The news of Martin Gardner's death sent me digging through my archives—which in my case is a fancy word for messy filing cabinets and cardboard boxes stuffed with decades of detritus. Despite the chaos, I found what I was looking for.It was my privilege to be acquainted with Martin and to have been in touch with him at intervals. Most recently, I was given the task of creating the index to his revision of Silvanus Thompson's Calculus Made Easy. (Check the index for yourself. I sneaked my name into it.) More significant, however, was the opportunity to interview him in 1979, right on the eve of his retirement from the “Mathematical Games” column in Scientific American magazine. That legendary column was a wellspring of inspiration for mathematicians of all stripes, whether recreational, professional, or wanna-be.
The Martin Gardner interview was under the auspices of The Two-Year College Mathematics Journal of the Mathematical Association of America. (The journal continues in existence today as the somewhat sleeker College Mathematics Journal.) The magazine had previously commissioned me to interview Stan Ulam, who was in residence as a visiting professor for the 1979 winter quarter at the University of California, Davis. The journal's editor, Donald J. Albers, liked the result enough to suggest some additional projects, one of which involved Gardner. (The other subject was Benoit Mandelbrot.)
Much of the Gardner interview ended up on the cutting-room floor as it made its transition to printed form. I could not, however, resist typing up a clean copy of the raw transcript for my archives. That is what I went looking for and that is what I found. And that is what I have reproduced below, after a lengthy scanning session.
It is the transcript of a live multi-party conversation, so there are interruptions and sentence fragments, but it is also the complete record of the extemporaneous responses and musings of one of the great expositors of the twentieth and twenty-first centuries.
This is for you, Martin.
AN INTERVIEW WITH MARTIN GARDNER
February 28, 1979
February 28, 1979
Participants
- 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
This is the literal transcript of a six-party conference telephone call. Short portions of the conversation which were lost while changing cassette tape cartridges are reconstructed from my notes and recollection. Bracketed comments inserted in the dialogue occurred at precisely those points in the conversation. Brackets are also used for explanatory interpolations. Ambiguous words or phrases are flagged by a bracketed question mark.
—A. Barcellos
AN INTERVIEW WITH MARTIN GARDNER
February 28, 1979
February 28, 1979
Donald Albers: Peter, you know everyone, so why don’t you take charge of the introductions?
Peter Renz: All right. Martin Gardner is, of course that distant-sounding voice from the east. And, I think, Martin, you know Ron Graham, of course.
Martin Gardner: Sure. Hi, Ron.
Ron Graham: Hi, Martin. How’re you doing?
Gardner: Pretty good.
Renz: And myself. And, you probably know Stan Ulam, but I—
Graham: Yeah. Yeah, we had dinner once.
Ulam: Hi.
Gardner: Yeah, sure, I know Stan. Hi, Stan.
Renz: Good.
Gardner: Is Persi [Diaconis] on the line?
Graham: No, I— Who knows where Persi is? [Gardner: I see. Okay.] He’s in the east as far as I know.
Renz: He’s hard to catch hold of. Okay, and speaking sort of as the interviewer for The Two-Year College Mathematics Journal is Tony Barcellos. Hello, Tony?
Barcellos: Yes, I’m right here. It’s a pleasure, Mr. Gardner.
Gardner: Hi, Tony. Glad to meet you.
Renz: And also the editor of The Two-Year College Mathematics Journal, Don Albers.
Albers: Hi.
Gardner: Hi, Don.
Albers: How are you?
Renz: And I just, as background, would mention that the Journal has interviewed quite a few people, or will be interviewing them. Pólya was their first one. They’ve interviewed Paul Erdős. And Tony just did an interview with Stan; and they’re having an interview with Coxeter, and Constance Reid is scheduled, too. So you’re in good company.
Gardner: Yeah, I’m out of my depths in this company.
Renz: Well, why don’t I turn the chair over to Tony and let him ask a few questions.
Gardner: All right.
Barcellos: Thank you, Peter. Mr. Gardner, we’re going to try to get in your own words a few things about where you’ve come to your present estate and the route you traveled along the way, because we think a lot of people might be interested in knowing how a philosophy student at the University of Chicago finds himself writing about mathematical games and recreations for Scientific American. [Gardner: Uh-huh?] And so first off I’d like to ask you: Do you have any particular view on how this happened? Do you think there are reasons, or is this just a lucky, or unlucky, occurrence for you?
Gardner: Well, it was a combination of a life-long interest in mathematics, without any formal training, combined with just a series of accidents. When I was in high school my great love was mathematics, and that was my high school major—whatever that means. And I planned when I was in high school— My hopes were to become a physicist. And I wrote to Caltech, which was where I wanted to go, and found that I had to spend two years in college first before they would take me. So I went to the University of Chicago, and in my two years there I got hooked on philosophy, especially philosophy of science. So instead of transferring to Caltech I just stayed on at the University and got a bachelor’s degree. And I kept up my interest in math, but I didn’t take any courses in math in college. And then I— After I graduated I got into journalism, and then I spent four years in the Navy. And after my service in the Navy I went back to Chicago for a couple of years and took some graduate courses from Carnap, but didn’t get any higher degree; but it was in the field of philosophy of science. Then I went to New York City to become a free-lancer, and for the first eight years I was earning my living writing for a magazine for children called Humpty Dumpty.
Barcellos: I think I read it.
Gardner: [Laughs] And I did the work at home, but I got paid a moderate amount for it. And I did the puzzles for the magazine. And then I sold to Scientific American an article that ran as a regular article in the magazine on the hexaflexagon.
Barcellos: You just wrote this and sent it off to them, or did someone—?
Gardner: No, I just wrote it and sent it off to them. I had sold them one previous article on logic machines a few years before. And so I queried them about this second piece, explained what the flexagon was, and they said, “Go ahead.” So I made a trip to Princeton and I interviewed John Tukey, who was one of the discoverers of flexagons. And Bryant Tuckerman was also there, and I interviewed him. He—Tuckerman, Tukey, and Richard Feynman were the three who—and there was a fourth man named [Arthur H.] Stone, from England—and they were the four that did the pioneer work on hexaflexagons when they were undergraduates at Princeton. I never met Stone, and I’ve never met Feynman, but I did talk to Tukey and Tuckerman; and then I put together a piece on hexaflexagons. And after that ran in the Scientific American, Gerard Piel, the publisher, called me in and asked me if I thought there was enough material in the field of recreational mathematics to justify a monthly feature. And at that time I don’t think I owned any books on recreational math at all, but I knew that there was a big field out there.Graham: Wow.
