Paul J. Nahin

I spent years studying university mathematics, but I can't say that I really ever understood imaginary numbers. I was hoping to gain a much better understanding from this book, but I was a disappointed. I'm not really sure what its target audience is. You're not going to have any chance of understanding its mathematical formalism unless you've read advanced university mathematics. But on the other hand, if you have done such studies, then this book just puts some formulas into historical show more perspective. I don't think it really helps you understand complex numbers better than before.

The author goes through a great number of mostly 15th - 19th century mathematical derivations where imaginary numbers played an important role. This is interesting and illuminating in the first chapters where he presents authors who were puzzled by complex numbers and tried to come to terms with their meaning. It becomes less interesting when he goes on to present (in meticulous detail) a great number of proofs: "look, this problem, too, can be tackled by assuming a complex function, and it leads us to this amazing formula". This may help readers appreciate the utility of complex numbers, but I don't think it improves their understanding very much.

In the end, this book might be most pleasurable for people who have a very serious interest in the history of mathematics. The author seems to have done his own research in many original sources, and the stories are often far more interesting than the mathematical proofs. Too bad that the book's emphasis is 55% on formalism, 40% on stories and only 5% on explaining what complex numbers really mean in practice. show less

On occasion, I find myself in the math/science section of the bookstore. Having a very thorough background in mathematics, I find it interesting to read books written by notable professionals in their fields on certain subjects. This one caught my eye (pun unintended), and I just had to get it!

The book chronicles the history and usage of the imaginary number, i (or j, if you're an electrical engineer), or √-1.

For those of you who have taken a few math classes, you'll realize that i cannot show more possibly exist in the realm of Real numbers, as with respect to that set of numbers, it simply does not make any sense! Thus, Numbers are broken down into two sets: Real and Imaginary. And when a number contains both of these values, it is considered Complex, or a+bi. Complex numbers work very well as Cartesian coordinates.

But enough about math! Let's discuss Nahin's book. While not having the target audience of The Da Vinci Code in mind, Nahin paints a picture of a 2,000 year old known history of complex numbers, complete with the masterminds who tried to solve problems involving it.

So, if you've ever wondered why we make such a big deal about imaginary number, or how they came to be used in all the different technologies in which they're used, you might find this book interesting. If you think math is boring, but you have an acute case of insomnia, you may also enjoy this book, but for different reasons. The only instance in which I would recommend you avoid this book is if you hate mat and have no intentions of improving your intellect or knowledge of mathematical subjects. show less

This is a spectacular book. Yes, it's hard. I didn't understand quite a lot of it. I hope to come back to it after reading some Feynman etc and see if I get more out of it. But even missing so much, it's a delightful treatment of time travel in physics, philosophy, and sci fi. And it's wonderful to read about such an imaginative concept from the point of view of a scientist who thinks it just might be possible. Delightful. And tons of ideas for other things to read, whether sci fi fantasy show more stories or academic papers. Loved it. show less

Dr Nahin is a friendly kinda guy, almost as fluffy-looking as the two big tabby cats he says he lives with, and this is a friendly kinda book. Tricky to pull off with mathematics- sorry- math. -where the bookcovers tend to feature dour geometric drawings and angular typefaces and tend to prefer things that way thankyou very much.

(Nahin asks about when math became 'sexy' but we'll sidestep that can o' worms in favour of just knowing what's going on with the proofs and calculations... If you show more don't mind!)

So there's a middle ground to be trod between the comic book, horn-rimmed, simplification of mathematics as 'entertainment', all secret formulae and unassuming geniuses, and the more deadpan
experts of real-life. Deadpan's okay, if you can do the sums. Otherwise, it's unbearable. So I was glad to see lines of working in this book.

I imagine the target reader of this book to be someone who knows who Euler is ( ie pronounced 'Oiler') and what the formula is, but perhaps not all that much more- by 'professional mathematician' standards. So Nahin makes no assumptions about what the reader can or cannot do with algebra.

He strolls with us through a few passages of the type of stuff we may be more familiar with, more able to do ourselves. And if the rest of the book is a bit hazy on recollection, we can trust him that it's all kinda what he said it is. And kinda will do better than not at all. the next tutor- you know who, the deadpan guy- he can add to it with his deadpan course book and fill in the details.

One remembers what one needs to know and can relate to. As someone who has 'had a go' at teaching, I can concur that it isn't always easy to make easy things look easy. And it is harder still to make something tricky look do-able. You can look clever doing something difficult. But do the kids actually geddit?

I would make the case that Mathematics is a particularly 'get it or you don't' type of subject- especially if, like I was, you are not the most experienced teacher. Dr Nahin surely knows better than that and shows it by making careful choices of accessible material which, experience shows, could do with being talked over. He smooths out the edges of the scary math.

Euler and co remain distant geniuses but with some annotated algebra- hey- it's okay! The sea's awful rough over thataway but this bit's swimmable. And swim we do.

Bogan show less