User:Toploftical/Workpage 1

From Wikipedia, the free encyclopedia

  This is the Martin Gardner Topics page

dead links[edit]

[1]

  1. ^ Scott Kim, Puzzle Master: His Scientific American column Mathematical Games, which ran for 25 years, inspired my own career as a puzzle designer.

Trivia[edit]

Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue.

MG and math education[edit]

In 1998 Gardner wrote in an article reflecting on his experience writing his Mathematical Games column:

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.

Gardner believed that recreational mathematics was a natural and inviting introduction to significant mathematics. In a 2014 interview he said:[1]

The best way, it has always seemed to me, to make mathematics interesting to students and laymen is to approach it in a spirit of play. Surely the best way to wake up a student is to present him with an intriguing mathematical game, puzzle, magic trick, joke, paradox, mo del, limerick, or any of a score of other things that dull teachers tend to avoid because they seem frivolous. The frvolity keeps the reader alert. The seriousness makes the play worthwhile. The reader may be surprised by the amount of nontrivial mahematics he has absorbed without even trying.
education links

Other views[edit]

Over the years he 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).[2]

URL playlist for each of the past three Gatherings for Gardner[edit]

Scientific American columnist[edit]

In 1956 Gardner heard about the flexagons invented by British mathematician Arthur Stone and American mathematician John Tukey. He asked the editors at Scientific American if they would like an article about the intriguing paper shapes. When they said yes he got together with Stone and Tukey and wrote what was essentially his first mathematical games column.  This launched his career as a columnist and he remained at Scientific American for the next twenty five years.

Gardner had published and article in Scientific American in 1952.

Logic Machines[3]

1939 at Princeton University, with the arrival of mathematician Arthur Stone from the UK.

Hexaflexagons remained relatively obscure until Gardner heard about them in 1956. He asked a Scientific American editor if the magazine would like an article about them. The answer was yes. Gardner met Tuckerman & Tukey, wrote the article, and so launched his career in recreational mathematics.

His hexaflexagons article appeared in December 1956, beginning a craze for the shapes. Gardner, who was 42 years old, joined the staff of Scientific American, working from home. For almost a quarter-century he wrote a Mathematical Games column for the magazine. He retired in 1980, age 65. In retirement, he continued writing mathematical games articles freelance.

G4G13[edit]

bio[edit]

Martin developed an early interest in magic, publishing literally hundreds of tricks, from 1930 until 2010. While he loved to meet with fellow magicians he was loath to perform in public. He considered magic as exciting the scientific mind of the audience, in he sense that trying to figure out a trick is like trying to understand Nature.

Hoping to major in science, Martin attended the University of Chicago. However he changed to the philosophy of science and graduated in 1936, with honors. He took a desultory series of graduate courses, both before and after the war, including some at the Chicago Theological Seminary. The most influential professor he had was Rudolph Carnap. Gardner’s personal library was enormous, including an extraordinary number of works on the philosophy of science. He dwelt on this subject far more than he wrote about it. His interest was a personal quest, not an academic exercise.[4]

James Gardner recollections: NYT criptogram incident, letter to WP, first photo in his presentation

British Origami Society BIO[edit]

British Origami Society has some great bio for MG HERE

undigested material[edit]

  • the way MG worked–the index cards, the extensive correspondence, the visitors, the typewriter, etc.
  • Insist that Jim Gardner to write a book about his father and put into it all those wonderful anecdotes he related at G4G13. Then we can freely use them in WP!
  • email source of this material is HERE
  • "Math and Magic Friends" is the title of Chapter 17 of Undiluted Hocus-Pocus. MG doesn’t use any other term for his inner circle in that chapter. Just addresses them individually. Escher lady calls them MG-squared.
  • mention the fourth dimension, sphere packing, Newcomb's paradox, Mandelbrot's fractals.[5]

Doris Schattschneider remarks[edit]

Not mentioned in the section on Gardner and Conway (perhaps not known to you) is that in 1976, Conway visited Gardner at his home and Gardner pretty much held him prisoner for a week, pumping him for information on the Penrose tilings which had just been announced. Conway had discovered many (if not most) of the major properties of the tilings, and was slated to give a talk on the subject at a conference on Recreational Mathematics held at Miami University in Bowling Green, Ohio. Gardner was also slated to come to that conference, but just before they were to board the plane, Gardner bailed out and Conway came alone. The cover of the January 1977 Scientific American features a portion of a Penrose tiling by kites and darts, and Gardner's column, based on Conway's information, reveals many of the special aspects of that tiling. This fueled great interest in the Penrose aperiodic tilings.

