Post updated, 9/23/15 9/22/15. See below! This will be the first column in a series on the broad human behavioral dimension dubbed "clannishness" by HBD Chick. I've talked quite about clannishness here, and of course it is the main theme of HBD Chick's blog. For background, see: start here | hbd chick clannishness defined |... Read More
Writing The Principles of Mathematics in the spring of 1901, Bertrand Russell got stuck on a simple problem in the theory of classes (we would nowadays say "sets"): "Whether the class of all classes is or is not a member of itself." In his autobiography Russell recalled: "It seemed unworthy of a grown man to... Read More
Turing's Cathedral: The Origins of the Digital Universe, by George Dyson
This year marks the centenary of British mathematician Alan Turing, whose researches in the unlikely and very abstruse field of mathematical logic did much to create the world in which we now live. In 1936 Turing published a paper titled "On Computable Numbers" in the Proceedings of the London Mathematical Society. The paper received almost... Read More
The Poincaré Conjecture: In Search of the Shape of the Universe, by Donal O'Shea
It is a well-known fact that our universe has three dimensions of space. Imagine for a moment that it had only two, like E.A. Abbott's Flatland, or A.K. Dewdney's Planiverse. What shape might it have? Well, it might be flat, like an infinite sheet of paper on an infinite tabletop; or it might curve round... Read More
Stalking the Riemann Hypothesis, by Dan Rockmore
The author of a pop-math book must decide, before he sets finger on keyboard, how much he is going to demand of his readers in the way of willingness to engage with actual mathematics. As is often the case in writing, what is easier for the author is more difficult for the reader, and vice... Read More
Infinite Ascent: A Short History of Mathematics, by David Berlinski
The relevant library shelves in the Courant Institute of Mathematical Sciences hold no less than eighteen different general histories of mathematics in English. The author setting out to write yet another such book must therefore have an angle (so to speak), some original approach to the topic. What is David Berlinski's angle? "Short" doesn't cut... Read More
The Art of the Infinite: the Pleasures of Mathematics, by Robert Kaplan and Ellen Kaplan
Mathematicians are uncomfortably aware that theirs is a "cold" subject. Though full of wonders and delights, it has little appeal to the tender side of human nature, little connection with the clayey appetites and longings of our everyday lives. There is a story about the great German mathematician David Hilbert. Noticing that one of his... Read More
Knots, by Alexei Sossinsky
I was in the Army Cadets at school, but my best friend was in the Sea Cadets, and for a year or so I crossed over to join him. This phase of my life came to an end when I failed the oral exam for promotion to the rank of Leading Seaman. The exam was... Read More
The Millennium Problems, by Keith Devlin
It is difficult to think of any literary enterprise more challenging than the presentation of advanced mathematical topics to a general audience. It is not just that math is hard; there is, as Keith Devlin noted in a previous book, The Math Gene, (and as Bertrand Russell remarked in the introduction to Principia Mathematica), something... Read More
A load off my mind.
You are going to have to cut me a little slack today. I am somewhat light-headed, and finding it difficult to fix my mind on anything. I watched a lot of TV over the weekend — but don't ask me what, I can't remember a thing. I have been sleeping in 12-hour stretches, with naps... Read More
I am sorry. Really, really sorry. I apologize. I apologize to readers who e-mailed me last week and got bounced because my e-mailbox was full. I apologize to NRO for being disgracefully late with this column. I apologize for not having participated in The Corner for several days. Most of all, I apologize for having... Read More
A weekend away from home.
Any time I use a column to bang on about civilization (according to me) or high culture — opera, ballet, and the like — I get loyal readers e-mailing in with: "Hey, Derb, cut out this stuff, will you? Give us that old-time religion — another piece about killing rats, or a good rant against... Read More
The Universal Computer: The Road from Leibnitz to Turing, by Martin Davis
The Computer and...
That is from Bertrand Russell's autobiography. What was stumping him was the attempt to find a definition of "number" in terms of pure logic. What does "three," for example, actually mean? The German logician Gottlob Frege had come up with an answer: "three" is merely the set of all threesomes, the set of all those... Read More
Did Adam and Eve Have Navels? Discourses on Reflexology, Numerology, Urine Therapy and Other Dubious...
I find it difficult to speak temperately about Martin Gardner because I owe him so much. As a child in England, my keenest intellectual pleasure was reading Gardner's monthly "Mathematical Games" column in Scientific American. Along with a handful of books like Kasner and Newman's Mathematics and the Imagination and George Gamow's One Two Three... Read More
The teaching of mathematics.
Here is a math teacher's joke from around 1975, when the original "new math" movement was in full flood. New math is now a very old story, the opening campaign in a long drawn-out war between theory and reality, in which the advantage tipped sometimes this way, sometimes that. In April this year the National... Read More
The Nothing That Is, by Robert Kaplan
Suppose I ask you to step into the next room, count the people in there, and report the answer back to me. What is the smallest number you can report? Obviously the answer is zero, corresponding to the case when there are no people at all in the next room. Thus it is plain that... Read More
————————— John Kenneth Galbraith remarks in one of his books that if you've ever worked on a farm nothing else ever seems like work. Those of us who have studied mathematics at university level can make a similar claim. If you've ever grappled with advanced math, the study of other subjects seems like a joke.... Read More
The Man Who Loved Only Numbers, by Paul Hoffman
My Brain Is Open, by Bruce...
In an essay entitled The Maniac, G.K. Chesterton argued that madness is not so much a deficiency of reason as an excess of it. "Imagination does not breed insanity. Exactly what does breed insanity is reason. Poets do not go mad; but chess players do. Mathematicians go mad … but creative artists very seldom." Like... Read More
A sonnet commenting on an article about repeated exponentiation.
Another reader, John Derbyshire (Huntington, NY) commented — in the form of a Petrarchan sonnet — on "The limit of x^x^ … ^x as x tends to zero," J. Marshall Ash, this magazine, No. 69 (June 96), as follows: