Reference request for 'all' mathematics

Question

I am looking for a multidisciplinary book on mathematics that contains various subjects in one book or in volumes.

I am looking for one that is rather recent, by recent, I mean within 30 years. This book will cater towards higher undergraduates or graduate level mathematics, it may have topics in algebra, analysis, geometry, logic etc ...

I understand that most books can be called multidisciplinary to some extent, in that they may require knowledge in other areas, and shows those other areas in the book. The extent I'm looking for is much broader, containing more topics than would be expected in most books, if one does exist.

Answer 1

The first book that comes to mind that seems to fit the bill is The Princeton Companion to Mathematics. It is said to

introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music — and much, much more.

The book was published in 2008 and is intended "for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties".

You can view the table of contents here.

Answer 2

One beautiful book that comes to my mind is Mathematics Its Content, Methods, and Meaning.

This major survey of mathematics, featuring the work of $18$ outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses $20$ prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."

Hope this helps.

Answer 3

You may like Evan Chen's Napkin Project. It contains a sprawling array of material on algebra, topology, analysis, logic and so on.

The one requirement on which this suggestion may fail is that it is aimed slightly more at precocious highschool and undergrad students, but the material is far from trivial.

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Another book you may like, which is explicitly aimed at covering all the math you'll need for grad school, is All the mathematics you missed. It covers pretty a bit of everything you may see in an undergrad math syllabus.