Gardner: I said, “Oh, sure, there’s plenty of material. And we’ll go home and do a first column and we’ll take it from there.” I rushed around New York and bought all the major references that I could find—like [W.W. Rouse] Ball’s, for example, and [Maurice] Kraitchik’s book; and started a library. And so I turned in a column which ran in the next issue of Scientific American, and Jerry Piel liked it. And, I must say, this is about the time that [James R.] Newman had just brought out the four volumes of The World of Mathematics, Simon and Schuster. And Newman was the book review editor of Scientific American at the time. And nobody expected that these four volumes would become a best seller, but they did. They really took off and went through innumerable printings. And at that time Simon and Schuster was printing Scientific American books, so we had a close working relationship. So Jerry Piel, the publisher of Scientific American, suddenly realized there was this tremendous market out there among the readers of the magazine, that he thought were interested in mathematics. So it came as sort of a revelation. And so that was the start of my column. It was Jerry Piel’s idea that I do it. And I started it and it overlapped for a few months with my work for Humpty, and I found that I couldn’t do the two together—I just didn’t have enough time. So I dropped out of Humpty, and I’ve been doing the column ever since. And that’s how it started. And I have enjoyed doing it because I love mathematics, and I have a pretty good head for it, in general, on a rather low level. And the fact that I don’t know too much about mathematics really, I think, works to my advantage in the column: If I can’t understand what I’m writing about, why, my readers can’t either. So I’ve kept it going ever since. A lot of readers think I know a lot more about math than I do.
Albers: Can we get back to high school for a minute, where you said your interests [Gardner: Right.] were already quite strong? In fact, in your first Scientific American Book of Puzzles and Diversions you mention, in your dedication, Pauline Baker Perry, “My first guide in the endless labyrinth.” Was that in mathematics or was it in physics?
Gardner: That’s right. She was a mathematics teacher at the high school I went to in Tulsa and I was very—I thought she was an excellent teacher and was, taking courses from her. There was a course in geometry that I took from her. And that was my first introduction to mathematics. And somehow she managed to communicate some of the beauty and elegance of geometry. And I’ve always— She died many years ago, but I always felt [??] And so as I say, mathematics was my major and I made A’s in my math courses; as I say, I had no intention of becoming a mathematician at the time, because my major interest then was in physics.
Barcellos: Can you explain what it is about mathematics that makes you like it so much, or that interests you so much about it?
Gardner: Well, no, not—I can’t say anything different than mathematicians have said before. It’s just the patterns, and their order, and their beauty, and the way it all fits together so it all comes out right in the end. And you get an enormous feeling of satisfaction when you think through a proof or understand something. It’s an exercise in pure reason. Almost all the great mathematicians, when you think about it, said something like that.
Barcellos: What is it that causes you to choose topics now? Do you come up with most of them or are they suggested to you by and large? What mix?
Gardner: Well, it’s hard to say how I choose a topic. I have a lot of things in mind. I have a big file of possible future topics, gathered over the years, that I have in file folders. And I try to pick a topic that is as different as possible from the last few topics; that’s one of my criteria in choosing topics, so that I get a maximum variety from month to month. So if I do a column—let’s say it’s heavily loaded with geometry—in one issue, I’ll try to stay away from geometry in the next few issues, so that there’s sort of a surprise element in the column. And then I try to pick topics that tie in, that are half in the field of recreational math but also lead into what I think is significant mathematics, mathematical topics. So there’s always a big emphasis on the recreational aspect, but I hope that the column gets the reader into something a little less trivial.
Gardner: I think that eventually they were mostly amused, but it came as a tremendous surprise to me and also to the editors of the magazine; because when I turned in the column it seemed inconceivable to me that anybody would take it very seriously. [Laughter]
Graham: Big surprise though. Did you?
Gardner: Yeah. And, of course, the editors of Scientific American didn’t think anybody would take it very seriously either.
Barcellos: I almost sat down and started coloring the thing [5-color map] until I read some of the other “shattering” discoveries and realized that someone was pulling a joke on us.
Gardner: Right. And to the surprise of all of us, why, it drew, I think, a bigger response than almost any column that I’ve ever done. I got several thousand letters on it. And the thing that startled me most about the letters was that I was getting letters from people who took it all seriously except for one item in the column that was in their specialty. For example—
Renz: These are from mathematicians, right? You got letters from professional mathematicians?
Gardner: Well, and physicists—
Renz: And physicists.
Gardner: Yes, for example, I got about a thousand letters from physicists. And a typical letter would start off and say, “I enjoyed very much your column, and you’re doing us a great service by letting us know about these new breakthroughs, but I think you make a terrible mistake in demolishing relativity, because that paradox can be explained.” And then there would follow four or five pages of elaborate diagrams showing why it was not a paradox. Of course, I have even written a popular book on relativity theory, so they didn’t tell me anything I didn’t already know. But what surprised me was that the physicists who wrote me these letters apparently thought it was quite possible that the game of chess had been solved. One of my items was that it had been proved by computers that, I think, that black could always win by opening with pawn to king rook four. And I even exchanged some letters with physicists who told me quite frankly; they said, well, they didn’t know much about chess or about computers, and it sounded very plausible. [Laughter]
Barcellos: Why did you do it, Martin?
Gardner: What?
Barcellos: Why did you write the column? Was there a purpose?
Barcellos: You said that you got letters from all sorts of different people: mathematicians, physicists, and others. What is your readership like? Mostly professional? Mostly high school, college students?
Gardner: Well, I get a tremendous mixture. A lot of mathematicians read the column, and then a lot of high school students read the column. The map-coloring thing drew the most letters, and, as you mentioned a moment ago, a lot of people colored the map and then they sent me the colored map and showed that it could actually be colored. And that, by the way, that hoax, is still going on. About a year ago somebody sent me a clipping from an Australian paper. They had just published the fact that the four color theorem had been proved by Haken and Appel, and then some reader wrote in—and they published the reader’s letter—and said that this proof couldn’t possibly be true because Scientific American had published a map which was a counterexample.
Barcellos: So this will live on.
