OXFORD UNIVERSITY PRESS What Is Mathematics?: An Elementary Approach to Ideas and Methods

My professor used this book briefly in class in my first semester of my Master's degree. I've feel in love with the book and how it explain important concepts of mathematics. Although I haven't gone through the entire book, the content I've used so far is great. It's unique downside is the outdated diagramming. A book with that quality should be renewed to gain better illustrations and modern fonts.

This book was bought for my son who is a maths nut (a very rare breed). He was really happy with the book. For my part it arrived on time and well packaged.

Courantと聞くと難しい物理数学の著者を思い浮かべる。本書は学生、教師、研究者に向けて、素数、作図、トポロジー、最大値と最小値、微分積分などについて極めて初等的な数学入門書である。数学が頭の中のものでなく、自然現象や日常生活などと密接に関係していることが強調され、抽象化が必ずしも最上のものではないことが印象として残る。高校生でも理解できる内容だろうがこの厚さの原書を通読するのは根気がいることだろう。学部1年生なら数学と英語の勉強にちょうどよいかも知れない。版を改めるにあたり著者以外の他人が携わるのをわたくしは嫌う。整ったものをくずされるように思うからだ。幸い、二つの章が最後に追加されただけでよかった。(本文にはそう手が加えられたとは思わなかった。)邦訳の訳者によると、この追加された章に誤りがあるそうで、それは改版者も認めているそうだ。

Not quite what I wanted, but that's my fault - caveat emptor. I'm wanted something on the philosophy of maths, but this is basically a maths textbook, although it is much more discursive than the ones I remember from school and is quite a good read. Early on, the authors put me in my place by remarking that the mathematical object "exhausts itself in the totality of its possible relations with the perceiver [and although] these relations must be co-ordinated with the thing in itself" further speculation on this point can be let to the philosophers. Nevertheless it is a beautiful book and I shall keep it as a handy reference to the subject. I have one criticism, which is that the text dates from 1941 but recent developments are set out in an appendix written by Ian Stewart in 1996. It would have been useful to have the main text marked-up to show where there is further matter in the appendix.

This is a good book if you have a good level of mathematics knowledge already. The book is for university student, not for a high school student.