Paul J. Nahin

Very technical for a popular book, though admittedly most of my reference points are pop science rather than pop maths. (It's certainly no [b:The Road to Reality: A Complete Guide to the Laws of the Universe|10638|The Road to Reality A Complete Guide to the Laws of the Universe|Roger Penrose|https://images.gr-assets.com/books/1386924912s/10638.jpg|1077395], but it's far more mathematical than any other pop science book I can think of, and it's much more demanding than, say, Ellenberg's show more excellent [b:How Not to Be Wrong: The Power of Mathematical Thinking|18693884|How Not to Be Wrong The Power of Mathematical Thinking|Jordan Ellenberg|https://images.gr-assets.com/books/1387726285s/18693884.jpg|26542434], which is the only pop maths book I can think of off the top of my head.) In any case, I found it heavy going, and had to accept that a fair portion would go over my head unless I was willing to spend a huge amount of time and effort. So I'm not in a position to judge whether it would be enjoyable for readers with the background & intelligence to follow it closely (though I suspect that it would be).

For me it was worthwhile in parts & frustrating in others. Mostly that's simply the result of my own ignorance/laziness/stupidity, but I did sometimes feel that Nahin wasn't quite sure who he was writing for: he would occasionally pause to explain a very basic concept, then in the next breath launch into a torrent of formal mathematics with little in the way of verbal guidance. (Mostly, though, he was clearly aiming at people with a fairly solid mathematical background.) There were some sections that I could have grasped a lot more quickly & easily with just slightly more hand-holding; sometimes a logical leap that would be obvious to a mathematician took me an embarassingly long time to understand. I assume something similar is true of some of the proofs I gave up on following, though others were genuinely too hard for me, and by the final chapter I was doing a lot of skim-reading.

Anyway, I suspect I might have loved this book had I been a bit smarter or better educated. In reality, it was probably worth reading, but only just. 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

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 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

Despite the title, the detailed description of this book on its cover and in accompanying material by its publisher, it is NOT a biography. It only gives the appearance of being biographical. The title subjects only make their (brief) appearance in chapter three. Then it's on to the real business - math. I was expecting a very cool, parallel story of how the 19th century Boole foreshadowed the brilliant 20th century Shannon, how there were parallels in their lives, how coincidences piled up, show more how hints from one resulted in achievements in the other - how Shannon cashed in on what Boole couldn't even imagine from his own work. How Shannon redeemed Boole.

There's none of it.

This is a book on electrical circuit design, by a professor of electrical engineering and mathematics. It is a textbook for the enthusiastic student entering the field. Nahin is clearly far more at ease in formulas than in narrative. The ubiquitous exclamation points and overuse of italics are vivid testament to that. The biography reader will be lost after the first formula is built. This book is about the math, not the people.

But as such, there is nothing wrong with this book. It is clear, organized, inviting, and easy to digest if you are interested in the subject matter. But let's be clear - the subject matter is circuit design, not Boole and Shannon. After chapter three, Boole barely gets mentioned at all, while Shannon pops up here and there because of a relevant paper (and the occasional joke). But these appearances are as scientific references, not biographical events or descriptions.

Ironically, Nahin ends the book with the story of The Language Clarifier, a black box used to interpret legalese so that mere mortals could comprehend what the fatheads (his term) had written. If only the publishers had been required to use it, this book might not be so misleading. show less