I really enjoyed this book. Now what are we going to call the numerals used in the West that seem to have evolved from several sources? Arabic-Indian-Cambodian? AIC? Who knows what other cultures may have had a hand in them? Africa south of the Mediterranean countries and their near neighbors, sunken Southeast Asia?

Aczel has two main issues that he is looking into, although at time I think that they get a bit in each other's way. One is the form of the letters, and the other is the concepts of zero and infinity. He has mostly limited himself to Eurasia, with a brief side trip to Egypt. He isn't interested in the Americas because the numerals that interest him developed independently, but he does mention that the Mayans had a numeral representing zero. Interesting in view of Aczel's argument that he thinks the concept of zero originated from south Asian religion and philosophy.

That wouldn't apply to the Mayan zero, but I don't know that we know enough about indigenous American religions to say if they had the same ideas, especially with the realization that South America was much more heavily populated and had a lot more cities than we supposed. The history of Africa, particularly outside of the Mediterranean rim, is also in need of a lot more study. Similar things often develop independently around the world in any case.

Aczel includes a lot of personal information, as he is recording his search for a lost artifact that was written about in the early 2oth century. Sometimes this can get tedious, as in a certain book where the author kept going off on unrelated tangents, and filling the reader in on personal trivia. Aczel led a very interesting life, and tells his story well, so I enjoyed this. Most of his tangents related to interesting fact about famous mathematicians that were interesting in their own right, or mathematical controversies such as the arguments about Set Theory, as well as other mathematical systems that used base 60 and base 20 instead of base 10.

His father, of Hungarian heritage, was a cruise ship captain of the S. S. Theodor Herzl, named for the Hungarian political theorist, and his steward, Laci, a Hungarian mathematics student who ran afoul of the Soviets, was one of the most influential people in Aczel's life, who served as an informal tutor and developed his interest in mathematics and numbers.

A Hungarian-French mathematician named George Cœdès (another Hungarian connection) was a language teacher who discovered that he had an uncanny ability to decipher ancient scripts, and spent much of his life in Cambodia. In the 1920s and 1930s, there was a bitter linguistic debate about whether the zero originated in eastern or western Eurasia. Cœdès published a paper in 1931 arguing that the oldest zero represented by a character was on a seventh-century Cambodian inscription. on a stone marked designated as K-127, Unfortunately, it had disappeared, and with the destruction wrought by the Khmer Rouge, possibly destroyed. Aczel made it his mission to find the stone, and declared that he would spend the rest of his life trying to find it if need be. I won't ruin the suspense.

This is where the distinction between representation and concept gets a little murky. Other people's had the concept of zero, without developing a character to represent it, so one might question its tie to philosophy. They often simply left a space to represent it, which probably worked well enough to represent 20 cows, but not 2,000 soldiers. Europe and Indian weren't the only thinkers in Eurasia. An Egyptologist, Alan Gardiner suggested that the nfr hieroglyph, found in the the eighteenth century BC/BCE represented zero, although under his requirements, Aczel might dismiss it as not leading to the zero used in Western nations today. The Cambodian zero in the inscription was a round depression in a stone, part of the number 605. The Indian zero was a circle, and it is easy to see how in writing, rather than chiseling, the two characters could be interchanged.

Aczel presents an eloquent, even moving, description of the importance of the representation, especially for dealing with large numbers. It permits the same ten digits to be used to represent numbers of any size. I felt very fortunate to be one of the heirs of this system.

One of my favorite chapters was Six, in which Aczel is explaining Indian philosophy in which something can simultaneously be one both true and untrue, as opposed to Aristotelian philosophy in which something is or is not. His example is that a cup of coffee with a very small amount of sugar in it could be said to be neither sweet or unsweet. A friend long ago pointed out that Aristotelian logic doesn't really allow for something becoming. It also highlights something that has always frustrated me about the English language: the difficulty of expressing neutrality or indifference. If someone asked me if I like so-and-so, and I say "no" they are likely to assume that I dislike them, and ask what I have against them, unless I explain that I have no strong feelings or use.a double negative: "I don't dislike them," or perhaps shrug my shoulders. Yes and no stand in opposition to each other. ( )

Not what I expected, in a good way. Loaned the book to my father, who has a deeper love and better understanding of mathematics than I do - he also enjoyed reading it. ( )

an amazingly engaging read (since I am not much of a math person). ( )

Very cute ending. This book was an Odyssey in finding the numbers, zero and the void. I found it quite an enjoyable read. ( )

Very cute ending. This book was an Odyssey in finding the numbers, zero and the void. I found it quite an enjoyable read. ( )

I love the intersection of science/math and history and have read a dozen books in this genre. I thought this work feel short of the mark, as there is less historical rigor, less explanation of the under-pinning concepts, development, and hard facts bringing the reader from unknowing to understanding. This is instead more of a mathematician's travel log of southeastern Asia. There is some philosophy, some mathematical discussion, some history and the author's odyssey to find what he was looking for is told with a story teller's gift of intrigue. Nonetheless, not my favorite in this genre, though I am willing to give Aczel's other books a try.

