Martin Gardner
Martin Gardner | |
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Trevor Evans Award (1998) | |
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Charlotte Greenwald (m. 1952) |
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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 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-
He was a frequent contributor to The New York Review of Books.[20]
Biography
Youth and education
Martin Gardner was born into a prosperous family in
He attended the
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
Mid-career
In 1950, he wrote an article in the
In 1957 Gardner started writing a column for Scientific American called "Mathematical Games". It ran for over a quarter century and dealt with the subject of recreational mathematics. The "Mathematical Games" column became the most popular feature of the magazine and was the first thing that many readers turned to.[32] 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.[33]
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.[34] Charlotte died in 2000 and in 2004 Gardner returned to Oklahoma,[35] 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]
Mathematical Games column
I just play all the time and am fortunate enough to get paid for it.
– Martin Gardner, 1998
The "Mathematical Games" column began with a free-standing article on
It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:[38]
- Flexagons (Dec 1956)
- The Game of Hex (Jul 1957)
- The Soma cube (Sep 1958)
- Squaring the square (Nov 1958)
- The Three Prisoners problem(Oct 1959)
- Polyominoes(Nov 1960)
- The Paradox of the unexpected hanging (Mar 1963)
- Rep-tiles(May 1963)
- The Superellipse (Sep 1965)
- Pentominoes(Oct 1965)
- The mathematical art of M. C. Escher (Apr 1966)
- Fractalsand the Koch snowflake curve (Mar 1967)
- Conway's Game of Life (Oct 1970)
- Intransitive dice (Dec 1970)
- Newcomb's paradox (Jul 1973)
- Tangrams(Aug 1974)
- Penrose tilings (Jan 1977)
- Public-key cryptography (Aug 1977)
- Godel, Escher, Bach(Jul 1979)
- The Monster group (Jun 1980)
Ironically, Gardner had problems learning calculus and never took a mathematics course after high school. While editing Humpty Dumpty 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".[39] 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.[40]
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.[41] Over the next four decades fourteen more books followed.[23] Donald Knuth called them the canonical books.[42][43]
Influence
His depth and clarity will illuminate our world for a long time.[44]
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][37][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
His writing was credited as both broad and deep.
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]
–
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.[36][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.
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]
- Robert Ammann
- Mitsumasa Anno
- Elwyn R. Berlekamp
- Dmitri A. Borgmann
- Gregory Chaitin
- Fan Chung
- John Horton Conway
- H.S.M. Coxeter
- Erik Demaine
- Persi Diaconis
- M. C. Escher
- Solomon W. Golomb
- Bill Gosper
- Ronald Graham
- Richard K. Guy
- Frank Harary
- Piet Hein
- Douglas Hofstadter
- Ray Hyman
- Scott Kim
- David A. Klarner
- Donald Knuth
- Harry Lindgren
- Benoit Mandelbrot
- Robert Nozick
- Penn & Teller
- Roger Penrose
- James Randi
- Marjorie Rice
- Ron Rivest
- Tom Rodgers
- Rudy Rucker
- Lee Sallows
- Doris Schattschneider
- Jeffrey Shallit
- David Singmaster
- Jerry Slocum
- Raymond Smullyan
- Ian Stewart
- W. T. Tutte
- Stanislaw Ulam
- Samuel Yates
- Nob Yoshigahara
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
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.[34]
Gardner was a critic of
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
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
Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century.
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.
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
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.
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
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
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,
Novels and short stories
Gardner wrote two novels. He was a fan of the
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
Pen names
Gardner often used pen names. In 1952, while working for the children's magazine
In his January 1960 "Mathematical Games" column, Gardner introduced the fictitious "
Philosophy of mathematics
Gardner wrote on the
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 – 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
Gathering 4 Gardner
Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations.
A second such get-together was held in 1996, again with Gardner in attendance. A video was made for the
The attendees at G4G include magicians, mathematicians, jugglers, philosophers, scientific skeptics, fans of Lewis Carroll, puzzle collectors, fans of Conway's game of life, Rubic's cubers, chess masters, and any other topic that Gardner was interested in or 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.[159] The 2018 event was G4G13.[160] Because of the COVID-19 pandemic, the G4G14 event was not held until 2022.[161] Two years later G4G15 took place. All G4Gs up to 2024 have been in Atlanta.