I'm not sure the public is aware of how much Gardner's writings depended in input and vetting by many trusted others, and how much he shared information with those others and was alerted to interesting topics by them. All of the names mentioned in the WP article and many not mentioned have fat files of correspondence with Martin-- he must have devoted as much time to correspondence (often a hand-written postcard) as to writings to be published. I was one of those others, and so I speak from experience. Also, his enormous archive now at Stanford attests to the volume of his correspondence.

Conway and Martin Gardner[edit]

Conway's career is intertwined with mathematics popularizer and Scientific American columnist Martin Gardner. When Gardner featured Conway's Game of Life in his Mathematical Games column in October 1970, it became the most widely read of all his columns and made Conway an instant celebrity.[21][22] Gardner and Conway had first corresponded in the late 1950s, and over the years Gardner had frequently written about recreational aspects of Conway's work.[23] For instance, he discussed Conway's game of Sprouts(Jul 1967), Hackenbush (Jan 1972), and his angel and devil problem (Feb 1974). In the September 1976 column he reviewed Conway's book On Numbers and Games and introduced the public to Conway's surreal numbers.[24] Conferences called Gathering 4 Gardner are held every two years to celebrate the legacy of Martin Gardner, and Conway himself has often been a featured speaker at these events, discussing various aspects of recreational mathematics.[25][26]

Richard K Guy and Martin Gardner[edit]

It was in Gardner’s columns that I first learned of the popular early-20th-century writings of Henry Dudeney and Sam Loyd, which publicized the impartial game of Kayles and the solution to it written by Richard Guy and Cedric A.B. Smith. 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 (WW). 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. Some of his readers became students in courses taught by each of us, and/or thesis students under the Posted by Elwyn Berlekamp:

Conway, Berlekamp, and Gardner[edit]

He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays,[1]

Richard invited me to Calgary to give a colloquium on the game of Dots-and-Boxes and its relationship to Kayles. The talk got an enthusiastic reception, after which I pursued research on other mathematical games with increased vigor.

Martin Gardner’s influence on (from left) Richard Guy, John Conway, and Elwyn Berlekamp extended to an enthusiastic recommendation for their book Winning Ways for Your Mathematical Plays (“the greatest contribution of the 20th century to the burgeoning field of recreational mathematics”)[6]

It was in Gardner’s columns that I first learned of the popular early-20th-century writings of Henry Dudeney2 and Sam Loyd3, which publicized the impartial game of Kayles4 and the solution to it written by Richard Guy and Cedric A.B. Smith.

The Penrose Tiling at Miami University[edit]

This was the first time that most of us in the audience had heard about this intriguing set of two tiles, kites and darts, that tile the plane only nonperiodically. That is, no region of the tiling will tile by means of translations alone. The fol lowing January, 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.

Piet Hein & other sources[edit]

Links from MG page[edit]

Be sure MG page links to all of the following people: Persi Diaconis, Ronald Graham, Elwyn R. Berlekamp, John Horton Conway, H.S.M. Coxeter, Persi Diaconis, M. C. Escher, Solomon W. Golomb, Bill Gosper, Ronald Graham, Richard K. Guy, Piet Hein, Douglas Hofstadter, Ray Hyman, Scott Kim, Donald Knuth, Benoit Mandelbrot, Robert Nozick, Penn & Teller, Roger Penrose, James Randi, Ron Rivest, Lee Sallows, Doris Schattschneider, David Singmaster, Raymond Smullyan, Ian Stewart, Whitfield Diffie, Martin Hellman, Ralph Merkle, Bryant Tuckerman, John Nash, W. T. Tutte,

MAA tribute issue[edit]

