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1.The Penrose's book "The road ro reality" may be, arguably, considered as a very fast and dirty introduction to modern physics as well as to some related relatively modern math topics.

2. I recently encountered a book Aleksandrov, Kolmogorov, Lavrentev "Mathematics: its content, methods and meaning" which was writen in 1950th and looks as a fast and yet detailed introduction to many advanced and modern topics (of that time) for laymen.

A question: can somebody recommend a modern book of the same sort which tries with a reasonable amount of details to give an introduction to modern math topics and style for a non-mathematician? The two examples above prove books of such a type may exist, I just have no any idea how to find them. In fact, I encountered the Kolmogorov's book (which looks fantastically good for me) quite accidentally.