Bibliography
In a publishing career spanning 80 years (1930–2010),[162] 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.[163]
All Gardner's works were non-fiction except for two novels – The Flight of Peter Fromm (1973) and Visitors from Oz (1998) – and two collections of short pieces – The Magic Numbers of Dr. Matrix (1967, 1985) and The No-Sided Professor (1987).
References
- ^ a b c d e f g AMS Notices (2004)
- ^ "MAA Writing Awards Presented" (PDF). Notices of the AMS. 47 (10): 1282. November 2000. Archived (PDF) from the original on July 12, 2014.
- (PDF) from the original on March 4, 2014.
- ^ a b Martin (2010)
- ^ Singmaster, D. (2010) "Obituary: Martin Gardner (1914–2010)" Nature 465(7300), 884.
- ^ Kindley (2015): When it comes to explanations of Carroll’s books, no one has yet improved on the work of Gardner.
- ^ a b Martin Gardner obituary Telegraph Media Group (2010)
- ^ a b Top 10 Martin Gardner Books Archived 2016-03-25 at the Wayback Machine, by Colm Mulcahy, Huffington Post Books, October 28, 2014
- ^ Costello (1988): p. 114.
- ^ England (2014): Even apart from mathematics and puzzles, Gardner's output was staggering.
- ^ "Martin Gardner dies at 95; prolific mathematics columnist for Scientific American" by Thomas H. Maugh, Los Angeles Times, May 26, 2010
- ^ 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
- ^ Case 2014: Gardner is credited with the rebirth of recreational mathematics in the U.S.
- ^ Martin (2010): "His mathematical writings intrigued a generation of mathematicians."
- ^ Bellos (2010): "He became a kind of father figure to a generation of young mathematicians, who corresponded with him. Such was Gardner's influence between the late 1950s and 1980s that it would be hard to find a professional mathematician from those years who does not cite him as an inspiration."
- ^ "Martin Gardner – Mathematician". Martin Gardner Home Site. Gathering 4 Gardner. 2014. Archived from the original on November 18, 2016. Retrieved October 28, 2016.
- ^ originally published in 1952 as In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present
- ^ Shermer, Michael (2001). The Borderlands of Science: Where Sense Meets Nonsense. Oxford University Press. p. 50. Retrieved May 20, 2016.
Fads and Fallacies in the Name of Science [is] still in print and arguably the skeptic classic of the past half-century.
- ^ "About CSI". Committee for Skeptical Inquiry. Archived from the original on November 12, 2016. Retrieved October 28, 2016.
- ^ Reviews by and about Martin Gardner The New York Review of Books: 1973 to 1998
- ^ James Gardner later became the 8th President of the American Association of Petroleum Geologists.
- ^ a b Martin Gardner Famous Scientists
- ^ a b England (2014)
- ^ Suzuki (1996) at 17:20
- ^ MacTutor
- ^ a b c Shermer (1997)
- ^ Yam, Philip (December 1995) Profile: Martin Gardner, the Mathematical Gamester (1914–2010) Archived 2018-05-11 at the Wayback Machine Scientific American
- ISBN 978-1-56881-075-1.
- ^ a b c d Gardner, Martin (2013)
- Antioch Review, Winter 1950–1951, pp. 447–457.
- ^ Burstein (2011)
- ^ Hofstadter (2010): There were thousands of such people spread all around the world – mathematicians, physicists, philosophers, computer scientists, and on and on – who thought of Martin Gardner's column not as merely a feature of that great magazine Scientific American, but as its very heart and soul.
- ^ Demaine (2008): p. 24
- ^ a b c d Richards (2014)
- ^ Albers (2008)
- ^ a b Mulcahy (2014)
- ^ a b The Economist (2010)
- 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.
- ^ Antonick, Gary (2013). Martin Gardner’s The Monkey and the Coconuts in Numberplay The New York Times:, October 7, 2013
- ISBN 0-393-02023-1
- ^ Martin Gardner: Mathematical Games Collections Archived 2016-06-29 at the Wayback Machine by David Langford
- ^ The New Martin Gardner Mathematical Library Archived 2016-12-26 at the Wayback Machine Cambridge University Press
- ^ The Canon: The fifteen "Mathematical Games" books at martin-gardner.org Archived 2015-02-16 at the Wayback Machine
- ^ Princeton University Press: Reviews of Undiluted Hocus-Pocus
- ^ Princeton University Press: Reviews of Undiluted Hocus-Pocus: "Martin Gardner occupies a special place in twentieth-century mathematics. More than any other single individual, he inspired a generation of young people to study math."–Barry Arthur Cipra
- ^ Bellos (2010): He was not a mathematician – he never even took a maths class after high school – yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.
