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Archimedes' Revenge: The Challenge of the Unknown
Syndicated columnist Paul Hoffman provides an acclaimed account of the world of modern mathematicians in the bestselling tradition of accessible scientists Stephen Jay Gould and Tracey Kidder. An extremely clever account.--The New Yorker.
300 pages, Paperback
First published May 1, 1988
10 people are currently reading
409 people want to read
About the author
Paul Hoffman
137 books89 followersPaul Hoffman (born 1956) is a prominent author and host of the PBS television series Great Minds of Science. He was president and editor in chief of Discover, in a ten-year tenure with that magazine, and served as president and publisher of Encyclopaedia Britannica before returning full-time to writing and consulting work.
He lives in Woodstock, New York. Author of at least ten books, he has appeared on CBS This Morning and The NewsHour with Jim Lehrer as a correspondent. Hoffman is also a puzzlemaster using the pseudonym Dr. Crypton. He designed the puzzle in the 1984 book Treasure: In Search of the Golden Horse. He also designed the treasure map in the 1984 film, Romancing the Stone, starring Michael Douglas, Kathleen Turner, and Danny DeVito.
Hoffman holds a B.A. degree summa cum laude from Harvard. He is the winner of the first National Magazine Award for Feature Writing and is a member of the American Academy of Arts and Sciences.
He lives in Woodstock, New York. Author of at least ten books, he has appeared on CBS This Morning and The NewsHour with Jim Lehrer as a correspondent. Hoffman is also a puzzlemaster using the pseudonym Dr. Crypton. He designed the puzzle in the 1984 book Treasure: In Search of the Golden Horse. He also designed the treasure map in the 1984 film, Romancing the Stone, starring Michael Douglas, Kathleen Turner, and Danny DeVito.
Hoffman holds a B.A. degree summa cum laude from Harvard. He is the winner of the first National Magazine Award for Feature Writing and is a member of the American Academy of Arts and Sciences.
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Displaying 1 - 15 of 15 reviews
July 16, 2011
I generally like to mix in some popular science books but this didn't do it for me. It was a disjointed read because it jumped into four separate areas of mathematics and none of the areas really held my attention and I ended up skipping through some pages. The four sections covered are number theory, shapes and topology, computer science, and the mathematics of voting.
Of the four, the number theory section is the most interesting but if that's your bag then just go read Simon Singh's two books: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem and The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography.
The chapter on computing machines is weakened by the fact that the version of the book I read was published in 1989 and so was dated.
Of the four, the number theory section is the most interesting but if that's your bag then just go read Simon Singh's two books: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem and The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography.
The chapter on computing machines is weakened by the fact that the version of the book I read was published in 1989 and so was dated.
may-read
October 15, 2019I saw the following excerpt on Hacker News
The ILLIAC IV was a gigantic machine built in the 1970s at the University of Illinois. It had sixty-four processors, each as big as an upright piano because it was built before its time. In fact, they had to use a forklift to plug in the units. It took seven or eight years to build, and the machine was obsolete by the time it was finished. The university gave it to NASA, which promised to use it but had difficulty doing so.
That the project was too ambitious, given the available technology, was not what Minsky meant by the ILLIAC IV mistake. He told Hillis that the concept itself was flawed; it was a mistake, he said, to restrict all the sixty-four processors to doing exactly the same thing at the same time, an expanded electronic version of the Olympic event synchronized swimming. Minsky told Hillis that the processors should be able to operate independently.
"About a month later," Minsky recalls, "Danny came back to me and said, 'Well, I've decided to make the ILLIAC IV mistake.'" Hillis told Minsky that the problem was not in what the processors did but in how they communicated. He said that intraprocessor signals got stuck in traffic jams because, among other things, the connecting wires were restricted to two dimensions. Hillis recognized that a richer connection scheme was required, all the more so since he wanted to hook up not 64 processors but 65,536. The signal traffic would be equivalent to a telephone network serving 65,536 customers who placed a quarter of a billion calls per second. That was the chief technical problem Hillis faced in designing the Connection Machine.
In the end, Hillis and his co-workers at Thinking Machines settled on a three-dimensional architecture in which the processors were connected as if they formed a sixteen-dimensional cube. What this means is that each processor, although directly connected to only 16 others, was never more than sixteen steps away from any of the other 65,536 processors. Moreover, the possibility of a traffic jam was reduced because in sixteen dimensions there are numerous possible routes between any two processors. [1]
[1] From the book Archimedes' Revenge: The Joys and Perils of Mathematics by Paul Hoffman (New York: Ballantine Books, 1988), pp. 203--4.
