Imagining Numbers :

by Barry Mazur

It sounds impossible, yet as this enchanting, quizzical and evocative book shows, the art of mathematical imagining is not as mysterious as it seems. Drawing on poetry, literature and philosophy, Barry Mazur shows how we can all make the leap of imagination in order to start visualizing the enigmatic 'imaginary numbers' tha

Genres: Mathematics, Nonfiction, Science, History, Stem

288 pages, Paperback

First published January 1, 2002

About the author

Barry Mazur (Harvard University)

Reviews

[David · Rating 1 out of 5]

An irritating and badly realised attempt to compare poetic and scientific imagination, with particular reference to conceptualising 'i' and its relatives. As is too often the case with this kind of book, the layout is confusing and the trickier mathematical concepts are hurried through.

[Ami Iida · Rating 1 out of 5]

I fail to read the book.
You must not read it absolutely.

[Vicki Cline · Rating 4 out of 5]

This is an interesting mix of poetry, history, algebra and geometry, leading the reader to appreciate the development of the understanding of i, the square root of minus one. I was particularly struck by the explanation of arithmetical operations (addition, subtraction, multiplication) as manipulations of the real number line. Thus adding 5 to each number shifts the line 5 places to the right (or subtracting shifts it to the left), and multiplying by a positive number causes the number line to expand or contract uniformly, depending on whether the number is larger than one or smaller than one. Next, multiplying by -1 causes the line to flip around 180 degrees. And finally, multiplying by i rotates the line 90 degrees counterclockwise, giving you the complex plane. Once we have this plane, it's easy to visualize addition and multiplication of complex numbers. I've forgotten a lot since studying complex variables 50 years ago, but this book brought a lot of it back.

[Ginnz · Rating 1 out of 5]

Ok so the book was billed as an explanation of imagery numbers, which it was.
A brief history of imaginary numbers from then they were first encountered through to the nineteenth century. The issue I had with the book was it was a rather slow progress through the history and the author tried to compare the mathematics with poetry.
Now as all mathematicians know, mathematics is a form of poetry. It has a grace and form that are beautiful and astounding however Barry rather laboured this point. As such I rather switched off which is why this has taken so long to be completed.
Just when I felt we were getting to a good bit, we'd step back and then look at something else. The peak of the moment was then lost and as a result when we finally made it to that point it was an anti-climax.

[Viki · Rating 2 out of 5]

This was a surprising disappointment. The intersection between poetry and mathematics doesn't need to be nearly as tedious and dull as this - the author clearly enjoyed this transferring this incessantly rambling narrative out of his head and into book form. I got a distinct sense that it was edited and cleared for publication by literary folks who mistook its density for complexity. I finally gave myself permission to toss this across the room and move on, without guilt. :-)

[Caomhghain · Rating 4 out of 5]

The author is trying to relate the concept of, say, a tulip and the square root of a negative number. He relates rather well the enjoyment and excitement of the development of the ideas and presents them with exemplary clarity. That is not to say the book is tough going. It is. But well worth the candle.

[Jan · Rating 3 out of 5]

It was an enjoyable review of complex numbers and a bit of trigonometry, along with some good history of mathematical thought. The analogies to poetry, however, struck me as just bloviating, and I started to skip those bits.

[Yofish · Rating 3 out of 5]

Really more like 3.5 stars.

I appreciate the effort, but I don’t think it quite works. (Though I’m surely not the audience he was aiming for.)

The book starts through a discussion that the author---a professional mathematician, and a fairly famous one---had with a non-mathematician. He was asked to explain why we have and care about imaginary numbers (or possibly complex numbers). I think he did a good job of explaining it.

However. There was a whole lot of (what seemed to me) superfluous stuff. Like a whole bunch on the philosophy of what it means to “imagine”. It seemed like he felt obligated to pad it out to closer to a full book-length; or maybe he was aiming at the intellectual snob and needed to demonstrate his bona fides.

The math was pretty good, I think; you shouldn’t read it without having pencil and paper at hand if you really want to follow. Showing it by using a geometrical argument isn’t the only way to explain it (IMO), but it’s pretty good. And having the story of the solution to the cubic at hand was also useful.

Weirdly, the square root of minus fifteen (as in the subtitle of the book) didn't really play a part larger than any other imaginary number.

[David Ambrose · Rating 2 out of 5]

I wanted to see if this book might be appropriate for teaching students about imaginary numbers given that many students object to them (largely because of the name). I have to say it would be wildly inappropriate for that, as the author spends far too much time solipsistically musing on the nature of imagination. For instance, the author talks about how the imagination conjures a picture onto one's "mental movie screen," seemingly not understanding that some people don't think by means of pictures. Another example is a focus on what one thinks of considering the phrase, "the yellow of the tulip," going so far as to say, "Maybe the shock of the image evoked by 'the yellow of the tulip' ...," not considering that even if the phrase does conjure an image for someone, they might not find it shocking in the least. In all I was hoping to read more about the concept of the imaginary unit and its acceptance over time (which, to be fair, is covered in the book), and not how the author views (his own) imagination or such things as (a few particular) poets' descriptions of their processes for creating poetry.