Hexaflexagons (December 1956)
Eight Problems (February 1960)
The Game of Life (October 1970)
Mandlebrot's Fractals (December 1976)
Penrose Tiling I & II (January 1977)
Trapdoor Ciphers (August 1977)
The Wonders of a Planiverse (July 1980)
Remembering Martin Gardner
MAA Tribute to Martin Gardner

MG obits[edit]

MG and chess[edit]

In Martin Gardner’s October 1976 Mathematical Games column in Scientific American, he discussed the following problem: "What is the minimum number of counters that can be placed on an n×n chessboard, no three in a line, such that adding one more counter on any vacant square will produce three in a line?"[7] He dubbed this the minimum no-3-in-a-line problem but it has since been called the eight queens problem.

He was a fan of chess and once played two tournament games with the famous grandmaster Sammy Reshevsky.[8]

Gardner biography[edit]

Martin Gardner was born on October 21, 1914, the son of a geologist and a kindergarten teacher in Tulsa. The father worked as a successful oilseeker and so Gardner grew up in a wealthy household. After studying philosophy with Rudolf Carnap , Gardner initially worked as a freelance science journalist for Esquire, but changed after his marriage to the children's magazine Humpty Dumpty, where he had to look after the puzzle and craft corner. With mathematical pranks for children Gardner had such success that in 1956 he got the offer to write for the Scientific American a mathematics column.[9]

These columns appeared as books in Germany and gave Gardner a loyal readership, not least because of the physicist and science writer Heinz Haber who vigorously promoted Gardner in Germany and frequently featured his work in his television broadcasts.

Quotes[edit]

"Newton said that his many mathematical accomplishments came because he stood on the shoulders of giants. For those of us who have tried to make mathematics accessible to a wider audience, there is one giant who towers well above anyone else: Martin Gardner."[10]

Gardner helped change mathematics from a solitary occupation to a collaborative, social enterprise.

––Jim Henle of Smith College[11]
  1. ^ [Five Martin Gardner eye-openers involving squares and cubes] by Colm Mulcahy, Plus Magazine, 20 October, 2014
  2. ^ Gardner, Martin (1981). Science, good, bad, and bogus – Martin Gardner – Google Books. ISBN 9780879751449. Retrieved 2012-04-14.
  3. ^ Scientific American March 1952 Issue: Logic Machines
  4. ^ Dear Martin Dear Marcello: Gardner and Truzzi on Skeptic WorldScientific, p. 10
  5. ^ A Gardner's Dozen—Martin's Scientific American Cover Stories martin-gardner.org
  6. ^ Berlekamp (2014)
  7. ^ Martin Gardner’s minimum no-3-in-a-line problem by Alec S. Cooper, Oleg Pikhurko, John R. Schmitt, and Gregory S. Warrington; July 19, 2012
  8. ^ Martin Gardner, Mathematician and Lifelong Chess Fan, Dies at 95 By Tom Braunlich, May 28, 2010
  9. ^ Ich bin nur ein einfacher Journalist. Zum Tode von Martin Gardner. by Detlef Borchers, Heise Forums, May 23, 2010
  10. ^ Testimonial on Cover of The Colossal Book of Mathematics by Keith Devlin
  11. ^ Facebook Twitter Youtube Instagram RSS A Day to Experience the 'Cooler Aspects' of Math

MG and Oulipo[edit]

  1. ^ Playing with Poetry: using mathematics to discover new verses by JoAnne Growney, Mathematical Association of America blog
  2. ^ I miss you, Martin Gardner Intersections–Poetry with Mathematics: JoAnne Growney
  3. ^ Review of Imaginary Numbers by William Frucht Mathematical Association of America Press release

RSA Crytography[edit]

This is a translation of the Spanish MG WP page

In August of 1977 in his column of the Scientific American (published in "Investigation and science" in October) and under the title of "Keys of new type whose deciphering would take a few million years" ("a new kind of cipher that would take millions of years to break "), Martin Gardner introduced three previously unknown MIT professors and the result of their research.