- ^ Mulcahy (2014): It's been said that he had a million readers there at his peak.
- ^ Malkevitch (2014): Martin Gardner's columns and books have been referenced by huge numbers of research papers that involve mathematics.
- ^ 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.
- ^ 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.
- ^ Antonick (2014): Martin Gardner was well known for inspiring generations of students to become professional mathematicians.
- ^ a b Antonick (2014): "Martin Gardner's column in Scientific American was one of the two things that, above all others, convinced me I wanted to be a mathematician."–Ian Stewart
- ^ Demaine (2008) p. ix: Many of today's mathematicians entered this field through Gardner's influence.
- ^ Crease (2018): "As a columnist for Scientific American, Gardner inspired generations of physicists, mathematicians, philosophers, puzzle-makers, logicians, magicians and others, including me."
- ^ a b c d Mulcahy (2013)
- ^ a b Brown (2010)
- ^ Dirda (2009)
- ^ 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).
- ^ a b c Auerbach (2013)
- ^ a b Mulcahy (2017)
- ^ 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
- ^ Malkevitch (2014): The range of wonderful problems, examples, and theorems that Gardner treated over the years is enormous. They include ideas from geometry, algebra, number theory, graph theory, topology, and knot theory, to name but a few.
- ^ Bellos, Alex (2010): I discovered how good [the columns] really were, covering everything from public-key cryptography to superstring theory. He was the first to cover so many breakthroughs.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ MacTutor: Gardner has produced a number of mathematical papers, written with leading mathematicians.
- ^ 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.
- ^ 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
- ^ a b c Hofstadter (2010)
- ^ AMS Notices (2004): "His crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization." —Allyn Jackson.
- ^ Lister (1995): Martin Gardner's supreme achievement was his ability to communicate difficult and often profound subjects with a few deft, but human strokes of his pen.
- ^ Mirsky (2010): "His writing has been valued by generations of professional mathematicians."–Ian Stewart
- ^ Teller (2014): "Gardner writes with authority and ease. You trust him to take you wherever he feels like going."
- ^ Hofstadter (2010): Martin had a magical touch in writing about math.
- ^ a b c Peterson (2014)
- ^ a b c Case (2014)
- ^ David A. Klarner, editor (1981), "In Praise of Amateurs" in The Mathematical Gardner, Weber & Schmidt, 1981.
- ^ 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."
- ^ 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.
- ^ Gardner (2013) page 144: Conway had been making new discoveries about Penrose tiling, and Mandelbrot was interested because Penrose tiling patterns are fractals.
- ^ Cole, K. C. (March 11, 1998), "Beating the Pros to the Punch", Los Angeles Times.
- ^ AMS Notices (2011)
- ^ BBC News (2014): His secret was a fantastic card index system of his own, going back to the 1930s, stored in shoe boxes.
- ^ Stanford University Archives: Gardner (Martin) Papers Online Archive of California
- ^ Discrete Geometry, Combinatorics and Graph Theory : Revised selected papers; Jin Akiyama, William Y.C. Chen, Mikio Kano
- ^ a b BBC News (2014)
- ^ a b Gardner (1998)
- ^ a b Teller (2014)
- ^ The Math Factor Podcast Website John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.
- ^ medium.com, Jan 9, 2022
- ^ Robinson, Sara (June 2003). "Still Guarding Secrets after Years of Attacks, RSA Earns Accolades for its Founders" (PDF). SIAM News. 36 (5).
- ^ Public Key Cryptography History Living Internet
- ^ RSA Cryptography: History And Uses Telsy Communications
- ^ medium.com, Jan 6, 2020
- ^ 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."
- ^ 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.
- ^ 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"
- ^ 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.
- ^ 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.