Gardner: That was about a year ago.
Albers: This has really been a memorable column to you then, certainly. Among your many columns is there anyone or two that you are especially proud of?
Gardner: Well, I always enjoy—since I’m very much interested in philosophy—I particularly enjoy writing columns that get over into philosophical things. And so I think that the columns that I’ve done that overlap with philosophical issues are the ones that I’ve most enjoyed. For example, I did a column a few years ago on a marvelous paradox called Newcomb’s paradox, in decision theory. And that drew an enormous number of letters too. And that’s something that I picked up from Coxeter, and wrote an article on that. And that I particularly enjoyed doing because it’s a very tricky paradox in decision theory, and I’m not sure that it’s even yet resolved. And that drew so many letters that I persuaded Professor Nozick at Harvard, who was the person Who wrote a paper about the paradox, to do a guest column on it. So the following year he did a column for me; as I said, he had done a paper on it. And that produced another flood of letters. I think that’s one of my favorite columns. And then every once in a while I get a sort of a scoop. The last scoop that I got was when I heard about the public cryptograph from Ron Rivest at MIT. And he wrote me a letter about it and I realized what a big breakthrough this was for cryptography, and I based a column on it. And that was the first publication the general public had on public-key cryptography. And I think that column probably aroused more interest—professional math interest—than any other column. The first time they’d heard about it.
Barcellos: Do you get many scoops? Are you very frequently the first person beside the discoverer to know what has just happened in something or other?
Gardner: Oh, no, no. No, that happens very, very rarely, and the Rivest feat was quite an exception; and that was really a significant discovery, I think, on the part of Ron, of course. I have one coming up, that is, another kind of a first publication, and that’s the generalization of tic-tac-toe that was done by Frank Harary. It ties in with Ramsey’s number, but this is more on a recreational level.
Renz: I have a question that runs along the same lines. You indicated that your initial sources were all the standard books on recreational mathematics that you could lay your hands on at the time. But you must have developed other interesting [Gardner: Right.], more arcane, sources; and also, obviously, both a network of correspondents and then also—not only people who write in to you—but people that you might consult with about something or other; something comes along that’s—
Gardner: That’s right. Aside from the books—and I try to buy all those books that come out in the recreational math field—the second big source, of course, are periodicals, and I subscribe to about ten journals that are most inclined to publish stuff in recreational problems and so on. And, of course, there’s the Journal of Recreational Mathematics. And the third big source is just a big correspondence with readers who send me ideas.
Renz: Okay, how long did it, was it, before you, or how did you begin to develop people that, you know, when something came in that seemed interesting but you might wonder whether this was quite right, or what the long and short of it was, in other words, a kind of underground spy network, if you will. [Gardner: Right.] When did you find that developing; very soon, or did it—? Do you have such a thing?
Gardner: Yes, I think it developed very soon. Once the column became popular and the people interested in recreational math started reading it, why, they started writing to me. And then if I replied on my own stationery, why then they could write to me directly, and not have to go through Scientific American. So about half the correspondence I get comes through the magazine and about half I get directly. And then if it’s something that I don’t quite understand, why I rely on mathematicians that I know like Stan Ulam and Ron Graham and so on to give me an opinion.
Barcellos: I’d like to know whether or not you had any thoughts about something you said in Fads and Fallacies quite some time ago. And the sentence I was speaking about was the one where you say “It is not at all amusing when people are misled by scientific claptrap.” Now that was quite some time ago when you wrote Fads and Fallacies in the early fifties. Do you think things have gotten any better or-are people more gullible, susceptible, to pseudoscience than ever before?Gardner: Oh, I think things have gotten tremendously worse in the last twenty years, as far as science is concerned. I don’t observe any great increase in pseudo-mathematics. And I don’t know why that is. There are always people around who are trisecting the angle and things like that and, of course, I hear from them occasionally; but I haven’t noticed any increase, in the last fifteen or twenty years, in the number of pseudo-mathematicians. But the interest in pseudoscience on the part of the general public has been on an incredible rise for the last few years. I’m not sure I know exactly why. But this gets away from mathematics in the direction of pseudoscience. I don’t know whether you want to go into all that or not.
Renz: Well, in terms of your writing activity, is it something that you ever had any inclination to return to, I mean, to strike another blow directly against—?
Gardner: Well, I’ve often thought of doing a sequel to Fads and Fallacies—a volume that would sort of update it, but I didn’t have enough time to do it. I don’t know if you’ve all heard about John Wheeler’s blast at the AAAS. You’ve all heard about that? [No.] Because this is the first time, I think, that a really major scientist has taken a strong position on the rise of pseudoscience. And it’s kind of amusing. Wheeler was, as I understand it, and this comes to me directly from friends— Wheeler had been attending a conference in Switzerland, and he was speaking on the subject of quantum mechanics and consciousness. And a parapsychologist from France rushed up to him afterward and embraced him and said, “I’m so happy, Dr. Wheeler, to learn that you think quantum mechanics provides an explanation for psychic phenomena.” And poor Wheeler was taken aback and realized for the first time that the papers that he’s been writing on quantum mechanics had been picked up and misinterpreted by the parapsychologists, and that they were quoting him all over the place as justification. The most popular view now among the parapsychologists views quantum mechanical phenomena as related to parapsychology. So when Wheeler got back and attended the AAAS conference in Houston and found himself on the same panel with Puthoff and Targ of SRI, who lectured on their clairvoyance tests; and Charles Honorton, a parapsychologist from Maimonides. And so he really gave a strong statement which appears as an appendix to the paper which started out by saying that if he had known that they were on the panel he wouldn’t have come. And then he goes on to recommend that the AAAS have a new vote to decide whether the parapsychologists should remain an affiliate of the AAAS, and he said that when Margaret Mead had first recommended it ten years ago he had voted against it. And in the ten years since that the situation had gotten so much worse, and funding was being diverted now into crazy theories. And he pointed out that we now have two thousand professional astronomers whereas there are twenty thousand professional astrologers. So he thought it was time for the AAAS to reconsider whether the parapsychologists should have a special affiliation with the organization. And he’s made a formal request for a new vote. I don’t know how that will turn out. But he had a marvelous subhead for his appendix which reads “Where There’s Smoke There’s Smoke.” [Laughter]
Barcellos: When I found out that I was going to get to talk to you, Mr. Gardner, I asked some of the mathematicians here at UC Davis whether or not they’d like to ask you any questions in particular. Sherman Stein wants to know if you think mathematicians are doing anything wrong in their public relations and whether or not you know of other scientists or disciplines that do it better, so people out there know what we’re up to.
