For access to a lot of mathematical concepts at a reasonable reading level, not at all expensive, I recommend Concepts of Modern Mathematics by Ian Stewart.
Ian Stewart is a mathematician who loves to write popular writings on mathematics, and you can hardly go wrong with anything he has written.
From Zero to Infinity: What Makes Numbers Interesting by Constance Reid
is very accessible and covers a number of interesting topics.
The Art of Problem Solving by Richard Rusczyk and Sandor Lehoczky
is a straight-up contest preparation book, in two volumes, that your son may find interesting. Volume 2 is for high school level contests.
For an interesting (in places laugh-out-loud funny) book about the place of mathematics in modern life and how mathematicians think about mathematics, I recommend The Pleasures of Counting by T. W. Körner.
This one is more challenging as to reading level and as to mathematical level than the recommendations above, but well worth having around the house.
was solved by a mathematician who was educated in Russia. But also to this day, the United States and Britain enjoy an astonishing degree of political and economic freedom and rule of law
and gain many of their best mathematicians and mathematics educators as immigrants from non-English-speaking countries. It is too early to say whether a lot of engineering-trained persons in government is mostly a feature or mostly a bug. I wish China well in going the direction of Taiwan (another place long ruled by technocrats) in developing the rule of law and an open political system with many guarantees of personal liberty. But it is by no means an invariant characteristic of human societies that those with the best math and science minds thrive best over the long term.
P.S. You did see below the fold on the submitted article, didn't you, what the blog author thinks China can count on just from the fact of the educational background of its leaders? Not much, just from that fact.
P.P.S. to respond to first reply: It's my understanding that the government of the Federal Republic of Germany consciously DE-emphasized technical education after World War II in favor of more emphasis on humanities and social science in the primary and secondary school curriculum. I thought it would trigger a mention of Godwin's Law
if I brought this up at first, but I've read that many observers of prewar Germany under the Third Reich looked at the quality of the scientists there (very high indeed) and thought that Germany would be hard to beat in the war. It is well known to people who read interesting histories of World War II, such as mathematician T.W. Körner's book The Pleasures of Counting,
that there was a battle of scientists versus scientists in the war to find smart methods for fighting the other side. Ultimately, despite the great advantage that German's prewar primary and secondary schools and universities and civil service system gave Germany in building up a supply of smart technocrats, the Nazis' disregard of personal liberty drove away many of Germany's best scientists (notably, many Jewish scientists) and added talent to the Allied side.
Concepts of Modern Mathematics by Ian Stewart
Numbers and Geometry by John Stillwell.
The Pleasures of Counting by T. W. Körner
Mathematics: A Very Short Introduction by Timothy Gowers
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