- ^ Articles by Martin Gardner: 115 Results Skeptical Inquirer
- ^ Prometheus Books The New Age: Notes of a Fringe-Watcher by Martin Gardner
- ^ Confessions of a psychic : the secret notebooks of Uriah Fuller University Of Wisconsin–Madison Library
- ^ Oprah Winfrey: Bright (but Gullible) Billionaire Archived 2016-05-01 at the Wayback Machine Skeptical Inquirer, March/April 2010
- ^ Skeptical Inquirer Magazine Names the Ten Outstanding Skeptics of the Century
- ^ About the IIG Awards Independent Investigations Group
- ^ "CSICOP Council in Atlanta: Police Psychics, Local Groups". The Skeptical Inquirer. 7 (3): 13. 1983.
- ^ The Pantheon of Skeptics Committee for Skeptical Inquiry
- ^ Martin Gardner's Magic Influence Archived 2016-05-21 at the Wayback Machine at martin-gardner.org
- ^ Costello (1988) p. 115: His father had taught him his first trick, the "Knife and Paper" trick, a bit of legerdemain involving a butter knife with bits of paper on it.
- ^ a b Bellos (2010)
- ^ a b c Gathering 4 Gardner (2014)
- ^ Demaine (2008) p. 12
- ^ Reviews of Martin Gardner's Impromptu Archived 2017-03-21 at the Wayback Machine The Miracle Factory
- ^ Demaine (2008): pp. 4–5
- ^ a b Lister (1995)
- ^ from Dover Publications: Mathematics, Magic and Mystery Archived 2016-05-06 at the Wayback Machine "As a rule, we simply accept these tricks and 'magic' without recognizing that they are really demonstrations of strict laws based on probability, sets, number theory, topology, and other branches of mathematics."
- ^ The Dover Math and Science Newsletter Archived 2015-05-03 at the Wayback Machine May 16, 2011
- ^ "Hall of Fame". The Academy of Magical Arts. Archived from the original on November 20, 2016. Retrieved December 24, 2017.
- ^ a b Carpenter, Alexander (October 17, 2008). "Interview: Martin Gardner on Philosophical Theism, Adventists and Price". Spectrum. Archived from the original on July 13, 2016. Retrieved December 21, 2019.
- ^ Gardner (2013) p. 191
- ^ a b Groth (1983)
- ^ Martin Gardner: 1914–2010: Chris French mourns the passing of Martin Gardner, The Guardian, May 25, 2010
- ^ The Whys of a Philosophical Scrivener by Martin Gardner, Quill, 1983, pp. 238–239
- ^ "A Mind at Play: An Interview with Martin Gardner" by Kendrick Frazier, Skeptical Inquirer Volume 22.2, March/April 1998
- ^ a b "Gardner's Whys" in The Night is Large, chapter 40, pp. 481–87.
- ^ Dirda (2009): With this book Gardner virtually launched the entire mini-genre of annotated classics.
- ^ Jan Susina. Conversation with Martin Gardner: Annotator of Wonderland. The Five Owls. Jan./Feb. 2000. 62–64.
- ^ Alice Still Lives Here by Michael Sims, Nashville Scene, July 06, 2000
- ^ Richards (2018)
- ^ Kindley (2015): Just as importantly, though, The Annotated Alice gave rise to a new popular genre.
- ^ Richards (2018): The look and feel was entirely due to Martin Gardner.
- ^ 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.
- ^ Brown (2010): Faith was also the subject of his 1973 semi-autobiographical novel, "The Flight of Peter Fromm," in which the title character and his atheist professor of divinity grapple for decades with questions about God.
- ^ Grooks by Piet Hein Archived 2014-10-10 at the Wayback Machine
- ISBN 978-0691159911, Reviewed by Andy Magid
- ^ Eckler, A. Ross (2010) "Look Back!" Word Ways: Vol 43: Issue 3, Article 6
- ^ Farrell, Jeremiah (November 2020). "More Word Ways?". Word Ways. 53 (3): 4. Retrieved September 19, 2020.
- ^ Don Albers' interview of Gardner, Part 4: The Trap Door Spiders Archived 2008-11-19 at the Wayback Machine
- ^ a b Top 10 Martin Gardner Alter Egos Archived 2017-03-17 at the Wayback Machine at martin-gardner.org
- ^ 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.