Gardner: Well, that’s a tough one, because almost all the really exciting research going on in mathematics is not the sort of thing that the public can understand. It takes considerable knowledge of mathematics to know what the breakthroughs are. And the really big breakthroughs that take place are just—it seems almost impossible to put it in terms that the general public can understand, whereas big breakthroughs in biology and so on are popularized, I think, fairly easily. So I really, I really don’t know what could be done that would improve public relations more. Certainly mathematicians like Sherman Stein have done a marvelous job of doing popular articles on the subject, and books that the layman can read and understand. But I really don’t know what could be done that isn’t already being done.
Ulam: Well, I think that you, Martin, do that. In fact, you know, yesterday Ron Graham gave a marvelous, really interesting lecture about some esoteric question; and I was wondering during it, Well, the question sounds very complicated, why devote so much ingenuity? Then I remember what, I think, Fourier or Laplace wrote: That mathematics—one reason for its being—is to defend the honor of the human mind. And I think your column does it, defends the honor—maybe [Gardner: Why, thank you.] also the sense of humor—of the human brain, in mathematics. This is possible.
Gardner: Well, it would be good if other science magazines would run similar columns on mathematics, and perhaps they will. Right now Time magazine is making preparations for a new magazine devoted to science; and there’s a good probability that it will go through, edited by Leon Jaroff. And I think he’s planning to have some sort of a department devoted to reporting on mathematics; and if so, why that would be good.
[End; Side I]
Renz: Will this be a magazine along the same lines as Omni?
Gardner: No, it won’t be at all like Omni. It’s going to be a much more serious science magazine—same kind of popular presentation, but a little more responsible. The dummy is being prepared now, and then after the dummy is completed and printed the decision will be made as to whether it will become a monthly or not. And that’ll be made probably in spring. I hope it goes through, because I think Leon Jaroff will do a very good job on it, and it’ll fill a place that should have filled but I don’t think quite does it because Guccione is pressing for more and more emphasis on the paranormal. And I think that the magazine is going to have more and more of that in it. For example, the March issue has a horrendous article about how three psychics found a sunken ship somewhere. It’s just pure pseudoscience—presented as genuine science.
Barcellos: If perhaps the scientific community made a greater effort to tell the public what they’re up to and What’s going on, do you think perhaps increased public relations would make people more appreciative of what science is as opposed to what is being ladled out in—?
Albers: It seems to me you’re saying there’s a responsibility to know what the opposition is up to that scientists have perhaps ignored.
Gardner: Yeah, I think so. The other day I was reading some old essays by T. H. Huxley, for example. And I have a book of Huxley’s collected essays, and I noticed that quite a number of them deal with what he regarded as pseudoscience of the time, and has the word “pseudoscience” in the title. And Huxley, who, as you know, was one of the great popularizers of science, and not only a good geologist and biologist, but a very skillful writer. And he wrote quite a number of articles in his day that were specific exposes of attacks on the theory of evolution, and other kinds of pseudoscience floating around at the time.
Renz: Martin?
Gardner: Yeah?
Renz: Martin, I wonder if you could mention some of the books or magazines or columns which you think would be of—well, that not everyone might know about that you think are particularly attractive to people who are interested in, say, recreational mathematics, or learning more about mathematics.
Gardner: You mean columns that I’ve written?
Renz: No, no; well, I was thinking of—
Gardner: Oh, you mean—
Renz: Further reading kind of—
Gardner: Oh. Well, there are a number of classics in the field. Certainly the great English classic is Ball’s book on recreational math, Essays in Recreational Mathematics. Is that the title? [Renz: Uh-huh.] And Kraitchik’s book on mathematical recreation—another classic, in English. And then Kasner and Newman did a marvelous job of popularizing modern mathematics in their Mathematics and the Imagination; that’s not so much recreational math although they have some in it. But it’s just a very exciting and well-written survey of certain aspects of modern mathematics which were made clear to the reader, and I think that was a very enlightening book. And there are quite a number of others: Honsberger has written two books called Mathematical Gems that I think are excellent.
Albers: He’s doing a column for us, too.
Gardner: For who?
Albers: For The Two-Year College Mathematics Journal. [Gardner: Oh, really?] Called “Mathematical Gems.”
Gardner: Uh-huh. Oh, very good.
Graham: He has a third book: Mathematical Morsels.
Albers: And a fourth one in preparation.
Gardner: Oh, really. I didn’t know about that.
Graham: Yeah, Morsels now is out.
Albers: Mathematical Plums is on the way.
Renz: We’re going to continue in this gastronomic way?
Gardner: Yeah. Uh-huh.
Albers: If we as teachers are involved, in a way, in an on-going public relations effort with our students, what advice can you give to teachers of mathematics to make the subject more interesting, to have them leave the classroom with warm feelings about the subject?
Gardner: Well, I can only repeat what I’ve said before in some of the introductions to some of my collections, and that is, I’ve always felt that if a teacher can introduce what I call recreational math—and I’m defining it in the very broad sense to include anything that has a spirit of play about it—that I don’t know of any better way to hook the interests of the students than to throw in this kind of material. And I think that up until a few years ago the teachers were sort of unacquainted with the whole field of recreational mathematics, and now I think they’re beginning to discover that it does have pedagogical value. And the proof of it is that Mathematics Teacher Magazine, for example, is running more and more articles in the field of recreational math. And successful textbooks like Jacobs’ Mathematics: A Human Endeavor, published by Freeman, are heavily loaded with recreation. And writers like Donald Knuth, who wrote a marvelous new book about computer programming; you’ll notice that he throws in as much recreational material as he can. And so I think this is a rapidly developing approach, and I think you can do a lot in a couple of years. Because if they don’t make mathematics to a certain degree “fun” to those first coming to it, the students are so bored that they get turned off by the topic, especially if the teachers are dull teachers.
Albers: Do you think that will sell better than the “applications” bandwagon that people are trotting out now? Everyone is talking applications, applications, applications.