The ILLIAC IV was a gigantic machine built in the 1970s at the University of Illinois. It had sixty-four processors, each as big as an upright piano because it was built before its time. In fact, they had to use a forklift to plug in the units. It took seven or eight years to build, and the machine was obsolete by the time it was finished. The university gave it to NASA, which promised to use it but had difficulty doing so.
That the project was too ambitious, given the available technology, was not what Minsky meant by the ILLIAC IV mistake. He told Hillis that the concept itself was flawed; it was a mistake, he said, to restrict all the sixty-four processors to doing exactly the same thing at the same time, an expanded electronic version of the Olympic event synchronized swimming. Minsky told Hillis that the processors should be able to operate independently.
"About a month later," Minsky recalls, "Danny came back to me and said, 'Well, I've decided to make the ILLIAC IV mistake.'" Hillis told Minsky that the problem was not in what the processors did but in how they communicated. He said that intraprocessor signals got stuck in traffic jams because, among other things, the connecting wires were restricted to two dimensions. Hillis recognized that a richer connection scheme was required, all the more so since he wanted to hook up not 64 processors but 65,536. The signal traffic would be equivalent to a telephone network serving 65,536 customers who placed a quarter of a billion calls per second. That was the chief technical problem Hillis faced in designing the Connection Machine.
In the end, Hillis and his co-workers at Thinking Machines settled on a three-dimensional architecture in which the processors were connected as if they formed a sixteen-dimensional cube. What this means is that each processor, although directly connected to only 16 others, was never more than sixteen steps away from any of the other 65,536 processors. Moreover, the possibility of a traffic jam was reduced because in sixteen dimensions there are numerous possible routes between any two processors. [1]
[1] From the book Archimedes' Revenge: The Joys and Perils of Mathematics by Paul Hoffman (New York: Ballantine Books, 1988), pp. 203--4.
January 12, 2025
A breezy and lighthearted account of a number of topics in and around the periphery of mathematics." It's rather out of date in several areas now. For example, at the time of publication (1988), there were 30 perfect numbers known. Now, with the help of powerful computers, that number is up to 52. The commentary on the potential of chess playing computers, and the likelihood of AI is also behind the times.
March 12, 2021
3.5 stars
February 11, 2024
Not bad. The discussion of supercomputers and chess playing programs is very dated now since the book was written in 1989.
August 5, 2025
A pleasant read of some neat mathematical curiosities! Some of the details were already known so it might not have an abundance of new learning. Consider, though, that these types of books are already an interest of mine so I already have a significant base of knowledge here.
The section on cryptography is an excellent, brief overview of how that works. The section on computers was probably decent when written (1988) but is necessarily dated now. The section on voting is excellent! It clearly illustrates the problems in the system and even presents what seems to be the best, most fair solution. Too bad the American government/states can't see the value of such a system! The section on chess also gives a good overview of how those systems WERE setup. The learning software of today is different and better than what was done in 1988, but this shows how it was done back then.
The use of graphs/illustrations add very effectively to the text. Furthermore, the style is very easily readable and flows smoothly. The math details are effectively integrated into the text so that one does not get overwhelmed with numeric minutia but also gets enough detail to understand/see how the topic works with the numbers.
Overall, this is a decent, relatively quick, entertaining, interesting read for those with an interest in numbers. Hate math? Don't particularly like math? This book is probably not for you! Otherwise, enjoy the essays at your leisure or interest as the ordering/sectioning of the book is convenient but not at all necessary. Each chapter could be read independently with no connection to any other section/detail of the book.
The section on cryptography is an excellent, brief overview of how that works. The section on computers was probably decent when written (1988) but is necessarily dated now. The section on voting is excellent! It clearly illustrates the problems in the system and even presents what seems to be the best, most fair solution. Too bad the American government/states can't see the value of such a system! The section on chess also gives a good overview of how those systems WERE setup. The learning software of today is different and better than what was done in 1988, but this shows how it was done back then.
The use of graphs/illustrations add very effectively to the text. Furthermore, the style is very easily readable and flows smoothly. The math details are effectively integrated into the text so that one does not get overwhelmed with numeric minutia but also gets enough detail to understand/see how the topic works with the numbers.
