idea to Greenwood Periodicals and nominated Dmitri Borgmann as editor. The resulting journal, Word Ways, carried many 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.
Gardner often used pen names. In 1952, while working for the children's magazine Humpty Dumpty, he contributed stories written by "Humpty Dumpty Jnr". For several years starting in 1953 he was a managing editor of Polly Pigtails, a magazine for young girls, and also wrote under that name. His Annotated Casey at the Bat (1967) included a parody of the poem, attributed to "Nitram Rendrag" (his name spelled backwards). Using the pen name "Uriah Fuller", he wrote two books attacking the alleged psychic Uri Geller. In later years, Gardner often wrote parodies of his favorite poems under the name "Armand T. Ringer", an anagram of his name. In 1983 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.
In his January 1960 Mathematical Games column, Gardner introduced the fictitious "Dr. Matrix" and wrote about him often over the next two decades. Dr. Matrix was not exactly a pen name, although Gardner did pretend that everything in these columns came from the fertile mind of the good doctor. Then in 1979 Dr. Matrix himself published an article in the quite respectable Two-Year College Mathematics Journal. It was called Martin Gardner: Defending the Honor of the Human Mind and contained a biography of Gardner and a history of his Mathematical Games column.
Gardner was known for his sometimes controversial philosophy of mathematics. He wrote negative reviews of The Mathematical Experience by Philip J. Davis and Reuben Hersh and What Is Mathematics, Really? by Hersh, both of which were critical of aspects of mathematical Platonism, and the first of which was well received by the mathematical community. While Gardner was often perceived as a hard-core Platonist, his reviews demonstrated some formalist tendencies. Gardner maintained that his views are widespread among mathematicians, but Hersh has countered that in his experience as a professional mathematician and speaker, this is not the case.
Over the years Gardner held forth on many contemporary issues, arguing for his points of view in 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). He was a frequent contributor to The New York Review of Books. His philosophical views are described and defended in his book The Whys of a Philosophical Scrivener (1983, revised 1999).
The numerous awards Gardner received include:
In 1997, Martin Gardner became a Fellow (Class: Humanities and Arts, Section: Literature) of the American Academy of Arts and Sciences.
Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations. Moreover, his influence was so broad that many of his fans had little or no contact with each other. This led Atlanta entrepreneur and puzzle collector Tom Rodgers to the idea of hosting a weekend gathering celebrating Gardner's contributions to recreational mathematics, rationality, magic, puzzles, literature, and philosophy. Although Gardner was famously shy, and would usually decline an honor if it required him to make a personal appearance, Rogers persuaded him to attend the first such "Gathering 4 Gardner" (G4G), held in Atlanta in January 1993.
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 Conway, Elwyn Berlekamp, Ronald Graham, Donald Coxeter, and Richard Guy, to newcomers like mathematician and mathematical artist Erik Demaine and mathematical video maker Vi Hart.
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. The 2018 event was G4G13.
Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson. The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters explaining functions, limits, and derivatives; an appendix of recreational calculus problems; and notes for modern readers. Gardner changes "fifth form boys" to the more American sounding (and gender neutral) "high school students," updates many now obsolescent mathematical notations or terms, and uses American decimal dollars and cents in currency examples.
Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern non-standard analysis and smooth infinitesimal analysis.
The original text is now in the public domain under US copyright law (although Macmillan's copyright under UK law is reproduced in the 2008 edition from St. Martin's Press). It can be freely accessed on Project Gutenberg.Fads and Fallacies in the Name of Science
Fads and Fallacies in the Name of Science (1957)—originally published in 1952 as In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present—was Martin Gardner's second book. A survey of what it described as pseudosciences and cult beliefs, it became a founding document in the nascent scientific skepticism movement. Michael Shermer said of it: "Modern skepticism has developed into a science-based movement, beginning with Martin Gardner's 1952 classic".The book debunks what it characterises as pseudo-science and the pseudo-scientists who propagate it.Gathering 4 Gardner
Gathering 4 Gardner (G4G) is an educational foundation and non-profit corporation (Gathering 4 Gardner, Inc.) devoted to preserving the legacy and spirit of prolific writer Martin Gardner. G4G organizes conferences where people who have been inspired by or have a strong personal connection to Martin Gardner can meet and celebrate his influence. These events explore ideas and developments in recreational mathematics, magic, illusion, puzzles, philosophy, and rationality, and foster creative work in all of these areas by enthusiasts of all ages. G4G also facilitates a related series of events called Celebration of Mind (CoM).Graham's number
Graham's number is an immense number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is named after mathematician Ronald Graham, who used the number as a simplified explanation of the upper bounds of the problem he was working on in conversations with popular science writer Martin Gardner. Gardner later described the number in Scientific American in 1977, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was published in the 1980 Guinness Book of World Records, adding to its popular interest. Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem. Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid.
