CTK Insights

Probably every math teacher has the experience of facing such questions; most likely the students who asked them were not looking for the answers as arguments to study mathematics, but rather in support of their conviction that the effort is not necessary. Most of the answers teachers give perfectly serve this purpose. I wrote about [...]

Kozma Prutkov is a collective pen name of the count Aleksey Konstantinovich Tolstoy and two of his cousins - Zhemchuzhnikov brothers, Alexei and Vladimir. Mostly in the 1850s-60s, Kozma Prutkov published aphorisms, fables, epigrams, satiric plays, humorous and nonsense verses. Many of the aphorisms became an authentic part of Russian folklore. If ever asked what [...]

A few days ago my 11 years old son told me he would like to forward me an email he received from one of his friends and whether I would mind. The boy was noticeably agitated and appeared on the verge of tears. The message he sent is below. I just want to say how [...]

In an odd sort of events I came across a quote from an old Russian chess book. The author instructed his readers to place the rook behind a pawn, as long as it was a correct move. Wisdom to live by. I was reading City of Thieves by David Benioff - an American writer, a [...]

In a recent post I have opined that an engaging book on the follies of gambling well deserves to be included in the classic Extraordinary Popular Delusions and the Madness of Crowds by Charles Mackay, LLD. In fact the latter mentions (p. 425) that gambling was a matter of concern during the third crusade (led [...]

As I just mentioned a collection of articles Judgement under uncertainty: Heuristics and biases edited by D. Kahneman et al, I thought that perhaps it would be worth adding a quote or two from the text, especially because some ideas appear to have bearing on what is happening with math education. Here's one from an [...]

I have recently posted a simple result picked from a very early (1930s) Moscow Math Olympiad for the middle schoolers: In triangle ABC, AE and BD are the altitudes to sides BC and AC, respectively. M is the midpoint of AB. Prove that MD = ME. Vladimir Nikolin, an elementary school teacher from Serbia, noticed [...]

The news are sometimes overwhelming. The latest I read came from National Geographic Daily News. A new research by Satoshi Kanazawa, an evolutionary psychologist at the London School of Economics and Political Science, suggests "that human evolution may have a big influence on whether you're liberal or conservative—not to mention how smart you are, whether [...]

Leisure is the mother of philosophy. And further, From this it was that the place where any of them (AB: philosophers) taught and disputed was called schola. which in their tongue signifieth leisure; and their disputations, diatribae, that is to say, passing of the time. Thomas Hobbes Leviathan, ch. 46 Penguin Classics, 1982 Gentelfolks in [...]

I am still reading A. Einstein's collection Ideas and Opinions. Some of these seem to be naive but most I agree with. Here is one written some time in 1934: The power of conscience and of international spirit has proved itself inadequate. At present it is being so weak as to tolerate parleying with the [...]