Outstanding synthesis of mathematics,
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This review is from: The Princeton Companion to Mathematics (Kindle Edition)
My formal maths education ended 30 years ago with university level mathematics for engineering. A renewed interest had me looking for a book that explains how the many topics within mathematics are linked together, in a way that limits the use of the formal language of maths. The search is over....this is the book.
It is not a textbook, and you won't earn a college degree by reading it, but anyone reading part 1 will understand fundamentals which will make textbooks much easier to read. Part 2 is also a good path to understanding the history of mathematics, and both why and how it was developed to solve real problems that man has faced down the years.
Further sections explain key concepts in language as close to laymans's terms as possible, and give more detailed guides to major subtopics, significant contemporary questions, prominent figures, applications to other area of science and life as a mathematician.
The book is not 'light' reading in any sense. Maths can be inherently difficult, and the contents of the Companion are essays without illustrations. The hard copy is also physically daunting, which is why I would recommend the digital kindle version for each of access and use.
Nonetheless, if you have an interest in mathematics and have some level of maths education then, whether you use it as a guide to the subject or as a companion to deeper study, this is a book you should have.