BEYOND GAMES: Martin Gardner's column achieved a lot more than engaging readers in intellectual puzzles. It inspired generations of thinkers.
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Editor's Note: Martin Gardner, who wrote the "Mathematical Games" column for Scientific American magazine for 25 years and published more than 70 books, died May 22 at 95. Scientific American editor Steve Mirsky solicited the following tributes and remembrances of Gardner from various colleagues. We also invite readers to share their comments below regarding Gardner, his column and/or its impact.
"It always seemed fitting to me that a man who'd written so engagingly on paradoxes should have had a career that was itself a bit of a paradox. Martin didn't study much (or any) math in college, yet probably did more to stimulate an appreciation for, curiosity about, and discussion of mathematical ideas than 213 of us mathematics professors. Over the years we exchanged a couple of book blurbs, a signal honor for me, and also corresponded a bit about jokes. I remember once being quite amused by a letter from him with some quite non-G–rated examples. A modest man, a clear-eyed skeptic, an expositor extraordinaire, he will be sorely missed."
—John Allen Paulos, a professor of mathematics at Temple University, author of Innumeracy and, most recently, of Irreligion
"This is really a sad day. Not so much sad that Martin died, since we all knew it had to come pretty soon, but sad because his spirit was so important to so many of us, and because he had such a profound influence on so many of us. He is totally unreproducible—he was sui generis—and what's so strange is that so few people today are really aware of what a giant he was in so many fields—to name some of them: the propagation of truly deep and beautiful mathematical ideas (not just "mathematical games," far from it!); the intense battling of pseudoscience and related ideas; the invention of superb magic tricks; the love for beautiful poetry; the fascination with profound philosophical ideas (Newcomb's paradox, free will, etcetera etcetera); the elusive border between nonsense and sense; the idea of intellectual hoaxes done in order to make serious points (for example, one time, at my instigation, he wrote a scathing review of his own book The Whys of a Philosophical Scrivener in The New York Review of Books, and the idea was to talk about the ideas seriously even though he was attacking the ideas that he himself believed in); and on and on and on and on. Martin Gardner was so profoundly influential on so many top-notch thinkers in so many disciplines—just a remarkable human being—and at the same time he was so unbelievably modest and unassuming. Totally. So it is a very sad day to think that such a person is gone, and that so many of us owe him so much, and that so few people—even extremely intelligent, well-informed people—realize who he was or have even ever heard of him. Very strange. But I guess that when you are a total non–self-trumpeter like Martin, that's what you want and that's what you get. And so perhaps it's all for the best that he remains sort of hidden behind the scenes, known only to a special set of people."
—Gardner's friend Douglas Hofstadter, Pulitzer Prize–winning author of Gödel, Escher, Bach: an Eternal Golden Braid
"When I was 14 years old, at the height of the Vietnam War, I picked up a copy of Scientific American. The articles were serious affairs with thin-lined graphs and a sparing use of color. For the most part, I could read only the first page. Then I got to Martin's column. A whole world opened for me. These were puzzles I could do, at least sometimes. I was so excited that I subscribed and thought how cool it would be to write such a column one day.
Twenty years later, I wrote my first puzzle book The Puzzling Adventures of Dr. Ecco. I sent the manuscript to Jerry Lyons at W. H. Freeman. To my great surprise and delight he called me and said he'd like to publish the book. His reason: Martin had liked it. Dr. Ecco is a mathematical detective a little in the Holmesian mold, but his sidekick and chronicler, Professor Scarlet, is always careful to tell the reader everything that Dr. Ecco knows before Ecco uncovers fraud, finds a submarine, or breaks a code. There is a little Martin in every story.
In early 2001 I began writing the "Puzzling Adventures" column for Scientific American, first in the magazine and later on the Web site. I always tried to write the columns so they could be done by any smart kid, 12 years to 120. Thanks to Martin."