Gardner: Well, no. I think the two should go together. And I think that’s a big part of it, too. And the two should somehow be combined. I certainly don’t think that a teacher should spend all the time on puzzles and recreational math, of course; then the whole thing will become trivial. But the applications— If the math can be applied somehow that’s useful in the child’s experience and things can be introduced so they’re challenging and have a play aspect, why, I think the two sort of go together. And, of course, we’re entering a revolution now in which everybody’s going to own a pocket computer and a programmable computer. And so this is another important aspect of the whole thing. And the kids love to work things out on a programmable computer. So I think that if the applications in math and the recreational aspects of math are tied in with computer programming then that will do a lot to get to the students.
Barcellos: You’ve had occasion, writing your column and working on puzzles and the like, over the past twenty-five years to be an observer of what’s going on in mathematics and math education. You mentioned the advent of pocket calculators and the revolution they should be, and apparently are, creating. What changes have you noticed over that particular time in mathematical tastes and interests?
Gardner: Well, there’s certainly a tremendous interest now in computer games. And especially games that can be played on a scope that is tied up to the computer; and I think that’s a very rapidly developing field, especially as the programmable computers are coming down in price. And, as you probably know, this is the big trend in modern games. The big field in games now is no longer the board game, played with counters on a board. All the games that are selling very well now are electronic games that involve some type of computer. And so I think that this is a rapidly developing field. And more and more books are coming out on computer game playing. Well, what else can I say about it? At the same time it is true that a lot of students are forgetting how to do ordinary arithmetic.
Barcellos: I guess this is where we ask you about the New Math and let you speak your piece on it.
Gardner: Yeah. And that’s unfortunate, and, of course, if— That’s one of the dangers of having a pocket calculator, is that you forget how to do ordinary arithmetic. And I suppose it’ll all work itself out. But I had this brought home to me very recently. I had a problem in a column a month or so ago; I had a collection of short columns and one of the problems was to arrange the integers in such away that the first two numbers were divisible by two, and the first three numbers divisible by three, and the first four numbers divisible by four, and so on until the final number was divisible by nine; and you were to use the nine positive integers. And it has a unique solution. And I have received, I think, now about between two or three hundred letters from readers that all say that “I read that it had a unique solution, but I have found two more.” And then they all list the same two “solutions,” and none of them have the first eight digits divisible by eight. And this had me enormously puzzled, until suddenly I realized what had happened, and that is that they were all using small pocket calculators that had an eight-digit read-out. And so they got as far as eight, and When they divided by eight it didn’t show any remainder so they went off— [Laughter] And I have hundreds of letters from readers who say “What about these two numbers?” And they all list the same two numbers and not one of them bothered to divide by eight by hand. And, of course, I have a little piece coming out in the column about it, a little paragraph pointing out that there’s a simple divisibility rule: that if the last three digits of a number is divisible by eight, why, so is the number. And none of them knew that, which means that no one has taught them divisibility rules during basic arithmetic; otherwise, they could have divided by eight very quickly. But that’s an example that brought home to me how easy it is to rely on a pocket calculator and not do any work at all.
Albers: Well, make a mistake in this case.
Gardner: Yeah, in this case they even wrote a letter about it without bothering to do the division by hand. And apparently, and without even being aware that their pocket calculator didn’t show a remainder if they were dividing an eight-digit number by eight.
Albers: Hmm. How is that going to get sorted out in the—?
Gardner: I don’t know. I think in the long run though it’s going to turn out the pocket calculator is a blessing rather than otherwise, because it does free one from the drudgery of doing ordinary arithmetic. And if the students are interested in math at all, why, it’ll help more than it slows them.
Barcellos: By now you probably have, well, you’ve seen many open questions in mathematics, and I was wondering if you had a small collection, a select group, of open problems you would really like to know the answers to. Are there some specific questions that have seized your imagination, you would really like to know the answers to?
Gardner: Well, yes. Of course, there are a lot in every field of mathematics—that are open questions. Nothing comes to mind right now as the outstanding one. Ogilvy wrote a rather interesting little book about it, one called Tomorrow’s Math, dealing entirely with unsolved problems in math. And, of course, Ulam’s little book on problems contains all kinds of unsolved problems.
Albers: But would you urge him to get that reprinted?
Renz: How about a new book?
Albers: Or a new one.
Gardner: Yeah, or a new one.
Albers: Yeah.
Graham: He’s working on it, right?
Ulam: Yeah.
Gardner: Oh, very good. Ogilvy finally did a revision of his book. The second edition came out and is updated and it reports on problems that had been solved since the first book came out. But, oh, yes, there are problems all over the place that are unsolved; and some of them are very simple to state.
Barcellos: Peter reminded me before we started this discussion that you started out, and, in fact, still are, a writer principally; and at the present time you write mainly about mathematics, recreational mathematics. But you’ve ventured apart from that; for instance, Fads and Fallacies. And you’ve even tried your hand at a novel. Are you Peter Fromm?
Gardner: Well, you must be one of the thirteen people who read that novel.Barcellos: Oh, it must be fourteen now; Sherman told me it was thirteen last week.
Gardner: Oh, I see. Well, yes, basically that’s sort of an autobiographical piece. And I never went to theological school and Peter Fromm has a different personality [Barcellos: Right.] from myself, but basically the novel is about the changes that I went through when I was a freshman and sophomore in college. Because I came from a family that was orthodox Protestant family in Tulsa—especially my mother, a rather devout Methodist. So— And Tulsa is the fundamentalist capital of the world, home of Oral Roberts and so on. So I went through a Protestant fundamentalist stage when I was in high school, and I quickly got over it in college. And so I drew on that experience when I wrote the novel. But you’re right, the stages that Peter goes through in that novel are sort of roughly the way I thought myself out of the situation. So in that sense it’s autobiographical.
Albers: So there was a dramatic shift there in moving from high school to college. In high school you were still thinking about doing physics seriously and continuing with the mathematics that would be needed to do physics, and yet when you went to Chicago you did not enroll in a freshman math course, if I understood you correctly.
Gardner: That’s true, I didn’t. Well, there really wasn’t much opportunity to in the first two years. Because when I was in Chicago they had just instituted what they called the “New Plan” under Hutchins; and the idea was for the student to get a general liberal education the first two years, and so there really wasn’t a chance to take any introductory math courses. You had a little math that was part of your science courses, and professors of math would come in and lecture as part of that theory. So the first chance to really take a math course would have been the third year, and by that time, why, I had decided to major in philosophy, so I concentrated in that area. But that was— The other big change was, of course, that I got over my Protestant orthodoxy in college. I finally got it all off my chest in that novel.