The professors were none other than Rivest, Shamir and Adleman , specialists in computer science and a new cryptographic system was announced that shortly afterwards was known as RSA by the initials of the names of the three researchers). In his article, after describing public key cryptography and the advances of Diffie and Hellman, he presented as Rivest, Shamir and Adleman through prime numbers and the difficulty of factoring a product number of two large cousins ​​had achieved a cryptographic method that fulfilled the conditions of the public key cryptosystem. For the first time, the RSA cryptosystem was presented to the public, and in its article Gardner and the MIT group left a challenge to their readers in the form of a coded message and giving the public key used to encrypt it.

The challenge was to factor the public key into its two factors and use them to decipher the message. Plain text is an English phrase converted to a number by the usual procedure (a = 0, b = 1 ...) raised to 9007 module r. Rivest estimated that using the best known factorization algorithm and the fastest of the available computers (year 77) would be necessary in the order of 40 quadrillion years to solve the challenge. In the article, Gardner did not have enough space to explain all the practical details of the RSA so he asked interested readers to request the details from MIT's computer lab. The three researchers were inundated with some 7,000 requests for documentation. However, they were slow to answer for about a year, until solving certain legal and other problems related to the patent. Far from Rivest's prediction, Gardner's challenge took "only" 17 years to be deciphered. On April 26, 1994 a team of 600 volunteers, in a challenge of collaborative computing, using some 1,600 machines for more than six months. Note the improvement in factoring algorithms (since the original publication) and that the challenge proposed by Gardner used a key of 129 decimal places. Martin Gardner's original article on the RSA is also published in his book "Penrose Mosaics and Encrypted Hatchways." Other books by Martin Gardner related to cryptography: "The language of spies", "Codes, ciphers and secret writing". Far from Rivest's prediction, Gardner's challenge took "only" 17 years to be deciphered. On April 26, 1994 a team of 600 volunteers, in a challenge of collaborative computing, using some 1,600 machines for more than six months. Note the improvement in factoring algorithms (since the original publication) and that the challenge proposed by Gardner used a key of 129 decimal places. Martin Gardner's original article on the RSA is also published in his book "Penrose Mosaics and Encrypted Hatchways." Other books by Martin Gardner related to cryptography: "The language of spies", "Codes, ciphers and secret writing". Far from Rivest's prediction, Gardner's challenge took "only" 17 years to be deciphered. On April 26, 1994 a team of 600 volunteers, in a challenge of collaborative computing, using some 1,600 machines for more than six months. Note the improvement in factoring algorithms (since the original publication) and that the challenge proposed by Gardner used a key of 129 decimal places. Martin Gardner's original article on the RSA is also published in his book "Penrose Mosaics and Encrypted Hatchways."

general[edit]

other sources and things[edit]

A collection of articles by those who have been inspired by Martin Gardner to enter mathematics, to enter magic, to bring magic into their mathematics, or to bring mathematics into their magic.
This book collects articles Gardner wrote for the MAA in the twenty-first century, together with other articles the MAA published from 1999 to 2012 that spring from and comment on his work.
2 unused Colm links - [3][4]


  1. ^ Mulcahy, Colm (2013). Celebrations of Mind Honor Math’s Best Friend, Martin Gardner Scientific American, October 29, 2013
  2. ^ DRH speaking about MG in his essay.
  3. ^ Minutes of the Meeting of the Irish Mathematical Society Annual General Meeting, August 28 2015
  4. ^ Mathematical (and Poetic) Offerings From the Land of Saints and Scholars by Colm Mulcahy, HuffPost Science May 23, 2015

Martin Gardner and popular culture[edit]

Among the topics I am considering are:

chess, wordplay, Pentaminos, flexagons, game of life, penrose tiles, origami, M. C. Escher

Gardner's writing often became of a part of mainstream popular culture.

