The Annotated Alice, of course, does tie in with math, because Lewis Carroll was, as you know, a professional mathematician. So it wasn’t really too far afield from recreational math, because the two books are filled with all kinds of mathematical jokes. I was lucky there in that I really didn’t have anything new to say in The Annotated Alice because I just looked over the literature and pulled together everything in the form of footnotes. But it was a lucky idea because that’s been the best seller of all my books.

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?

Although Lewis Carroll thought of The Hunting of the Snark as a nonsense ballad for children, it is hard to imagine—in fact one shudders to imagine—a child of today reading and enjoying it.

As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.

As I have often said, electrons and gerbils don’t cheat.

Bad science contributes to the steady dumbing down of our nation. Crude beliefs get transmitted to political leaders and the result is considerable damage to society. We see this happening now in the rapid rise of the religious right and how it has taken over large segments of the Republican Party.

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals—the flotsam and jetsam of historical currents. The men who radically altered history, the great creative scientists and mathematicians, are seldom mentioned if at all.

Chess combines the beauty of mathematical structure with the recreational delights of a competitive game.

Consider a cow. A cow doesn’t have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain’s ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.

Debunking bad science should be constant obligation of the science community, even if it takes time away from serious research or seems to be a losing battle. One takes comfort from the fact there is no Gresham’s laws in science. In the long run, good science drives out bad.

Ever since I was a boy, I’ve been fascinated by crazy science and such things as perpetual motion machines and logical paradoxes. I’ve always enjoyed keeping up with those ideas. I suppose I didn’t get into it seriously until I wrote my first book, Fads and Fallacies in the Name of Science. I was influenced by the Dianetics movement, now called Scientology, which was then promoted by John Campbell in Astounding Science Fiction. I was astonished at how rapidly the thing had become a cult.

I believe that the human mind, or even the mind of a cat, is more interesting in its complexity than an entire galaxy if it is devoid of life.

I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.

I don’t know whether there is a finite set of basic laws of physics or whether there are infinite sets of structure like an infinite set of Chinese boxes. Will the electron turn out to have an interior structure? I wish I knew!

I have recently read an article on handwriting and forgeries in which it is stated that ink eradicators do not remove ink: but merely bleach it, and that ink so bleached can be easily brought out by a process of fuming: known to all handwriting experts. Can you give me a description of this process, what chemicals are used: and how it is performed?

I think of myself as a journalist who writes mainly about math and science, and a few other fields of interest.

I think popular belief in bogus sciences is steadily increasing. … Almost every paper except the New York Times, not to mention dozens of magazines, features a horoscope column. Professional astrologers now outnumber astronomers.

I’ve never consciously tried to keep myself out of anything I write, and I’ve always talked clearly when people interview me. I don’t think my life is too interesting. It’s lived mainly inside my brain.

I’ve never made a discovery myself, unless by accident. If you write glibly, you fool people. When I first met Asimov, I asked him if he was a professor at Boston University. He said no and … asked me where I got my Ph.D. I said I didn’t have one and he looked startled. “You mean you’re in the same racket I am,” he said, “you just read books by the professors and rewrite them?” That’s really what I do.

Ideologues of all persuasions think they know how the economy will respond to the Administration’s strange mixture of Lafferism and monetarism. Indeed, their self-confidence is so vast, and their ability to rationalize so crafty, that one cannot imagine a scenario for the next few years, that they would regard as falsifying their dogma. The failure of any prediction can always be blamed on quirky political decisions or unforeseen historical events.

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.

If you look over my Scientific American columns you will see that they get progressively more sophisticated as I began reading math books and learning more about the subject. There is no better way to learn anything than to write about it!

Imagine Aristotle revivified and visiting Manhattan. Nothing in our social, political, economic, artistic, sexual or religious life would mystify him, but he would be staggered by our technology. Its products—skyscrapers, cars, airplanes, television, pocket calculators—would have been impossible without calculus.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

In the medical field [scientific ignorance] could lead to horrendous results. People who don’t understand the difference between a controlled experiment and claims by some quack may die as a result of not taking medical science seriously. One of the most damaging examples of pseudoscience is false memory syndrome. I’m on the board of a foundation exposing this problem.

It took me so long to understand what I was writing about, that I knew how to write about it so most readers would understand it.

Just as knowing how a magic trick is done spoils its wonder, so let us be grateful that wherever science and reason turn they finally plunge into darkness.

Many professional mathematicians regard their work as a form of play, in the same way professional golfers or basketball stars might.

Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It’s made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They’re not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there’s a sense in which matter has completely dissolved and what is left is just a mathematical structure.

Mathematics, a creation of the mind, so accurately fits the outside world. … [There is a] fantastic amount of uniformity in the universe. The formulas of physics are compressed descriptions of nature's weird repetitions. The accuracy of those formulas, coupled with nature’s tireless ability to keep doing everything the same way, gives them their incredible power.

Phrenology is the only major pseudoscience I know about that once flourished around the world and has since faded away.

Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.

Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.

Speaking about symmetry, look out our window, and you may see a cardinal attacking its reflection in the window. The cardinal is the only bird we have who often does this. If it has a nest nearby, the cardinal thinks there is another cardinal trying to invade its territory. It never realizes it is attacking its own reflection. Cardinals don’t know much about mirror symmetry!

Superstrings are totally lacking in empirical support, yet they offer an elegant theory with great explanatory power. I wish I could be around fifty years from now to know whether superstrings turn out to be a fruitful theory or whether they are just another blind alley in the search for a “theory of everything.”

Suppose physics soon succeeds, as Stephen Hawking and a few other physicists hope and believe, in reducing physics to a single equation or a small set of equations that will “explain” all of nature’s fundamental laws. We can then ask the unanswerable question, "Why this set of equations?”

Thanks to the freedom of our press and the electronic media, the voices of cranks are often louder and clearer than the voices of genuine scientists. Crank books—on how to lose weight without cutting down on calories, on how to talk to plants, on how to cure your ailments by rubbing your feet, on how to apply horoscopes to your pets, on how to use ESP in making business decisions, on how to sharpen razor blades by putting them under little models of the great Pyramid of Egypt—far outsell many books… I reserve the right of moral indignation.

The greatest scandal of the century in American psychiatry … is the growing mania among thousands of inept therapists, family counselors, and social workers for arousing false memories of childhood sexual abuse.

The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity.

The line between entertaining math and serious math is a blurry one.

The universe is made of particles and fields about which nothing can be said except to describe their mathematical structures. In a sense, the entire universe is made of mathematics. If the particles and fields are not made of mathematical structure, then please tell me what you think they are made of!

There are, and always have been, destructive pseudo-scientific notions linked to race and religion; these are the most widespread and damaging. Hopefully, educated people can succeed in shedding light into these areas of prejudice and ignorance, for as Voltaire once said: “Men will commit atrocities as long as they believe absurdities.”

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

Why does the universe, as Hawking has recently phrased it, go to all the bother of existing? Why is there something rather than nothing? Things would be so much simpler if nothing, absolutely nothing, existed, not even a God.

Martin Gardner is one of the greatest intellects produced in this country in this century.

[Martin Gardner is] the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.

For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.

Gardner writes about various kinds of cranks with the conscious superiority of the scientist…. He asserts that the scientist, unlike the crank, does his best to remain open-minded, so how can he be so sure that no sane person has ever seen a flying saucer…? … A.J. Ayer once remarked wryly “I wish I was as certain of anything as he seems to be about everything”.

He was not a mathematician–he never even took a maths class after high school–yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.