Barcellos: Was that the purpose of the novel, just to express it, even though no one apparently is much listening to it?
Gardner: Well, yeah, actually I really, when I started out freelancing, I started out writing fiction and that was what I most wanted to do. And when I got out of the Navy and went back to Chicago, I had been in public relations work before the Navy and—at the University of Chicago—and the only reason I didn’t take my old job back was that I sold a short story to Esquire magazine. And this was followed by a series of stories, so I was supporting myself for about the first two years, ‘46 and ‘47, by selling fiction to Esquire. And I had about a dozen stories published in the magazine. It was during that period really that I wrote the first draft of this novel, and I found it to be totally unsalable. And so I just put the thing on the shelf, and it was when Bill Kauffman, who had formerly been with W. H. Freeman, came out to see me one day and asked me if I had any manuscripts lying around that I thought of this thing; and I pulled it out and let him see it. It was in pretty rough shape and it had been written, oh, twenty years earlier. And he said he would publish it if I revised it. So that’s how that got published, an old novel that I had written way back in my youth. And then I just rewrote it, and sort of updated it.
Albers: Do you have another one in the works?
Albers: What kind of writing program do you have? Do you discipline yourself to so many hours per day, in working on columns and various books?
Gardner: No, I don’t have any rigorous schedule. I just put in the equivalent, I suppose, of about a typical eight days’ work writing. The only thing is that if I take a day off it doesn’t have to be on the weekend, it can be in the middle of the week—a very flexible schedule. I don’t have any set hours that I sit down and work. I work when I can find the time.
Barcellos: I’ve been hearing things suggesting that you might not be writing the column for Scientific American the—
Gardner: Well, that’s true. I’ll be sixty-five in October and eligible for retirement benefits. Even though I contribute on a free-lance basis, I’m actually considered on the staff of the magazine, so I’m eligible for their health benefits, retirement benefits, and so on. So I have an option to resign from the column in October, and I also have an option to continue it; in other words, it’s not a forced retirement. And I just haven’t made up my mind yet. And I don’t know quite how to work it out, because if I could stop doing the column I would have time to do books that I would like to do and that otherwise I can’t do. For example, this book of philosophical essays, I’ve been trying to work on that for the past two or three years, and I seem to get to work on it about two days a month, and at that rate I’ll never finish it.
Barcellos: Well, I believe Scientific American might have some qualms about letting the column evaporate. Would—?
Gardner: Oh, they would continue the column, and they’ve asked me to continue, and I don’t know quite how to work it out. I think that my only suggestion was to have—that it might be good to have it replaced by a column that would emphasize computer recreation, because that’s a really growing field. But I don’t know who would be a good person to do that. And then there might be a compromise in which maybe I would do, alternate, columns with somebody who would alternate columns more on the computer side. Because the whole computer field is breaking very, very rapidly, and it’s a field that I don’t know too much about. And that would—I wouldn’t even be competent to do the kind of column that I think ought to be done in that field. I mean it should be done by someone trained in computer science and knows how to take recreational-type problems and games, and program, and so on. Up until now I don’t think it would have had a big readership, but I’m thinking that it would have in the next four or five years. And that’s the only thought I’ve had on it.
Albers: I’d hate to be in Scientific American's boots when it comes to trying to find a successor to Martin Gardner, and that raises another question of sorts. From what you said you kind of drifted into doing this column, and I wonder [Gardner: That’s right.] if, now that a few years have passed, you might have done anything differently. You know, the traditional, “How would you do it if you could do it over again?”
Gardner: Oh, I don’t have any regrets about doing the column, because I’ve enjoyed every column that I’ve written. And also the success of the column has made it possible for me to sell books in other fields that I don’t think I could have sold otherwise. So it’s just a question of whether I want to go on for the next ten years writing the same kind of thing, or whether I shouldn’t at this point stop the column and get into the things that I want to write while I still have my wits about me.
Ulam: If I may interrupt, I will say that’s almost an hour about mathematics but we could spend another hour dealing from your—about the other marvelous things you’ve done in physics, relativity, articles and books, and also Annotated Alice, and so on. That is entirely different. You haven’t mentioned it yourself. That’s marvelous.
Gardner: No, but I would like to do more books of that sort, too. And it’s just very, very difficult to do them and keep the column going. And each year the column gets more and more difficult, in a way, to do because my correspondence on it increases.
Barcellos: Do you do it all yourself? Do you have any assistants?
Gardner: No. I do it all myself. My wife proofs it for me. That— I guess that helps. She’s a very good proofreader, so she does check it over for grammatical errors and spelling and things like that. And otherwise, I, no, I’m— I type fast; I was a yeoman in the Navy.Renz: You did yeoman service.
Gardner: Yes, so it’s faster for me to type than to dictate anything, so I do all my own typing.
Albers: Excuse me for breaking in here. My students are waiting for me. [Barcellos: Yes, Don.] And I will step out and just let me say on behalf of the Journal how delighted I am that you’ve been willing to talk with us, Martin.
Gardner: Oh, well, thank you very much.
Albers: Bye-bye. Thanks all of you.
Barcellos: Thank you, Don.
Gardner: So long.
Barcellos: I think that as a novice interviewer with such a good backup here, with Graham and Ulam—and Peter’s still on the line—that I should circulate around, Ulam did mention your other projects, and I have this one question here: What are your greatest interests apart from math? I’d like to know what the other people here on the line would like you to mention or speak on before we wrap this up.
Operator: This is Menlo switchboard. Dr. Albers’ line has hung up. Are you still speaking with him?
Barcellos: No. You may turn his line off.
[End; Side 2]
Renz: I think Stan’s last remark turned the conversation, the interview, in a good direction. And I think that for your readers it would be nice to mention these other things that Martin has done. I think I have a list of some of them.