Graham's number is much larger than many other large numbers such as Skewes' number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot even be expressed in this way by power towers of the form .
However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Graham. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers. Though too large to be computed in full, the sequence of digits of Graham's number can be computed explicitly through simple algorithms. The last 12 digits are ...262464195387. With Knuth's up-arrow notation, Graham's number is , whereIrving Joshua Matrix
Irving Joshua Matrix — born (Japan, 1908) as Irving Joshua Bush and commonly known as Dr. (I. J.) Matrix — was a fictitious polymath scientist, scholar, cowboy, and entrepreneur who made extraordinary contributions to perpetual motion engineering, Biblical cryptography and numerology, pyramid power, pentagonal meditation, extra-sensory perception, psychic metallurgy, and a number of other topics. He was an accomplished prestidigitator and an intuitive mathematician, two qualities which he put to good use in most of his enterprises. Being a fictitious character he could perform tasks that were logically impossible; for example, he could "clap one hand in the air" when summoning a waiter or a minion.Dr. Matrix was the satirical creation of Scientific American columnist Martin Gardner (1914–2010) who introduced him in his "Mathematical Games" column in January 1960. The mythical doctor appeared frequently thereafter and the relevant columns were eventually collected into a book. The intent was partly to provide colorful context to mathematical puzzles and curiosities, partly to spoof various pseudo-scientific theories, and always to provide a humorous introduction to the serious topic at hand.John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway is currently Professor Emeritus of Mathematics at Princeton University in New Jersey.Lincoln–Kennedy coincidences urban legend
Claimed coincidences connecting U.S. Presidents Abraham Lincoln and John F. Kennedy are a piece of American folklore of unknown origin. The list of coincidences appeared in the mainstream American press in 1964, a year after the assassination of John F. Kennedy, having appeared prior to that in the G.O.P. Congressional Committee Newsletter. Martin Gardner examined the list in an article in Scientific American, later reprinted in his book, The Magic Numbers of Dr. Matrix. Gardner's version of the list contained 16 items; many subsequent versions have circulated much longer lists. The list is still in circulation today, having endured in the popular imagination for over 50 years. In 1992, the Skeptical Inquirer ran a "Spooky Presidential Coincidences Contest." One winner found a series of sixteen similar coincidences between Kennedy and former Mexican President Álvaro Obregón, while the other came up with similar lists for twenty-one pairs of US Presidents.List of Martin Gardner Mathematical Games columns
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 7½ years, through June 1986, Gardner wrote 9 more columns, bringing his total to 297, as other authors wrote most of the "Mathematical Games" columns. The table below lists Gardner's columns.Twelve of Gardner's columns provided the cover art for that month's magazine, indicated by "[cover]" in the table with a hyperlink to the cover.Marcello Truzzi
Marcello Truzzi (September 6, 1935 – February 2, 2003) was a professor of sociology at New College of Florida and later at Eastern Michigan University, founding co-chairman of the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), a founder of the Society for Scientific Exploration, and director for the Center for Scientific Anomalies Research.
Truzzi was an investigator of various protosciences and pseudosciences and, as fellow CSICOP cofounder Paul Kurtz dubbed him "the skeptic's skeptic". He is credited with originating the oft-used phrase "Extraordinary claims require extraordinary proof", though earlier versions existed.Martin Gardner bibliography
In a publishing career spanning 80 years (1930-2010), popular mathematics and science writer Martin Gardner (1914-2010) 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).Mathemagician
A mathemagician is a mathematician who is also a magician.
The name "mathemagician" was probably first applied to Martin Gardner, but has since been used to describe many mathematician/magicians, including Arthur T. Benjamin, Persi Diaconis, and Colm Mulcahy. Diaconis has suggested that the reason so many mathematicians are magicians is that "inventing a magic trick and inventing a theorem are very similar activities."A great number of self-working mentalism tricks rely on mathematical principles. Max Maven often utilizes this type of magic in his performance.Mathematical puzzle
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer video games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle.
Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set, the rules of the puzzle determine all subsequent changes and moves. Many of the puzzles are well known because they were discussed by Martin Gardner in his "Mathematical Games" column in Scientific American. Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques. Creating thinking (Thinking outside the box) often helps to find the solution.
This list is not complete.Mutilated chessboard problem
The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book Critical Thinking (1946). It was later discussed by Solomon W. Golomb (1954), Gamow & Stern (1958) and by Martin Gardner in his Scientific American column "Mathematical Games". The problem is as follows:
Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?