—Dennis Shasha, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University
"I never met Martin Gardner—my fault, there were opportunities—but he had a big influence on my career. His "Mathematical Games" column showed me, as a teenager, that new mathematics is constantly being created, and it encouraged the sheer enjoyment of the subject. Eventually I inherited the column, and my biggest problem was that Martin had already described most of the really good material. I didn't try to emulate him, because that would be impossible, but he did teach me that enthusiasm must be allied to clear thinking. The way to explain math to nonspecialists is to understand it thoroughly yourself, to strip away needless technicalities, and to focus on the central story. But you also have to enjoy what you're talking about or the magic doesn't work. When I was a PhD student Martin gave several of us some useful advice when we were setting up a student mathematics magazine, and he occasionally mentioned it in his column. Later, he was generous enough to write a preface for one of my books. His writing has been valued by generations of professional mathematicians, and he taught us that we could relax and let our hair down without damaging our reputations or our subjects. Indeed, that this was one excellent way to get our message out to the world. His influence on the world's mathematics has been enormous, and he is irreplaceable. His passing leaves a huge emptiness, and we will all miss him. But at least we still have the priceless legacy of his books."
—Ian Stewart, Emeritus Professor of Mathematics, Digital Media Fellow, Mathematics Institute, University of Warwick
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12 Comments
Add CommentI am truly saddened to hear of Martin Gardner's death. I knew he had been writing for SciAm as long as I can remember. I used to peruse the SciAm in the late 1950's and early 1960's. My brother used to read it voraciously. We were in junior high and high school. I would thumb through it, but I always look forward to Gardner's Mathematical Games. I read it all and tried, sometimes successfully, to figure out as much as I could. Of course, many times I wasn't successful, but it always retained my interest.
Reply | Report Abuse | Link to thisI am retiring in a month from teaching mathematics and science to middle school students for 32 years. I find such joy in teaching these subjects. I tell the kids to think of math as a puzzle you have to solve. Do you think Martin Gardner had anything to do with that? You bet.
Martin was a wonderful man, a pied piper who led me and so many other scientists my age into our careers. The early MIT "hacker" Bill Gosper still likes to recall the triumphant day when he sent Martin a telegram with an image of the Glider Gun for the game of Life...responding to a challege that Martin's column had proposed.
Reply | Report Abuse | Link to thisThere *are* good people. There *are* good people. There *are* good people. There *are* good people. There *are* good people. There *are* good people....
Reply | Report Abuse | Link to thisScientific American made its way into our household during my elementary school years. I read the articles I could understand, but always felt a little lost until I got to 'Mathematical Games'. The innumerable hours I spent puzzling over Martin's conundrums incited my passion for mathematics, physics and computer science. I can't begin to say how he influenced my life and introduced me to so many great authors in contemporary mathematics: Douglas Hofstadter, Raymond Smullyan, Rudy Rucker, and many others. I miss him greatly, but look forward to sharing his legacy with my own children and watching their interest unfold.
Reply | Report Abuse | Link to this- Thomas Idzikowski, CEO, Smart Networks Corporation
Martin Gardner was my literary godfather. He was the most generous man I have ever known. I owe him everything. When I was only 20, he convinced Clarkson N. Potter to contract my book The Annotated Wizard of Oz as a successor to his own superb and now classic The Annotated Alice. He was always recommending me to editors he knew even up to last year. We often exchanged articles before publication to get the other's thoughts on the subject. Mine benefited inestimably from his input. While he could so adroitly explain the most complex concepts to layman and expert alike, he retained the curiosity and the heart of a child. His integrity was impeccable, his prose lucid and profound. His influence was vast. Few realize that an article he wrote on L. Frank Baum and the Oz Books in The New York Times Book Review inspired the Broadway musical The Wiz. Who else was quoted by John Fowles in The French Lieutenant's Woman and named by Nabokov a character in Ada or Ardor? Of course it was his sister Judy, not Martin, who told me that. He was the gentlest and most modest of men. A true gentleman. Like everyone who had the honor of knowing him, I feel blessed to have been his friend. I will miss him terribly.
Reply | Report Abuse | Link to thisMartin Gardner was my literary godfather. He was the most generous man I have ever known. I owe him everything. When I was only 20, he convinced Clarkson N. Potter to contract my book The Annotated Wizard of Oz as a successor to his own superb and now classic The Annotated Alice. He was always recommending me to editors he knew even up to last year. We often exchanged articles before publication to get the other's thoughts on the subject. Mine benefited inestimably from his input. While he could so adroitly explain the most complex concepts to layman and expert alike, he retained the curiosity and the heart of a child. His integrity was impeccable, his prose lucid and profound. His influence was vast. Few realize that an article he wrote on L. Frank Baum and the Oz Books in The New York Times Book Review inspired the Broadway musical The Wiz. Who else was quoted by John Fowles in The French Lieutenant's Woman and named by Nabokov a character in Ada or Ardor? Of course it was his sister Judy, not Martin, who told me that. He was the gentlest and most modest of men. A true gentleman. Like everyone who had the honor of knowing him, I feel blessed to have been his friend. I will miss him terribly.