Memoir meets travelogue meets mathematics and archaeology meets philosophy and religion. There was a lot in here that I enjoyed, particularly the segments of the book that dealt with Aczel's quest to find a particular important artifact, encountering many of the challenges that archaeologists and other scholars face in the field -- bureaucracy, corruption, wartime destruction of antiquities, unscrupulous scholars out to steal your find. When he focused instead on his obsession with understanding the origin of the zero, delving into Eastern religions and philosophy, I got a bit frustrated at times with his perhaps-overstated claims about the differences between Eastern and Western minds, while also sympathetic to his desire to redress some of the wrongs Western societies have done in colonial and post-colonial times. Ultimately, I found the story of his personal quest at least to be satisfying.

The author isn't obsessed with a conceptualization. He was eager to geographically identify the specific earliest plaque known to depict the actual number zero in use.
More a memoir, and a pleasantly compelling one, than a book about mathematics or history, this includes academic intrigue, ancient history, twentieth century smuggling and more. For those who enjoy historical oddities or memoirs, it's a pleasant, easy read. Perfect beach reading. ( )

Summary: When the author was a young boy (as he tells it, the first time he's taken into a casino by the steward of a ship on which his father was captain), he became obsessed with numbers, where they came from, why the mean what they mean. Our numerical system influences the ways we can use mathematics, and may well shape the even the way we think, but its origins are not well understood. This book chronicles the author's investigations into where our numbers come from - particularly, when the idea of (and symbol for) zero entered our understanding, and from where. Aczel argues that the earliest zero came from Cambodia, and that the concept of zero - the idea of representing nothingness - has its roots in Buddhist philosophy.

Review: Amir Aczel really, really wants to see himself as Indiana Jones; that was my primary take-away from this novel. The idea was certainly planted by the cover copy (one blurb blatantly states "Amir Aczel is the Indiana Jones of the mathematical world"), but it was backed up by his own words from the book itself, as well as the way he recounts the "exciting personal adventure" and "drama that erupted" (more blurbs) of his finding evidence of the earliest known zero in a carved rock in Cambodia. In the preamble, he states "In my search, I explored uncharted territory, embarking on a quest for the sources of these numbers to India, Thailand, Laos, Vietnam, and ultimately to a jungle location in Cambodia, the site of a lost seventh-century inscription. On my odyssey I met a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and suspected archaeological thieves." Sounds exciting, right? However, in reality, his "adventures" mostly involved e-mailing people and dealing with passport officials and lost taxi drivers. Not exactly cinematic stuff.

Also, his "suspected archaeological thieves" were in fact other researchers who - upon hearing about his discovery - decided to work on the artifact… something which they had government permission to do (and Aczel did not). I absolutely don't mean to diminish Aczel's work - his investigations and deductions that lead to his discovery of the artifact were clever, and I agree with his argument that this rock with the earliest known zero is an important piece of scientific history. However, his comparison of the event to the first scene of Raiders of the Lost Ark ("Once again, Dr. Jones, something that was briefly yours is now mine!") struck me as kind of petulant. "These two Italians were grabbing my find - right in front of me - after so many years of my searching for it." "I began to suspect that she had another motive: Was she planning to try to pass it off as her own discovery, by publishing an academic paper, perhaps?" And since this scene was the centerpiece around which the whole book revolves, it left kind of a bad taste in my mouth.

Ultimately, I did learn some interesting things from this book. And, as was the case in Aczel's previous book, The Cave and the Cathedral, while I'm not sure I entirely buy all of his theories, they certainly present interesting possibilities. However, I think the author is trying to oversell the adventure angle of things in order to flesh the story of his discovery out to book-length; most of the real material in here would have fit very comfortably into a National Geographic-style article. 2 out of 5 stars.

Recommendation: If you're interested in the history of science and mathematics, this book may appeal to you, but if you want the key factual points without all of the "personal adventure", I recommend just reading the May 2013 Huffington Post article on the discovery, also written by the author. ( )

Six-word review: The drive to seek, find, know.

Extended review:

(An Early Reviewer review)

This is not a book about mathematics. It's the story of a quest, of a man on a mission to satisfy a personal desire as much as to solve a great mystery of the past.

An all-consuming question about the history of human intelligence and abstract thought drives the author's lifelong search. His goal is to locate the birthplace of the concept of number and especially of the number zero. For Aczel, this is not some bodiless mental pursuit but a thrilling intellectual and geographical quest for a historical moment of invention that stands alone among peak human achievements.