- ^ Skeptic Martin Gardner Dies Archived 2015-10-02 at the Wayback Machine by Loren Coleman, CryptoZoo News, May 23, 2010
- ^ Is Mathematics for Real? by Martin Gardner, The New York Review, Aug 13, 1981
- ^ Hersh, Reuben (October 31, 1997). "Re: Martin Gardner book review". Foundations of Mathematics mailing list. Retrieved May 22, 2010.
- ^ A Quarter Century of Recreational Mathematics, by Martin Gardner Scientific American blog on May 29, 2010
- ^ Mathematics Teacher website National Council of Mathematics Teachers
- ^ Martin Gardner's Awards Archived 2016-03-18 at the Wayback Machine
- ^ JPL Small-Body Database Browser Archived 2018-07-06 at the Wayback Machine 2587 Gardner (1980 OH)
- ^ The Mathematical Association of America's Trevor Evans Awards Archived 2017-05-16 at the Wayback Machine
- ^ Magic magazine, Jun 1999, page 60
- ^ MAA MathFest 2019 Invited Addresses
- ^ Doris Schattschneider MAA: 2021 Martin Gardner Lecturer
- ^ Brick Installation Honors Martin Gardner Archived 2017-06-28 at the Wayback Machine MAA New release
- ^ John Conway Reminiscences about Dr. Matrix and Bourbaki by Dana Richards & Collm Mulcahy, Scientific American, October 1, 2014
- ^ 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
- ^ Robert P. Crease, Gathering for Gardner Archived 2018-03-28 at the Wayback Machine, The Wall Street Journal, p. W11, 2 April 2010
- ^ Suzuki (1996)
- ^ Gathering 4 Gardner's G4G13 Presents "Poetry, Drumming, and Mathematics" with Professor Manjul Bhargava The Atlanta Journal-Constitution, April 15, 2018
- ^ Crease (2018)
- ^ G4G13 Information Archived 2018-05-20 at the Wayback Machine gathering4gardner.org
- ^ Hello interflexionality: what I learned from the 14th Gathering for Gardner, by Robert Crease, 03 August 2022. Physics World
- The Sphinx.
- ^
The Bibliography of Martin Gardner Dana Richards (editor), ISBN 1684000327
Sources
- Albers, Don (2008). The Martin Gardner Interview (in five parts) with MAA Editorial Director Don Albers, fifteeneightyfour: the blog of Cambridge University Press
- AMS Notices (2004). Interview with Martin Gardner Notices of the AMS, Vol. 52, No. 6, June/July 2005, pp. 602–611
- AMS Notices (2011). Memories of Martin Gardner Notices of the AMS, Vol. 58, No. 3, March 2011, p. 420
- Antonick, Gary (2014). Ignited by Martin Gardner, Ian Stewart Continues to Illuminate The New York Times, October 27, 2014
- Auerbach, David (2013). A Delville of a Tolkar: Martin Gardner’s “Undiluted Hocus-Pocus” Los Angeles Review of Books, November 4, 2013
- BBC News (2014). Martin Gardner, puzzle master extraordinaire BBC News Magazine, October 21, 2014
- Bhargava, Manjul (2018). An Interview with Manjul Bhargava with Colm Mulcahy, G4G13, April 2018
- Bellos, Alex (2010). Martin Gardner obituary The Guardian, May 27, 2010
- Berlekamp, Elwyn R (2014). The Mathematical Legacy of Martin Gardner Society for Industrial and Applied Mathematics (SIAM), September 2, 2014
- Berlekamp, Elwyn R., John H. Conway, and ISBN 0120911507.
- Brown, Emma (2010). Martin Gardner, prolific math and science writer, dies at 95 The Washington Post, May 24, 2010
- ISBN 978-0-930326-17-3.