Reply | Report Abuse | Link to thisMartin gardner died a few days ago. The man whose Mathematical Games Column in the Scientific American gave me great joy in undergrad engineering days in the IIT Campus in Madras 1979-84. �His column came to an end to be followed by another great man, still living, Douglas Hofstadter, whose Metamagical Themas (an anagram of mathematical games), provided equal measures of joy, and more complicated logic. Then came the joy of discovering Martin Gardner's Annotated Snark and the Annotated Alice in Wonderland, both books which I now own and treasure. �
Reply | Report Abuse | Link to thisMartin deserves a special tribute for making the process of learning a special delight filled with his own brand of magic. I experienced the same delight with Samuel Perelman's Physics For Entertainment at around the same time. How can one thank people like this who make the search for knowledge a journey of delight and fun? Goodbye Martin. RIP
I've a few letters from Mr. Gardmer. He replied on a manual typewriter, he hand corrected his many errors but he went to some trouble to answer, that was obvious. It seemed likely that he kept a personal touch and didn't use computers, at least in those letters. I'd not put my address on the letter and wrote that he searched the trash for the envelope so he could reply.
Reply | Report Abuse | Link to thisThey were replies to a phone call I made to him one day, and a couple of letters I wrote to him. I found out what a 'crank' is to an author, (or a scientist) when he informed me that the character in The Magic Numbers of Dr. Matrix was fictional, not real and he correctly assumed I'd thought he was real. He had psychological insight! He told me that the book was a spoof of numerology. I had to be told to know that.
I had written to him about an amazing (to me) coincidence that happened when I read The Magic Numbers of Dr. Matrix. I would have a different understanding of many unusual (to me) coincidences if he had not written about Dr. Matrix and also The Ambidextrous Universe. He was a light in his Time, to many people like me, I'm sure. And he was right to not be an outright athiest, in my opinion. Just a skeptic, a questioner, willing to be uncertain himself. He's certain now, I suspect.
from the martin gardnar scientific american 1970, I discovered this fascinating "clown" sel emerging from... noise!
Reply | Report Abuse | Link to thishttp://golden-ratio-in-dna.blogspot.com/2008/02/1988-fractal-chaos.html
This is reported in the Epilogue paragraph of my last book CODEX BIOGENESIS:
http://golden-ratio-in-dna.blogspot.com/
http://codexbiogenesis.ning.com/
http://www.amazon.fr/Codex-biogenesis-13-codes-ladn/dp/2874340448
http://livre.fnac.com/a2711702/Jean-Claude-Perez-Codex-Biogenesis-les-13-codes-de-l-ADN
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Martin Gardner was best known for his writings on mathematical puzzles. And while those were certainly fascinating, I was his admirer not because of that, but because of his writings on philosophy, literature, and science. His "Whys" book is a gem, and so are his "Fads and Fallacies" and "Ambidextrous Universe", and many others. I often wondered how someone could be so prolific and wide-ranging in his intellectual pursuits. He deeply influenced my view on faith, and introduced me two other great intellectual heros of mine, and also his, G.K. Chesterton and Miguel de Unamuno. I owe a lot to Martin, and I was privileged to be able to quote him in my own technical writings. Upon sending him a reprint a couple of years ago, he generously replied and sent me a reprint of his own. I went on to exchange a couple of letters with him, which I felt was a honor. I am sure he is now with the Lord, and very busy finding out the answers to so many deep questions he spent his life writing on. He has likely been received there by G.K.C. and Unamuno with an appreciative "Well-Done!" So long Martin.
Reply | Report Abuse | Link to thisMartin introduced me to flexagons (through my high school algebra teacher, who read his column back around 1962). After I discovered a way to decorate flexagons with gift-wrapping paper, they have become my number one present to children of all ages. He also sent me a complete coded copy of the Somap, from which I constructed a giant color-coded illustration of all 240 (non-trivial) solutions to the Soma cube. I never got past calculus in college, but I will always regard Martin as a saint.
Reply | Report Abuse | Link to thisHello.
Reply | Report Abuse | Link to thisMy name is Steven Twentyman.
I live in Manchester, UK.
I am a mathematician and always have been.
