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What Is Mathematics?: ...
Richard Courant
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What Is Mathematics?: An Elementary Approach to Ideas and Methods: An Elementary Approach to Ideas and Methods

4.29 of 5 stars 4.29  ·  rating details  ·  620 ratings  ·  20 reviews
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads...more
Unknown Binding, 1086 pages
Published May 27th 2014 by Not Avail (first published January 1st 1967)
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This is the ideal book to read during the last years at school, or early in an undergraduate degree. School maths is often about understanding mathematical concepts intuitively via rote learning, repetition and visualization. This book teaches you how mathematical knowledge is arrived at by looking carefully at a few simple ideas and building upon them.

This book is also ideal reading for anybody who wants to improve their general mathematical literacy. Perhaps many people who don't know much abo...more
"The difficulty is that it is easy to prove a problem is easy, but hard to prove that it is hard!"

I'm probably not unique in that I made it through a lot of math without ever really understanding what I was doing, just flipping equations around until an answer poured out. I had a trigonometry professor who at least pushed understanding what you were doing. It was in my first semester of the calculus that math started to make sense. "What Is Mathematics?" was a clear inspiration for some of the l...more
Jul 11, 2010 Thierry is currently reading it  ·  review of another edition
Shelves: math
Einstein put it best when he said: "[this book is:] a lucid representation of the fundamental concepts and methods of the whole field of mathematics." It really is.
Hristo Hristov
От тази книга тръгна моят интерес към математиката. Показва красотата на точните науки, водейки читателя за ръка по много интересна пътечка.
Nick Black
Wow, that was absolutely beautiful! Thanks for the heads-up, Alex! I really, really wish I'd have had this book back as a senior or junior in high school; I'd have been able to plan out my math classes early on much better (why on earth did I take Dynamics and Bifurcations?!?! and how did I avoid taking a serious vector spaces/manifold calculus class? would have been nice for upper-level physics! oh well!). I think this will be my default high school graduation present to anyone with an inkling...more
I wanted to like this book. I really did. But it's just too old. It will never be a classic; it's just outdated.

There are references to ongoing problems to solve Hilbert's 10th problem, but no acknowledgement of Alan Turing's contributions (probably because his work was still classified or unknown at the time of publication). Godel's "recent work on incompleteness" is a footnote to the summary of Russell's "great work", which made me snicker.

The notation is pretty bad as well. Many of the font...more
Alexi Parizeau
When I started this book I wanted something that would let me survey most of mathematics in one sitting. I ended up spending two months obsessing over the book. My progress was so slow because there were weeks where I would read just a few pages, spending the rest of the time diving deeper into an idea or branch of mathematics. I was an increadibly productive experience!
This is a heavy book. Literally and figuratively. This book went way over my head in the discussion of mathematics. I would recommend it to college math professors, but not many other people. It does have some interesting background, but many of those background stories are found in other books as well. Too mathy for me.
Skimmed through and it is quite useful, very similar to one of Felix Klein's books in terms of style. A little too mathematics for my purposes which is more towards physics, some insights are good nonetheless.
Letti solo alcuni pezzi che mi interessavano / servivano. Ottimo libro, andrebbe adottato come libro di testo. Spiegano bene e non sono noiosi. Awesome!
"A lucid representation of the fundamental concepts and methods of the whole field of mathematics" - Albert Einstein.

What else do I have to say!?
Dec 31, 2010 Thom marked it as b-shelved  ·  review of another edition
Shelves: non-fiction
Library copy returned, then removed from circulation for bad binding. No other copy available to read - I want to finish this one!
Una guía esencial para todo iniciado en el área científica. Excelente!!!
Ron Banister
One of my favorite books on mathematics. Also, one of Einstein's favorites.
Roberto Zanasi
Il mondo matematico spiegato ai principianti e agli esperti.
This is a very good text , but too much for me
Jan 10, 2011 Erik marked it as to-read
Excellent, actual use
This is one of the best high school level extensions in mathematics. Originally called -
Mathematics for Lori - it was written for his daughter.
George Pauly
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Oct 21, 2014
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“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.” 1 likes
“For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?” 0 likes
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