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Imagining Numbers :

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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

288 pages, Paperback

First published January 1, 2002

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Barry Mazur

36 books13 followers
Barry Mazur (Harvard University)

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5 stars
24 (13%)
4 stars
60 (33%)
3 stars
49 (27%)
2 stars
31 (17%)
1 star
15 (8%)
Displaying 1 - 30 of 31 reviews
Profile Image for David.
268 reviews1 follower
April 13, 2020
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.
Profile Image for Ami Iida.
546 reviews309 followers
February 8, 2017
I fail to read the book.
You must not read it absolutely.
Profile Image for Vicki Cline.
779 reviews43 followers
December 21, 2012
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.
Profile Image for Ginnz.
169 reviews4 followers
June 23, 2012
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.

Profile Image for Viki.
17 reviews
March 31, 2009
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. :-)
715 reviews2 followers
December 28, 2020
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.
Profile Image for Jan.
Author 12 books157 followers
February 25, 2017
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.
513 reviews3 followers
September 27, 2024
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.
Profile Image for David Ambrose.
123 reviews1 follower
December 1, 2020
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.
Profile Image for Brant.
83 reviews
August 18, 2022
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.
297 reviews
February 24, 2020
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.
Profile Image for Nilufer.
7 reviews2 followers
February 11, 2023
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!
33 reviews
September 30, 2023
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.
Profile Image for Lewis Waite.
17 reviews1 follower
January 11, 2023
If I remember rightly, the driest book on Mathematics I’d read in a long while
89 reviews24 followers
April 5, 2024
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
Profile Image for Upom.
229 reviews
March 26, 2011
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.
35 reviews
November 12, 2008
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.
210 reviews3 followers
March 14, 2007
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.
Profile Image for PMP.
251 reviews21 followers
March 16, 2007
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.
2 reviews
August 22, 2007
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.
Profile Image for Jarrod.
17 reviews2 followers
March 24, 2008
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.
47 reviews
June 12, 2008
Wonderful explanation of imaginary numbers - easily accessible and written with humor.
Displaying 1 - 30 of 31 reviews

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