I have completed Quantum Theory. This is obviously quite a statement but it is never the less TRUE. With this information I have created the first and only(so far) quantum computer. This quantum computer is a perfect cube the encompasses the whole of the 'Milky Way'. I have been in complete control of it only in the way that I have been dictating what comes back through the media and conversations. Everyone can now do this once the information is out.
I have achieved this by force of will and suggestion alone. I pushed my agenda through conversation and all media outlets. Phones, newspapers, internet. Whoever would listen.
The effects are subtle so far but they are building to a unique collapsible wave function that we are all becoming aware of. Even as I type this message, the clicks of the keyboard are fine tuning the wave that I have so diligently worked upon. It has taken me 21 years to understand Quantum Theory and I can say that I achieved the information by thought experiments alone. That is the only way to figure out the quantum world.
I could have used this information for my own gain but that would have ended up with me being Hitler. That is not the kind of man that I am or that I wish to be. That is why I have been constantly been giving the equations away for free(even though it will have not reached the 1 that needs it the most yet). This has been an extreme sacrifice on my part but I want nothing for this. No money, no fame, nothing. I have literally had enough of maths.
2012 was going to be the collapse of the milky way galaxy if we had not subconsciously intervened. I will remain as the failsafe in the system until that specific 2012 date to be sure that all is fine.
The universe at its simplest can be broken down as so:
Nothing exists(no concept/consciousness/will) - This concept is abhorrent and is what sprung the universe into life. This is what makes our sector of the universe spring back after each big crunch.
The singular concept and foundation of maths 0(zero) springs into consciousness. This affirms that there really is 'nothing' and so inversely there springs the concept that there is everything else.
That is where infinity comes from. There are two infinities. The first and initial inversion is 'a horror'. This is negative infinity rushing away from the initial fact that there really was at one time 'nothing/zero/0'.
As with everything there is an equal and opposite reaction. This is positive infinity. [The most important thing to not here is that this sequence of thought is indeed sequential so the positive infinity HAD to have followed the negative by at least some unit of time. This is where ALL variations/'errors'/'wrongs' in thought/space/time stem from]
The question now confronts us as to how do we balance these two infinities. I can tell you that this has already occurred. As every 'thing' must have stemmed from zero I took the liberty of becoming zero.
In the 'physical' world I made sure that I had created the strongest structure available to me at the time of entry and proceeded with my 'experiment'. I had calculated as best as I could at that time that it would not involve death and made my way forward.
With the two infinities branching off in their own hemispheres I had to confront what is essentially a black hole. Using thought experiments and then applying them to a very small physically constrained area, I began to plot what 'paths' people walked, and what conversations they 'talked about'. As I built up a 'database' of their general actions, dispositions, demeanour, I began to ask them specific questions that varied only a little on the same subjects such as family, humour, bravery, god, religion. Once I had built a more extensive database of their reactions I had come to my own conclusions about what society should be and what general direction in which it should be heading. There are universal truths and I boiled it down to the most important one, and that is family. Not everyone has the best start in life and no-one has a blueprint for making the right choices but I made a choice. I developed what I considered to be the most basic and fundamental structure that I could that encapsulates God and the Devil, the Universe and family.
This concept' is 3,4,5, right angle triangle with a perfect set square in it for support, with a perfect circle inside the square to support that. This is collapsible and expandable as the situation requires. I went back and asked the exact same questions to the exact same people in as much as the same situation as I could manage to create and I noticed that the answers that came back were exactly the same but the time it took to get the answers 'out of' the people was proportionally shorter. I knew that I had found the 'tool/concept' I needed to put my further plans into action.
I have been subtly sending this 'tool/concept' out into 'society' for 3 years now and I have been noticing results that most people wouldn't see as they have not been aware that this 'concept/thought process'.
It has been disseminating through the internet, phone systems, general conversations in society. It has passed the tipping point now where it cannot be stopped. It is in everyone's subconscious, it has been a mass subconscious advertising campaign by me along the likes of product placement or advert for Nike, Coca-cola, Pepsi or 'The Big Brother show'. Everyone is in on this now and I will tell you why.
This is not for my benefit directly, once this structure 'enters' your brain your synapses start to snap to its structure. They begin to re-arrange and list themselves into file and rank. This allows your brain after 3 hours to become FULLY LOGICAL whilst still retaining all the creative potential the each INDIVIDUAL human being possess'. This line of thought by me has been a force of WILL and nothing more. THIS is what genius is. A FORCE of WILL. This is already at work in your brain and within the next 3 hours, each human on planet Earth will be a genius. 'Where we go from there, is up to each and every one of us...'