Gardner: Well, The Annotated Alice, of course, does tie in with math because Lewis Carroll was, as you know, a professional mathematician, and that was why I— And as you know mathematicians are all into Alice books because of all the mathematical references. So it wasn’t really too far afield from recreational math because the two books are filled with all kinds of mathematical jokes. So I was lucky there in that I really didn’t have anything new to say much in The Annotated Alice, because I just looked over the literature and pulled together everything in the form of footnotes in the book. But it was a lucky idea because that’s been the best seller of all my books. It far outsold any book that I’ve done on any other topic. And it’s surprising. I really don’t know quite who buys it, but for the last four or five years it’s been selling each year better than the previous year.Barcellos: I have one.
Gardner: Yeah.
Renz: So you’re saying— I think, I think we have one at home. I’m sure I do. Yeah. My wife bought it.
Gardner: And it’s funny because it’s not an original book. It’s just a set of annotations of two books by Lewis Carroll.
Renz: Let’s see, and you annotated The Snark? Is that right, too?
Gardner: Yeah, and I later did The Snark, but that didn’t do too well. However, Bill Kauffman is bringing out a new edition of that, hopefully, this year.
Barcellos: And The Annotated Casey at the Bat, what prompted that?
Gardner: Oh, well, I have always been interested in the fact that there are poems that are not great poetry, but that seem to outlast the entire poetic output of poets that are very famous in their day, and, I guess, the best term for them is popular verse. They don’t pretend to be great poems, in the sense of a poem by Keats, for example; and yet a single poem written by an individual like Thayer, who wrote Casey at the Bat—and that was the only poem he wrote that was of any value; he wrote other poems, humorous poems, too, but none of them are remembered. And yet here is a poem that goes on and on and on, and everybody knows about it, and it’s created almost a mythology and will probably be remembered after everybody’s forgotten every poem ever written by, say, Ezra Pound. And so this has always struck me as a very curious phenomenon: that a poet could write one poem, one single poem, and the poem would go galloping down through the ages, and everyone would memorize it and remember it even though it had no great value as poetry. So I did an article about this that I sold to Sports Illustrated. That was how it started: I did an article on the history of Casey at the Bat. I was just curious to know who Thayer was, and I found it a fascinating story. And after that appeared it occurred to me that I might put together an anthology or sequels to Casey. And so that’s what the book is. It’s a collection of the original poem with sequels by various other people like Grantland Rice, the sportswriter, and so on. And then I annotated all the poems with sort of fake annotations to sort of tie them all together in a connected story. And the book is done as a kind of a joke. That didn’t sell too well either.
Renz: How about things in physics like your Ambidextrous Universe?
Gardner: Well, The Ambidextrous Universe was great fun to write, and I’m happy to say that Scribners is bringing it out in a new edition this month with four new chapters. Because when the book came out all the work on time-reversal was too late for me to catch, so the original book doesn’t have anything in it about the recent work that’s been done on time symmetry. So this gave me a chance to write four new chapters that deal with speculation about time-reversed galaxies and that sort of thing, and that’s— It’s off the press, but not officially published yet, and I have no idea how they’re doing it.
Barcellos: How about the magic?
Gardner: Well, it’s just been a minor hobby of mine ever since I was a boy. I never did anything professionally with it. I’ve always been interested in the field. I’ve written some books that sell only in magic stores. It just happens to be my hobby, like juggling is for Ron Graham.
Barcellos: You are affiliated with a group of mathematicians, magicians, scientists, who are debunkers, right?
Barcellos: What is the initial response? Is it encouraging?
Gardner: Yes, I think so. I think that the membership of the committee has been growing and the circulation of the magazine has been increasing. It’s being very well edited by Ken Frazier, who used to be the editor of Science News magazine. And I think it’s doing very well considering the fact that it’s only about a year or so old and we haven’t had too much publicity about it.
Barcellos: I think I know, but let me ask you. [Gardner: Yeah.] What do mathematicians— What do magicians do in the organization? Why would magicians be interested in this?
Barcellos: I don’t see the evidence that Geller has been discredited in the public mind. Do you think that he’s out of favor with the scientific community in general now? Is there anyone—?
Gardner: I think Geller is very much out of favor even among the parapsychologists right now. I think it’s finally filtered through to them that the guy is a magician. And I don’t know of any major parapsychologist today who takes him seriously.
Renz: What about the mathematical side, so to speak, of this parapsychological research? Certainly Persi Diaconis’ recent article and others have tackled [Gardner: Yeah.] this. It seems to me there are very substantial, interesting problems even beyond that of detecting outright fraud.
Gardner: Yeah, that’s right. All in all there are all kinds of fascinating problems involved in the statistical aspects of the work that they’re doing. By the way, I have a column coming up in a couple of months on magic and parapsychology, in reference to the piece you said Ron did with Persi [Graham: Uh-huh.], referring to the Stanford Technical Report bibliography and Persi’s Science article. So I’m going to do a column that will sort of discuss this whole aspect of contemporary parapsychology, and the need for a more sophisticated understanding of some of the statistics involved.
Gardner: No, not particularly. I think most of my readers were on my side there. I got some angry letters from parapsychologists, especially from Puthoff who was very—
Renz: He was somewhat put off. [Laughter]
Gardner: Right! Absolutely. He didn’t like it at all. But, I don’t know, the forces that are involved in making the public interested in this field are so deep, deep-seated, that articles on the other side seem to have almost no effect. So I really don’t know how well the skeptical side is doing. I just really can’t say.
Renz: Just to cheer you up, I noticed that some national poll indicated that something like 70 percent of all high school students interviewed believed that ESP was a proven fact.
Gardner: Absolutely, there’s no question about it. [Laughter] I mean, that most people believe that. And they really— If you try to tell them that 99 percent of the professional psychologists around the country take an opposite position, they can’t believe it. And it’s an example of how successful the campaign has been in the public media as compared with the efforts of the psychologists themselves to get their view across. They see these pseudo-documentaries on NBC, for example, in which these things are treated as though they’re genuine scientific breakthroughs. It just never occurs to them that the professional psychologists have a totally different attitude.
Renz: Do you feel that programs like—what is that thing?—is it “In Search Of,” or something? [Yeah.] Is it that they really are seriously undermining public understanding in these areas, or seriously misleading people?
Gardner: Well, I think they are. Of course, our committee has had a number of conferences with some executives at NBC, and their claim is that they’re simply responding to public interest. And I’m sure that they’re right; I mean, they’re going to do programs that are going to get high ratings. But then you get this feedback in operation, and that is when they respond to public interest with programs like the ones that they’ve been putting on, especially the one narrated by, one was narrated by Burt Lancaster [“Exploring the Unknown,” (1977)], for example, which was one of the worst.