A frequent contributor to Gardner's column was Solomon Golomb[1] who named and popularized the idea of Polyominoes, particularly in the December 1957 column–More about complex dominoes. The column created a great deal of international interest and Golomb's book Polyominoes, was translated into Russian, where it became a best-seller and came to the attention of Russian game designer Alexey Pajitnov who designed a game involving falling tetromininoes. That game was called Tetris and it became one of of the world's best-loved computer games.[2]

Without Gardner, the artist MC Escher would not have achieved the fame he did and the computer game Tetris would not have been invented.[3]

  1. ^ Obituary: Solomon Golomb By Alistair Bird, The Aperiodical, May 17, 2016
  2. ^ Alex's Adventures in Numberland, p.245 By Alex Bellos, Bloomsbury UK (April 1, 2011) ISBN 1408809591
  3. ^ Bellos, Alex (2008). The science of fun The Guardian, 30 May 2008

MG categories and templates and lists[edit]

Category:Works by Martin Gardner

Biography[edit]

Had a high school math teacher named Pauline Baker who introduced him to deductive reasoning.[1]

this interest in puzzles came early in his life when his father gave him a copy of Sam Loyd's Cyclopedia of Puzzles. MacTutor History: Martin Gardner

I was very good at math in high school. In fact, it and physics were the only subjects in which I got good grades. MacTutor History: Martin Gardner

Gardner, son of a petroleum geologist, grew up in and around Tulsa, Oklahoma and showed an early interest in puzzles and games. 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.

mother was primary school teacher MacTutor

Martin was the oldest of his parents' three children having a younger brother Jim and sister Judith. MacTutor

MG was the son of a geologist.

He often got to go with his father on digs. Had a high school math teacher named Pauline Baker who introduced him to deductive reasoning. [2]

He graduated Phi Beta Kappa in philosopy.[3]

Before he entered primary school, Martin had learnt to read.

Magic[edit]

Interview with Dana Richards[edit]

Gardner was personal friends with the editor/owner of Greenwood Press. He also persuaded them to publish the Word Ways: The Journal of Recreational Linguistics at the same time. It is still published but it has changed hands.

I am sure it is written down somewhere, but this is from an interview he gave me:

I had a magic friend, Bruce Elliott, who wrote books on magic and we be came very good friends. Bruce was friends with Harold Schwartz and when they started Humpty Dumpty magazine he recommended me to do their activity features. I met Harold. It turned out that not only did I do activity features, but I did a short story and a poem. Harold and I became very good friends. When he left Parents he founded a publishing company called Greenwood Press. He had a wonderful idea to start off the company. He decided to reissue, for libraries, reprints of complete runs of American radical magazines, early socialist and anarchist magazines. It turns out the most complete source was owned by Bryn Mawr. He made a fortune. He sold the company for a huge sum and retired to Maine.

Gatherings for Gardner[edit]

  • Siobhan Roberts' 4-26-16 New Yorker piece "The Dice You Never Knew You Needed"[4]
above ref mentions the G4G and Martins role as inspiritor

some unused material[edit]

  • He also played a major role in popularizing origami in the West.[5]
  • Undiluted Hocus-Pocus Reviewed by Andy Magid Notices of the AMS Volume 61, Number 3
  • 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.[6]
  • As a columnist for Scientific American, Gardner inspired generations of physicists, mathematicians, philosophers, puzzle-makers, logicians, magicians and others, including me.[7]
  • He once said that he "never gave a lecture in his life and that he wouldn't know how to."[8]
2014 gathering for gardner
life response[9]
enormous influence[10]
Gardner prepared each of his columns in a painstaking and scholarly fashion and conducted copious correspondence to be surethat he got all the ideas straight. reference is Knuth, Donald E. (2011)
  • Although he could in fact pull off technically impressive magic, Gardner especially loved the somewhat minimalist secrets of a wide-ranging genre that magicians deem “impromptu magic,” a casual branch of trickery that’s usually performed for friends and family after dinner with everyday objects.[11]
  • "Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children."
  • pen name Armand T. Ringer is not explained

References[edit]

