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Название: The Princeton Companion to Mathematics
Авторы: Gowers T., Barrow-Green J., Leader I.
Seldom one could identify this kind of object in human history. This book is treasure of human beings. It collects first-rate insights from first-rate mathematicians of human world, in the way of first-rate (I would say the editor has devised such a wonderful 'function' to transform the input to such output).
Anyone seriously interested in mathematics and any college student shall own this book. It is the best introduction to mathematics than any other book because it contains many lens rather than one. One could be exposed to different perspectives in the book, rather than an algebraist's, geometer's, analyst's, or a number theorist's view. T. Apostol's Calculus is great. But it's not the best math introduction because it's through a great analysis teacher's len and it purely focuses on rigorous analysis way of seeing and doing math. So for others, you need this book.
And this book is better than encyclopedia because it expresses the authors' personal insights, which are all first-rate. We love insights/wisdom more than cold facts. Facts of mathematical objects could be found anywhere. But how do some first-class mathematicians "see" such objects? How do they explain the object? This may be the gem they learned/reflected during their past years (and successful ones). Now some of the gem is here in the book.
An apprentice needs a general master for guidance on the overall picture of each specific field that the apprentice could further study from masters of each specialty. This book is the general master to math beginners. It opens a door to the math world. What a wonderful world.