Barcellos: What was that on?
Gardner: Oh, it was a documentary on all the new big breakthroughs in psychic phenomena, the Philippines and the surgeons in the Philippines, and all that. [Barcellos: Oh, my.] With pictures of them operating and taking parts out of the body without cutting the skin—that was one of the worst sections of the show—and all narrated by Burt Lancaster as though these were serious scientific breakthroughs. And they’ve done several, they’ve presented several documentaries of a similar sort with some famous movie star doing the narration. And so this— The public, of course, demands such films, but then when they’re produced, why, it just increases the demand and increases the belief on the part of the general public who are isolated from the science community. And I think it’s damaging to American education and damaging to American science.
Barcellos: Is there anything to do besides continuing to complain?
Gardner: I don’t know. I really don’t know what can be done about it except the occasional articles by people like Sagan who present the other side and the existence of our magazine which is now available to editors; and hopefully, if the magazine comes out. Leon Jaroff is a member of our committee, by the way, and feels very strongly about this whole thing, so it not only will be, in contrast to Omni, completely free from any emphasis on the paranormal, but Leon may even have a department devoted to giving the skeptic side of current paranormal topics.
Graham: Perhaps “Nova” should do something on public television.
Gardner: Well, it would be good. I think there is plenty of room for programs like that. And occasionally there are programs like that. There was one very good documentary on the Bermuda Triangle from the skeptical point of view that I think “Nova” did. And I thought it was very effective. But it’s very hard to get the major networks to back such programs or to get funding for them because the public is interested in the other side of the story.
Renz: So you would say that the PBS programs or your column on Puthoff and Targ’s work and so on, these are essentially preaching to the converted, or all the skeptical—should we say?—the already skeptical. [Gardner: Yeah.] And therefore that’s not as constructive as you would hope, although I certainly think your article on Puthoff and Targ, your column on Puthoff and Targ, was superb—the best kind of thing we hope for.
Gardner: Well, one program that hopefully will get off the ground in a year or two is the Children’s Workshop Theater. They’re the ones who produce “Sesame Street.” And they have finally gotten funding for a program dealing with science for children; and this will be a daily program and they’re working on it now. And I think that the people who are involved are going to be very careful to keep pseudoscience out of the program, and present it from the other point of view. And if they can do a very successful children’s program on science, I think that would be very effective.
Renz: Have you any interest in contributing, or consulting?
Gardner: Well, I was involved in some of the meetings. Phil Morrison and I were invited to some discussion groups about the program a year or so ago, about the shape it’s going to take. I wasn’t able to go to the last one. So I’m sort of involved as kind of an advisor, and I’m hoping that it’s going to be free of pseudoscience, although one of the advisors present at the meeting was the dean of the engineering school at Princeton University—a man named Jahn, J-A-H-N—and to everybody’s surprise he has suddenly become a new convert to parapsychology; and he has had a big article on his replication of the [Barcellos: Oh, my.] mind-viewing, remote-viewing experiments of Puthoff and Targ that ran in, of all things, the Princeton alumni magazine a few months ago. And the latest news is that Honorton, Charles Honorton, a top parapsychologist at Maimonides, he’s getting most of his funds from an elderly individual named McDonnell—not of MacDonald hamburgers. He owns a chain of fried chicken stores, I think, around the country, and a very wealthy man. He’s in his eighties. And he gave a whopping sum of money to Honorton, and he’s leaving Maimonides and—and teaming up with Dr. Jahn at Princeton; and they’re going to have a parapsychology laboratory in the engineering school at Princeton.
Barcellos: That must be a bit discouraging.
Gardner: So that’s a little discouraging. And Jahn is one of the major advisors to the Children’s Workshop Theater. So I don’t know how that’s going to work out.
Renz: Well, we’ll certainly expect to see some good effects. [Laughter] Let’s see, are there— We’ve been— Are there any things that we’ve failed to bring up?
Barcellos: I’ve gone through my entire list, Peter. I don’t know if Stan or Ron has something more that—
Graham: I think we’ve covered quite a spectrum here.
Renz: Well, I guess I was really asking Martin if there was something that—
Graham: Lehmer has not yet checked it. [Gardner: Oh.] But they were scheduled to hold— This is 23209, for the exponent. [Gardner: Yeah.] They had scheduled a [Gardner: Right.] press conference last week. That is, Curt Noll had called up and said he wanted one, but the press canceled it and said it would be held next Thursday, which is, I guess, tomorrow. And Lehmer hadn’t had the chance to verify it. I think his total computer budget right now is fifty dollars—and it doesn’t go far these days.
Renz: Does he need contributions?
Graham: Well, so he’ll verify it, I think, in the same way. I don’t think Tuckerman has verified it although—
Renz: Yeah, Tuckerman’s evidently not free to do so, or something like that.
Graham: Well, he did the other one although at first he said he wasn’t going to [Renz: He did the other one?], but then he did. [Gardner: Uh-huh.] But Lehmer just gets some of the output near the end and then continues it to see that it works out.
Gardner: I see.
Renz: Checks the last few stages.
Gardner: I see.
Graham: Yeah. Yeah.
Gardner: So that’s not really definite yet.
Graham: Well, it hasn’t been independently verified yet.
Renz: But that program worked before.
Gardner: Uh-huh. Okay, well, I won’t report that news to any of my friends yet, till I hear that it’s verified.
Renz: Okay, we’ll drop you a card as soon as we get—
Barcellos: Well, is there anything else then we need to attend to?
Gardner: Well, I can’t think of anything.
Barcellos: Nothing to volunteer. Well, I thank you very much for your time, Martin. This has been an exquisite pleasure for me.
Gardner: Well, I’ve enjoyed the conversation and thank all of you for taking the time to be on the phone with me.
Barcellos: We’re glad that you took the time to be with us.
Gardner: Yeah.
Ulam: I beat my own record by a factor of five, or four. [Laughter]
Graham: Okay.
Gardner: All right.
Graham: Okay, well, I’ll probably see you in the next month or two.
Gardner: Okay, Ron, very good.
Graham: Okay.
Gardner: So, so long everybody.
Barcellos: All right, good-bye. Thank you very much, Martin.
Gardner: Bye-bye.
[End of Interview]
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