- Case, James (2014). Martin Gardner’s Mathematical Grapevine By James Case, SIAM News, April 1, 2014
- Costello, Matthew J. (1988). The Greatest Puzzles of All Time New York: Prentice Hall Press, ISBN 0133649369
- Crease, Robert P (2018). Martin Gardner would have smiled Physics World: Education and Outreach Blog, 16 April 2018
- Demaine (2008). Edited by Erik D. Demaine, Martin L. Demaine, Tom Rodgers. A lifetime of puzzles : a collection of puzzles in honor of Martin Gardner's 90th birthday A K Peters: Wellesley, MA, ISBN 1568812450
- Dirda, Michael (2009). Book review by Michael Dirda: 'When You Were a Tadpole and I Was a Fish' by Martin Gardner The Washington Post, October 22, 2009
- The Economist (2010). Martin Gardner obituary Jun 3rd 2010
- England, Jason (2014). The puzzling life of Martin Gardner Cosmos Magazine, February 24, 2014
- Friedel, Frederic (2018). Remembering Martin Gardner, Jan 16, 2018
- Gardner, Martin (1998). A Quarter Century of Recreational Mathematics by Martin Gardner, Scientific American, August 1998
- Gardner, Martin (2013). Undiluted Hocus-Pocus: The Autobiography of Martin Gardner ISBN 0691159912.
- Gardner, Martin (2016). The Recreational Mathematics of Piet Hein Piet Hein Website
- Gathering 4 Gardner (2014). Martin Gardner – Magician
- Gould, Stephen Jay (1982). The Quack Detector The New York Review of Books, February 4, 1982
- Groth, George (1983). Review of Gardner’s Game with God The New York Review of Books, December 8, 1983
- Hofstadter, Douglas (2010). Martin Gardner: A Major Shaping Force in My Life Scientific American, May 24, 2010
- Klarner, David A. (1998). Mathematical Recreations: A Collection in Honor of Martin Gardner, Dover Publications, New York, pp. 140-166
- Kindley, Evan (2015). Down the Rabbit Hole: The rise, and rise, of literary annotation By Evan Kindley, The New Republic, September 21, 2015
- Kullman, David (1997). The Penrose Tiling at Miami University Archived 2017-08-14 at the Wayback Machine Presented at the Mathematical Association of America Ohio Section Meeting Shawnee State University, October 24, 1997
- Lister, David (1995). Martin Gardner and Paperfolding British Origami Society, February 15, 1995.
- MAA FOCUS (2010). Remembering Martin Gardner vol 30 (4), August/September 2010
- MacTutor (2010). History of Mathematics archive: Martin Gardner
- Malkevitch, Joseph (2014). Magical Mathematics – A Tribute to Martin Gardner American Mathematical Society, March 2014
- Martin, Douglas (2010). Martin Gardner, Puzzler and Polymath, Dies at 95 The New York Times, May 23, 2010
- Martin Gardner – Mathematician (official website)
- Mirsky, Steve (2010). Scholars and Others Pay Tribute to "Mathematical Games" Columnist Martin Gardner Scientific American, May 24, 2010
- Mulcahy, Colm (2013). Celebrations of Mind Honor Math’s Best Friend, Martin Gardner Scientific American, October 29, 2013
- Mulcahy, Colm (2014). The Top 10 Martin Gardner Scientific American Articles Scientific American, October 21, 2014
- Mulcahy, Colm (2017). Martin Gardner – The Best Friend Mathematics Ever Had The Huffington Post, January 23, 2014
- Peterson, Ivars (2014). Honoring a Century of Martin Gardner in MAA Focus, the newsmagazine of the Mathematical Association of America, Vol. 34, No. 5, Oct/Nov 2014
- Propp, James (2015). Martin Gardner Testimonials Belmont, MA, July 29, 2015
- Princeton University Press Reviews of Undiluted Hocus-Pocus: The Autobiography of Martin Gardner
- Richards, Dana (2014). Math Games of Martin Gardner Still Spur Innovation by Dana S. Richards & Colm Mulcahy, Scientific American, October 1, 2014
- Richards, Dana (2018). Martin Gardner, Annotator G4G13, April 2018 – video
- Shermer, Michael (1997). Martin Gardner 1914–2010: Founder of the Modern Skeptical Movement Skeptic Magazine, Vol 5, No. 2 (1997)
- Suzuki, David (1996). Mystery and Magic of Mathematics: Martin Gardner and Friends The Nature of Things, March 14, 1996 – video
- Teller (2014). ‘Undiluted Hocus-Pocus,’ by Martin Gardner The New York Times: Sunday Book Review, January 3, 2014
External links
- Official website – with Martin Gardner's Awards and Martin Gardner Appreciations
- Works by and about Martin Gardner at The Center for Inquiry Libraries
- Martin Gardner at Library of Congress, with 170 library catalog records