Overall, this is a decent, relatively quick, entertaining, interesting read for those with an interest in numbers. Hate math? Don't particularly like math? This book is probably not for you! Otherwise, enjoy the essays at your leisure or interest as the ordering/sectioning of the book is convenient but not at all necessary. Each chapter could be read independently with no connection to any other section/detail of the book.
November 5, 2011
This one is a good one to read a couple of chapters, then regurgitate math curiosity in the lunch room. Yes, I'm very popular at work.
Still, messing with cipher basics comes in handy, like how often certain letters and words occur in English. For example, pretend you teach first grade and you are watching six-year olds try to stretch out words like, "you."
They sound out, "/Yu as in "yarn"/, /aw as in "octopus"/, /uh as in "umbrella"/." Then they look at you like, okay, "yaawuh, I'm done." Their letter sounds prove accurate here but the combinations of the letters change the sounds. Thanks to a legacy of invaders leaving behind language while pushing into England, there are hundreds of similar words that surface in the first books kids read. Code math ranks certain letters and words as most likely to occur. Presto, these are the first words to teach and Hoffman helps us get there.
This book was first published in 1988. The information Hoffman presents here reads as something relevant. Still, I couldn't get that out of the back of my mind, reading, wondering what new information or manner of explanation usurped which parts of this book. I worry that I leant too heavily on what's new, and not present in this book, to let go enough for me to finish this book.
I liked the half I read, though, and encourage you to follow up with your reading of it. I'm also looking forward to reading Hoffman's book about Paul Erdos, a mathematician a la Larry Fleinhardt from Numb3rs. Thanks Karlito and Curtito for turning me toward Hoffmancito.
Still, messing with cipher basics comes in handy, like how often certain letters and words occur in English. For example, pretend you teach first grade and you are watching six-year olds try to stretch out words like, "you."
They sound out, "/Yu as in "yarn"/, /aw as in "octopus"/, /uh as in "umbrella"/." Then they look at you like, okay, "yaawuh, I'm done." Their letter sounds prove accurate here but the combinations of the letters change the sounds. Thanks to a legacy of invaders leaving behind language while pushing into England, there are hundreds of similar words that surface in the first books kids read. Code math ranks certain letters and words as most likely to occur. Presto, these are the first words to teach and Hoffman helps us get there.
This book was first published in 1988. The information Hoffman presents here reads as something relevant. Still, I couldn't get that out of the back of my mind, reading, wondering what new information or manner of explanation usurped which parts of this book. I worry that I leant too heavily on what's new, and not present in this book, to let go enough for me to finish this book.
I liked the half I read, though, and encourage you to follow up with your reading of it. I'm also looking forward to reading Hoffman's book about Paul Erdos, a mathematician a la Larry Fleinhardt from Numb3rs. Thanks Karlito and Curtito for turning me toward Hoffmancito.
April 19, 2014
I've been meaning to get to this book since I bought it some twenty-plus years ago. It was the worth the wait, and all the intricacies of current research in mathematics c.1988 were revealed. One of the more interesting chapters deals with cryptography, and made mention of the Beale Papers, unsolved ciphers that describe a buried treasure that is still awaiting discovery somewhere in Bedford, Virginia.
June 25, 2007
The earlier chapters deal with classic mathematical problems and history, but once the book gets "current" for the time it was written--the late 1980s--its a little dated. All in all, I'd skip this book and go straight to Hoffman's incredible biography of mathematician Paul Erdos, "The Man Who Loved Only Numbers".
June 9, 2013
Some highly interesting stories about the history of science and maths in particular. Yet, though it pretends to be written for people without any prior knowledge/talent and even while I took math classes for 6 year on college level, I found a lot of it incomprehensible.
December 22, 2022
It makes me want to go out and start breaking codes!
February 9, 2010
This was a really enjoyable read about some of the curiosities of mathematics. The game theory portion is a well written introduction and very readable.
December 31, 2012
I liked it. A great trip through varied areas of mathematics without any real mathematics (which would have made the book impossibly long).
February 8, 2015
somewhat outdated (especially the parts on computing and AI), but still a pleasant read.
March 11, 2013
Exploring my mathematical roots...
Displaying 1 - 15 of 15 reviews