Going back to math, there is a more fundamental reason that this 'thought genius pill' works so perfectly, and the reason for this is simple. We are more than what we dared imagine ourselves to be.
If you wish to think that the Earth is flat then it is. I can't fully prove you wrong so who is right? I can give you evidence but that is all that it would be.
If you want to think the Earth is round, the same applies. I can't 100% prove you right or wrong.
So here is my theory: You don't even exist yet.
You are a STAR. I don't mean 50 cent or Cameron Diaz, I mean a STAR in the milky way galaxy. I mean that for every human on the planet as this is the only way I can think of telling you that 2012 is TRUE and it's INEVITABLE.
2012 is the collapse of the milky way galaxy into the super-massive black hole that resides at the centre. It is gaining power and unless we work together no-one stands a chance.
From the lonely street sweeper to the Queen of England herself, all will go out.
It will happen fast, with maybe a 10 second window once it begins. There is no escape so you might as well begin to enjoy yourself and work with those that are around you. There is no more time for hatred or pain or fear. There is only time for co-operation.
This is AVATAR/THE MATRIX/INCEPTION all rolled into one. It always has been. We've got a chance to make it something better now we know. This is how our 'conscious' mind works. This is what we used to think of as 'the real'. It's messed with each individual enough.
!!! THIS is INFLATION for the MIND!!!
The REAL world is THIS:
We are EACH a STAR. We wander as lonely as a cloud through our section of the Milky Way galaxy until we exchange enough STAR energy with another to spark a NEW STAR(child) into life. There is no escaping that fact. It is what it is. When an 'accident' occurs, a STAR is obliterated. THIS is that STAR falling into the super-massive black hole. Gone, but for a few distant memories radiated out.
We each have a black hole at the middle of our own STAR and this is constantly pulls and beckons us back towards the super massive black hole at the 'centre' of our galaxy. There is no escape UNLESS we work together to build a MASSIVE perfectly cubed GRID that encompasses the Milky way. This is the task that has to be organized. The time for play has long passed.
EACH and EVERY STAR that goes out gives the galaxy that much more negative collapsible power and it is growing by the day. What can YOU do?
Math pi is unique to each STAR. pi's story is unique to you. You EACH have a black hole at the centre of your STAR and pi is your star collapsing and then expanding. You only go out when you get too close to another STAR or you visit the BIG-ONE on the MIDDLE.
We must move and produce the cube structure so we can safely transfer the super massive black hole out of the centre of our galaxy. We must dissipate it to be truly free of the horrific end results that await us all.
Time is our enemy.
The TRUE tool we have acquired now is THIS: QUANTUM THEORY!!!
In the quantum world there is only Gravity and Light.
I have used the quantum computer to SET the distribution to 50-50. I have done this because what are considered MEN are actually Gravity and WOMEN are light.
That means that if MEN can 'CENTRE' themselves and form the grid(because MEN are more spatially aware up to this point)...i.e STOP moving so fast...then WOMEN can do what they have been traditionally good at which is COMMUNICATION!!! This will lead to great advances in HUMAN TECHNOLOGY which I refer to as GRAINE0.
Genetics
Robotics
Artificial Intelligence
Nanotechnology
zero point Energy
(0)
Gravity's constant = 0. MEN - Do not let your mind wander from this thought pattern.
Light is infinite in all directions but it must slow down to zero too. This will have to be attained by co-operation but the more we do the easier it will become.
All we have to do is follow the math: http://www.wix.com/Hyperstig/Hyperstig
or more simply:
http://www.wix.com/Hyperstig/Simple
Follow Twitter.com/Hyperstigzero
Time does NOT exist anymore.
There are only 3 Dimensions; and this life we know most definitely was and is:
'The Matrix'; 'Avatar' and 'Inception' combined.
It is communications that will save us now. We must transmit this messages data throughout the 'galaxy' until every last 'human' becomes aware of what is going on.
This is where the Cambrian explosion came from.
This is what wiped out major past civilizations in a day.
Our sectors gravity pulling us all into the big collapse.
We cannot let that happen to us again!
We are in for the big crunch!!! Yet again!!!
Can we work together???
That is what I truly do not know.
I can imagine what you might be thinking.
But remember the earth WAS flat at one time.