Most considerations of this problem in literature provide solutions "in the conceptual sense" without proofs. John McCarthy proposed it as a hard problem for automated proof systems. In fact, its solution using the resolution system of inference is exponentially hard.Prometheus Books
Prometheus Books is a publishing company founded in August 1969 by the philosopher Paul Kurtz (who was also the founder of the Council for Secular Humanism, Center for Inquiry, and co-founder of the Committee for Skeptical Inquiry). Prometheus Books publishes a range of books, focusing on topics such as science, freethought, secularism, humanism, and skepticism. Their headquarters is located in Amherst, New York, and they publish worldwide. The publisher's name was derived from Prometheus, the Titan from Greek mythology who stole fire from Zeus and gave it to man. This act is often used as a metaphor for bringing knowledge or enlightenment.
Authors published by Prometheus include Steve Allen, Molefi Asante, Isaac Asimov, Jeremy Bentham, Rob Boston, Ludwig Feuerbach, Antony Flew, R. Barri Flowers, Martin Gardner, Guy P. Harrison, Sidney Hook, Julian Huxley, S. T. Joshi, Dr. Jack Kevorkian, John Maynard Keynes, Philip J. Klass, Leon Lederman, John W. Loftus, Joe Nickell, Friedrich Nietzsche, Mario Perniola, Robert M. Price, James Randi, David Ricardo, Nathan Salmon, George H. Smith, John Steinbeck IV, Victor Stenger, Tom Toles and Ibn Warraq.
Prometheus Books obtained the bulk of the books and manuscripts of Humanities Press International. It has been building and expanding this into a scholarly imprint named Humanity Books. This imprint publishes academic works across a wide spectrum of the humanities.
In 1992 Uri Geller sued Victor J. Stenger and Prometheus Books for libel. The suit was dismissed and Geller was required to pay more than $20,000 in costs to the defendant.In March 2005, Prometheus Books launched the science fiction and fantasy imprint Pyr. In October 2012 it launched the crime fiction imprint Seventh Street Books.
As of 2006, the company and its various imprints have approximately 1,600 books in print and publish approximately 95–100 books per year. Since its founding, Prometheus Books has published more than 2,500 books.
In 2013 Prometheus Books partnered with Random House in an effort to increase sales and distribution.Recreational mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject.The Mathematical Association of America (MAA) includes Recreational Mathematics as one of its seventeen Special Interest Groups, commenting:
Recreational mathematics is not easily defined because it is more than mathematics done as a diversion or playing games that involve mathematics. Recreational mathematics is inspired by deep ideas that are hidden in puzzles, games, and other forms of play. The aim of the SIGMAA on Recreational Mathematics (SIGMAA-Rec) is to bring together enthusiasts and researchers in the myriad of topics that fall under recreational math. We will share results and ideas from our work, show that real, deep mathematics is there awaiting those who look, and welcome those who wish to become involved in this branch of mathematics.Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics.Self-tiling tile set
A self-tiling tile set, or setiset, of order n is a set of n shapes or pieces, usually planar, each of which can be tiled with smaller replicas of the complete set of n shapes. That is, the n shapes can be assembled in n different ways so as to create larger copies of themselves, where the increase in scale is the same in each case. Figure 1 shows an example for n = 4 using distinctly shaped decominoes. The concept can be extended to include pieces of higher dimension. The name setisets was coined by Lee Sallows in 2012, but the problem of finding such sets for n = 4 was asked decades previously by C. Dudley Langford, and examples for polyaboloes (discovered by Martin Gardner, Wade E. Philpott and others) and polyominoes (discovered by Maurice J. Povah) were previously published by Gardner.Spoon bending
Spoon bending is the apparent deformation of objects, especially metal cutlery, either without physical force, or with less force than would normally seem necessary. It is a common form of stage magic, and a variety of methods are used to produce the illusion.
Spoon bending attracted considerable media attention in the 1970s when some people claimed to have the ability to cause such events by paranormal psychic means. The most notable was Uri Geller, who performed by bending metal spoons as well as metal keys and several other objects and materials. Geller's performances were attributed to stage magic by critics such as James Randi and Martin Gardner.The Ambidextrous Universe
The Ambidextrous Universe is a popular science book by Martin Gardner, covering aspects of symmetry and asymmetry in human culture, science and the wider universe.
Originally published in 1964, it underwent revisions in 1969, 1979, 1990 and 2005 (the last two are known as the "Third, revised edition"). Originally titled The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds, subsequent editions are known as The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings.The Annotated Alice
The Annotated Alice is a work by Martin Gardner incorporating the text of Lewis Carroll's major tales, Alice's Adventures in Wonderland and Through the Looking-Glass, as well as the original illustrations by John Tenniel. It has extensive annotations explaining the contemporary references (including the Victorian poems that Carroll parodies), mathematical concepts, word play, and Victorian traditions (such as the snap-dragons) featured in the two books.