  1. ^ Costello (1988)
  2. ^ Costello (1988)
  3. ^ Costello (1988)
  4. ^ The Dice You Never Knew You Needed by Siobhan Roberts, The New Yorker, 26 April 2016
  5. ^ Hyperbolic Crochet - Some Fiber for Thoughts about Art, Math, Crochet, and all ahe Various Threads in our Lives Daina Taimina
  6. ^ An Interview with Manjul Bhargava Gathering4Gardner, posted By Colm Mulcahy on April 6, 2018
  7. ^ Martin Gardner would have smiledPhysics World: Education and Outreach Blog, 16 April 2018 by Robert P Crease
  8. ^ Colm Mulcahy interview with Martin Gardner in 2006 in hyperbolic-crochet, a blog by Daina Taimina
  9. ^ Mulcahy (Oct 2014): "The Game of Life appeared in Scientific American in 1970, and was by far the most successful of Gardner's columns, in terms of reader response."–Colm Mulcahy
  10. ^ Scholars and Others Pay Tribute to Mathematical Games Columnist Martin GardnerScientific American, May 24, 2010 "His influence on the world's mathematics has been enormous, and he is irreplaceable."–Ian Stewart
  11. ^ Antonick, Gary (2015). Martin Gardner’s Impromptu NumberPlay in the New York Times, November 30, 2015

RSA and the Martin Gardner Games column[edit]

  • RSA numbers received widespread attention when a 129-digit number known as RSA-129 was used by Ron Rivest, A. Shamir, and L. Adleman to publish one of the first public-key messages together with a $100 reward for the message's decryption (Gardner 1977). RSA (cryptosystem)
  • The most famous of the public key cryptosystem is RSA which is named after its three developers Ron Rivest, Adi Shamir, and Leonard Adleman. At the time of the algorithm's development (1977), the three were researchers at the MIT Laboratory for Computer Science. Their algorithm was first announced in Martin Gardner's "Mathematical Games" column in the August, 1977, Scientific American. The article published one of the first public-key messages together with a $100 reward for the message's decryption.
  • It would be a new section called: Government reaction to RSA column, RSA and NSA, RSA column, or something.
  • The Magic Words are Squeamish Ossifrage is derived from the RSA column
from Spanish WP

In August of 1977 in his column of Scientific American (published in "Investigation and science" in October) and under the title of "Keys of new type whose decipherment would occupy a few million years" ("a new kind of cipher that would take Martin Gardner introduced three previously unknown MIT professors and the result of their research.

The professors were none other than Rivest, Shamir and Adleman, specialists in computer science and a new cryptographic system was announced that soon was known like RSA by the initials of the names of the three investigators). In his article, after describing the public key cryptography and the advances of Diffie and Hellman, presented as Rivest, Shamir and Adleman through prime numbers and the difficulty of factorizing a product number of two large cousins ​​had obtained a method Cryptographic system that met the conditions of the public key cryptosystem. For the first time the RSA cryptosystem was presented to the public, in addition in its article Gardner and the MIT group left a challenge to their readers in the form of a coded message and giving the public key used to encrypt it.

The challenge was to factorize the public key into its two factors and use them to decipher the message. The plain text is an English sentence converted into a number by the usual procedure (a = 0, b = 1 ...) raised to 9007 module r. Rivest estimated that using the best known factorization algorithm and the fastest available computers (year 77) would be necessary on the order of 40 quadrillion years to solve the challenge. In the article, Gardner did not have enough space to explain all the practical details of the RSA, so he asked interested readers to request details from the MIT computer lab. The three researchers were inundated with some 7,000 requests for documentation. However, they took about a year to answer, to solve certain legal problems and others related to the patent. Far from Rivest's prediction, Gardner's challenge took "only" 17 years to be deciphered. On April 26, 1994 a team of 600 volunteers, in a challenge of collaborative computing, using about 1,600 machines for more than six months. Note the improvement in factorization algorithms (since the original publication) and that the challenge proposed by Gardner used a key of 129 decimal places.

Interview with Martin Gardner[edit]

An interview with Martin Gardner

The participants were

Donald J. Albers, Department of Mathematics, Menlo College, Menlo Park, California; Editor, The Two-Year College Mathematics Journal
Anthony Barcellos, Department of Mathematics, University of California, Davis
Martin Gardner, “Mathematical Games” columnist and author, Scientific American
Ronald L. Graham, Head, Discrete Mathematics Section, Bell Laboratories, New Jersey
Peter Renz, Editor, W. H. Freeman and Company, San Francisco
S. M. Ulam, Department of Mathematics, University of Florida, Gainesville
Retrieved from "https://en.wikipedia.org/w/index.php?title=User:Toploftical/Workpage_1&oldid=1196450416"