50 Mathematical Ideas You Really Need to Know

I enjoyed this book very much. Contrary to some reviews, this isn't a text book; it's an informative reference book. It won't teach you how to find square and cube roots. It will, however, tell you the history behind who first discovered them, how and why it's important. I'm actually buying a second copy, as my brother "borrowed" my first copy and I don't expect to be getting it back.

This little book encapsulates the essence of 50 mathematical ideas which are of great interest to many although a lot of people would not realise it. Each idea presented here gives the germs of background which clearly the author hopes will take root in the conciouness of the reader suffice for them to go and examine more for themselves. I suspect that the target audience would be young students of pre-university age, perhaps taking up some quantative methods courses to support their chosen subject as well as some older, yet educated readers who may have not got so far into their mathematical development but who wish to aquaint them selves with the basics. Each chapter offers a taste, a tidbit of knowledge which whets the appetite for more and urges the reader on to consider the subject matter as a whole, underpinning other sciences and physical subjects such as engineering, while seeking to broaden the mind with the mathematical universe. An open mind can lead to imaginary constructions which sees the puzzles contained within the book as part of a unified theory of mathematics which connects them all together: just think of theories of multi-dimensional constructs and the neuron net just glows. I really like this book. The lack of detail serves to offer a clear perspective for thinking about the general nature of each puzzle although the limitations of only four pages can result in some zealous editing. Still it is a fun filled and exciting book which I am happy to recommend as an essential addition to any home library.

This is the best short survey of mathematics I know of, and I think the format works very well (4 pages each for 50 key mathematical ideas). I personally read one idea per day for 50 days, and this book delivered a bright spot for every one of those days. To address another reviewer's comments, I do agree that this book has lower and upper bounds to be aware of. The lower bound is that readers should come to the book with at least a general familiarity with the subject of mathematics, including having at least heard of concepts like complex numbers, calculus, probability, chaos, abstract algebra, group theory, Fermat's last theorem, the Riemann hypothesis, etc. And certainly readers should come to the book with a genuine interest in mathematics. In other words, this isn't a book for readers with no background or interest in mathematics, nor readers with a fear of mathematics. The upper bound is that the book doesn't (and can't) develop the mathematical ideas in step-by-step detail. Rather, the book goes into just enough detail to give a meaningful sense of what the ideas are about, and it does this quite well, with nice features like timelines, examples, historical asides, etc. This book isn't a mathematics textbook, nor does it purport to be, so it shouldn't be judged on that basis. The only thing I really found lacking was that the book doesn't include suggestions for further reading. But this omission isn't enough to lower my rating from 5 stars, and I highly recommend the book to anyone looking for a short survey of mathematics. Tony Crilly provides a wonderful and panoramic guided tour of the subject, spanning from elementary to fairly advanced ideas, and does it in a way that both entertains and reveals the rich beauty of mathematics. For readers who take the tour and feel sorry to see it end, I suggest moving next to the massive and outstanding The Princeton Companion to Mathematics.

This is a concise book covering from ancient Greek Math to 21st century Modern Math. The author has smartly picked the most important 50 ideas, from Greek time, to modern Algebra, FLT, Riemann, Fractal, Genetic Math... it is surprisingly fun stuff to read, unlike other boring Math textbooks, yet it opens the reader's eyes to the beauty and wonderful Math world. For high-school math students going to the University, this is a good transition book, laying the foundation for them to grasp the abstract math ideas in the University, where unfortunately the Math professors would hardly tell the students the roots of these math ideas dated since 3,000 years ago. Some interesting highlights: 1. Hardy-Weinberg Genetic Law: Cambridge Prof Hardy, as the greatest Pure mathematician in 20th century, prided Pure Math as being 'useless', yet he discovered independently the Genetic Law with Dr. Weinberg (Germany). He wrote the math proof at the back of an envelope after a cricket match in 1903. You can see Hardy's Pure math is not 'useless' at all - he proved the Genetic Law without being a Bio-Scientist, just by applying the beautiful Probability theory (the proof can be found in this tiny book). 2. Abstract Algebra: Since 825AD Arab Mathematician Al-khwarizimi introduced 'Al-jabr' dealing with numbers, Viète (France) in 1591 AD introduced symbols for known and unknown variables, Algebra was transformed into dealing with non-numbers 'Modern Algebra' by Emmy Noether (Germany) in 1920, with axiomatic structures and its 'isomorphism', etc. Bourbaki (France) in 1939 re-built the whole math using Set Axioms under rigourous structures. Together with the other Twin book: "50 Physics Idea You Really Need to Know" (by Joanne Baker) form a great gift for your to-be-university children or friends. They will definitely be enthused by Science & Math and excel in these 2 subjects in the University.