[Brant · Rating 2 out of 5]

Not sure what I was expecting here, but I was massively disappointed with this book. I'm a huge "recreational" math geek and have become fascinated with the history of the imaginary number. I'm always looking for new ways to think about complex topics (see what I did there?). This book had a few tidbits of pertinent history, but I skipped page after page (sometimes entire chapters) of the author's bombastic philosophical rambling; it never seemed that insightful to me. This is harsh, but I think this book fails to meet its goal by a long shot.

[Melita · Rating 4 out of 5]

I enjoyed this for the most part, though in the end I’m not sure what the finale really was, hence only 4/5. While long winded at times, I do think this was accessible to those interested but not necessarily versed in math theory or history. At the very least, it was entertaining to read Mazur’s prose.

[Nilufer · Rating 5 out of 5]

The book is exactly about what it writes on the title.

Personally, it has presented yet another proof that in the design process when working on models that seem impossible at one stage, you do not discard the thinking but keep going and see through iterations you may find the impossibility gets eliminated.

Love keeping this book, and happy there are mathematicians!

[Hope · Rating 1 out of 5]

I tried my best to connect the author’s ideas but I couldn’t. To me, it felt he’s jumping from subject to another without any connections between them. A lot of questions/ideas were discussed and left unfinished/unsolved without any explanation. It was really boring for me. I am definitely not the crowd for this book.

[Lewis Waite · Rating 1 out of 5]

If I remember rightly, the driest book on Mathematics I’d read in a long while

[Tom Blacklock · Rating 2 out of 5]

Disappointing and frequently tedious - and i am a mathematician that loves imaginary numbers!

[Francesca Fernandes · Rating 2 out of 5]

too philosophical blah blah blah also did not need to be an entire book... i feel like this could've been one very cogently written chapter

[Yimming Song]

Quite convoluted and boring

[Robert · Rating 4 out of 5]

Very imaginative and digressive essay on mathematics.

[Upom · Rating 3 out of 5]

A little tome about the history and approachable explanation of imaginary numbers. A lot of the book's value was probably lost since I knew about most of the material. But it did refresh my memory on the topic, as well as give me some unexpected insight into the nature of imaginary numbers( thinking of number multiplication as rotation operations, why negative times negative is actually positive, looking at multiplication and exponents of imaginary numbers as rotation, etc.) The book has these meditations on imagination and poetry that are somewhat interesting, but come off as slightly pretentious, and a bit off topic from considerations of imaginary numbers. Nonetheless, an interesting stroll down the mathematical shops of memory lane, with a smidgen of poetry to boot.

[Coco · Rating 5 out of 5]

This book was introduced to me by Ms. Jaffe. We talked about it in class when starting our Imaginary Numbers unit. This book is half of the things i think about and everything i never thought to think about put into a book. It connects ideas of math to english but mostly the way things work. If listed the facts it tells, you would think it had the most random information, but it flows quite well. It often talks about the difference in certain things we think about and about imagination. What imagination means, its affect on a person, etc. Fascinating.

[severyn · Rating 2 out of 5]

I have already learned that McGraw-Hill editors were encouraged not to use 'the word 'imagine' because people in Texas felt it was too close to the word 'magic' and therefore might be considered anti-Christian.'

Apart from that, which isn't really the point of the book, too much maths for someone as lazy as me, and not enough on trying to imagine things, which sort of was the point of the book.

[PMP · Rating 4 out of 5]

More poetry than mathematics, or illuminating the poetry in mathematics. The sort of cross-pollination between disciplines that gets me so thrilled. Taught me the incomparable word "onomatoid". You have to see the window display that Barry's wife Gretchen designed to advertise the book. It involved a coat hanger, a bee and a tulip. The store-owners called to ask if she had made a mistake.

[Adam · Rating 4 out of 5]

I remember a conversation with a friend at university who told me about imaginary numbers. He didn't explain them very well but he caught my interest.

This is the most entertaining book on mathematics you will ever read but a warning, if you're rusty on your sums like me, there is a lot of flicking backwards and forwards.

[Jarrod · Rating 2 out of 5]

Somewhat tedious and boring. The main concept I took away from the book was the idea that numbers can be conceptualized in completely abstract forms, which can allow the thinker to evaluate information in new or unusual ways. I would have enjoyed the book more had it been a pamphlet.

[Marcia · Rating 4 out of 5]

Wonderful explanation of imaginary numbers - easily accessible and written with humor.

[Elizabeth]

As seen in Nature .

[Ilib4kids]

512 MAZ

[David Howell · Rating 2 out of 5]

Never finished reading it - nothing of interest for me

[Brett · Rating 1 out of 5]

I gave up. I wanted to like it, but there is just nothing there to like.

[Jillian · Rating 3 out of 5]

3.5 stars.