# Reference request for 'all' mathematics

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.

• Wouldn't such a book be rather impractically large? Wouldn't you be better getting multiple books, or I guess a book containing a sort of summary for lots of topics? Is the latter the type you are looking for? Aug 8 '20 at 14:56
• you are right, I should have emphasized such a book as containing mainly summaries but with some depth to the topic. So the latter Aug 8 '20 at 14:58
• I see, that makes sense. I'm not aware of such a book - but hopefully someone else may see these comments and be able to recommend something helpful. I can imagine a book like this would be rather helpful, so I will follow this post to see Aug 8 '20 at 14:59
• You may be looking for a collection like The World of Mathematics by James R Newman. This fails your request that it be recent as it was written in the 1950's, but it covers many topics. I have it on my shelf as well. It doesn't go into great depth on any topic (how could it with so many) but it gives a good bit of history and a notable theorem or two for most topics and notable mathematicians from western mathematical history. Aug 8 '20 at 15:07
• Eyyyy nice! getting a lot of nice answers now, I'll have to pick up some of these books ;D Aug 8 '20 at 16:04

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".

• (+1) This is probably the closest to the OP's request that I can think of, although it's likely too advanced. Another example worth looking at is Encyclopedic Dictionary of Mathematics (Volume I), although this is probably too advanced as well. Aug 8 '20 at 16:07

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.

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.

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.