Mathematics and the Imagination

Rating:
Summary: Oldie but Goodie
Review: Having had this book around the house for ages, I picked it up and to my surprise within a few minutes really understood (not just enough to use, but actually understood) what logarithms really are, where they come from. The chapter on e, pi, and i is another great one to get the story behind the story, as it were. For me the book could better have continued in this vein of explaining concepts we've seen before but never really grasped intuitively, and perhaps because I'm not terribly interested in mathematical games I found that segment less fun. But in fairness, they've done a good job getting away from textbook math and into some interesting themes. I don't know if it's all still valid, as it is so old--references to Fermat's last theorem are at least outdated!

Rating:
Summary: Great for high schoolers with interest
Review: My only complaint is its lack of rigor and the fact that it is getting rather out-of-date; besides that, this is the sort of book that everyone interested in math should read while they're in high school.

Rating:
Summary: Indulge your enjoyment of mathematics and expand your mind
Review: My school teacher gave me this book to read when I was 13 years old, based on the interest I showed in Mathematics that went beyond the curriculum at school. In many ways it was way beyond my comprehension at the time, but little did I know that it would have such a lasting effect on me. Reading about concepts of infinity, that you could only describe to a fellow teenager as "different sizes of infinity", I realized that there really is a philosophy of mathematics that transcends all other subjects and that there is also an art to working with the subject. I can't recommend this book enough, and I never did give it back to my teacher!

Rating:
Summary: Somewhat dated but still well worth reading
Review: Originally published in 1940, the material in this book is beginning to show a little age. However, the quality of the writing renders those defects to near irrelevancy. Popular descriptions of mathematics are differentiated by the quality of the writing rather than the distinctiveness of the mathematics, and this one shines.
I like this book, starting with the title. It takes an enormous amount of imagination to do mathematics, something unappreciated by the public. It is easy to understand the use of linear segments to approximate the length of a curve. However, it requires an enormous leap of abstraction to believe that if they are made of zero length and then summed up, the result is the true length. Calculus students dutifully record and apply this, but in most cases don't appreciate the significance of the idea. In nearly all cases of major mathematical advancement, a fundamental change in thought processes was necessary. Those changes require imagination and the advances explained in this book are well documented and described.
Mathematicians are containers of some of the greatest concentrations of imagination that humans possess. Their leaps of abstraction often include descriptions of objects that cannot be visualized. Kasner and Newman capture this essential ingredient, serving it up in palatable portions.

Rating:
Summary: Mathematics and the Imagination
Review: This book came to me by chance.Instantly got my attention.It is written in such a way,that makes interesant to travel through different chapters.In each one you have the mathematical theme mixed with stories , mathematicians histories and puzzles.You learn about people with the greatest imagination.Their personality and a lot of other things,that make you enjoy the reading,no matter if you love mathematics or you have hated it all the time.I've enjoyed specially the chapter about Mathematical Analysis,with the story about rivalry between the egocentric Newton and the humble Leibnitz. This book is the opportunity to learn that mathematics are not the boring thing we have learned at school.