That the odyssey is a personal one is made plain by the structure of the book. It begins and ends with the author's connection to the man who set him on his course, a man whose own history lies in the shadows but whose enthusiasm for the ideas behind the numbers that are so familiar to us excited and inspired a young boy. In the course of his search for the ancient roots of mathematical understanding, the author sees links to religion and philosophy and especially to Buddhism, with its core concept of emptiness--shunyata. Here he refers to a passage in Zen master Thich Nhat Hanh's writing about the Buddhist idea of the void:

As I concentrated on these notions, I came to believe that I could even read the quoted verses above as saying: existence = 1, nonexistence = -1, and emptiness = 0. Emptiness was the door from nonexistence to existence, in the same way that zero was the conduit [sic] from positive to negative numbers, one set being a perfect geometrical reflection of the other along the number line. (page 106)

If this is mathematics, it's also mysticism; and the overlapping and merging of arbitrarily separated disciplines is one of the themes of this book.

It's not the discoveries but the passion that is the subject of this account; not the numbers but the zeal. An individual commits himself to a goal, and an ineffable something in him impels him to persevere and not give up. His hunger for the answer draws him on; his persistence and unflagging excitement infuse his tale, and that's what draws us on as readers.

If his ascription of supernatural significance to such things as the label number of the sought-after archeological artifact ventures over into woo woo territory, well, that might be one of the reasons for a moderate rating. That his approach and his narrative are not strictly rational simply confirms that this is not a book about math. ( )

I shouldn't look forward to books by Amir Aczel as much as I do, but I really enjoy them. The most miserable course I had in business school was Statistics and he was the lead editor of the text book. Problem was the instructor, not the book.

Finding Zero is a very personal memoir. Beginning with the very childlike wonder of Aczel being introduced to the mysteries of mathematics by the chief steward of the cruise ship on which his father was a captain, to the sense of adventure traveling through Laos and Cambodia to solve the mystery of the first zero, Aczel's voice is at once that of an adult and the age he was at each stage of his life. A quick read, a lot of fun. Highly recommended. ( )

I did not think I would enjoy this book, having always been a mathematics dummy, but I did - greatly. Not only did the author finally help to understand what 'Sets" are but I got closer to understanding "Primes" that I ever had before.

I have always believed that mankind is broadly split into two types of mind, either analytical or aesthetic and i was convinced that the twain could not meet, but only, like parallel lines in infinity ... Zero in fact. Dr. Aczel showed me the absolute value of zero and some of the impact on our culture in a very enjoyable read.

I think that some of the rather negative reviews about this work are expressing the disappointment from the analytical viewpoint that is is not more of a tome of pure mathematics.

it is instead a travel and adventure book about math. And what adventures as the author wanders around the far east, seeking the grail of finding the first recorded zero.

Recommended if you enjoy armchair travels, history ... and even math.

Finding Zero recounts author Amir Aczel’s discovery, more accurately rediscovery, of a Cambodian stele inscribed in the year 683 with text including a dot used as a place-holding zero in a number we would write today as “605”. He makes the case that this is the oldest surviving use of a modern zero, although his argument involves stipulations that result in ignoring Mayan and Sumerian precedents. Whether you agree with his argument or not, the material would add up to a reasonable magazine article. In fact, Aczel published such an article in the Smithsonian’s Discover magazine in May, 2013, where it generated some debate.

In order to make a book of it, the author has produced a sort of memoir or diary about how he went about his research. But even to fill up this slim volume, he has to include details such as the aircraft used by Air Asia, their lack of meal service, and the revelation that he had to pass through immigration on arrival in Cambodia.

Anyone interested in the mathematics of the story would be better off with the magazine article. The book version is a sort of blog, and might have been better suited to social, rather than printed, media. ( )

I won this book as part of LibraryThing.com's Early Reviewers. Over all, I really enjoyed this book. I never had an opinion about the origin of the zero, but I've always known it came later and was one of the most significant mathematical creations. We are made to believe that our numbers, including the zero, are an Arab creation, and Mr. Aczel sets out to correct our misconceptions regarding the first zero's origins. His curiosity regarding numbers started at a very young age, encouraged by a mathematician who worked on his father's boat as a child. It is amazing how much the interactions in our lives at childhood can set the path for later in life. This passion for numbers never died down, but instead stayed with him throughout his life and set him on the path to be a mathematician himself. Although, the writing style was very matter-of-fact in many places, lacking some descriptives that would have made the story flow a little easier, the adventure that Mr. Aczel had was, indeed, interesting. As a mathematician who has no archeological background, searching the world for this lost artifact, the odds seemed to be stacked against him. Through the right connections, and a lot of luck, everything works out in the end and the first known zero is rediscovered. (Until we find the next earliest zero.) If you are into math, or even history, you should give this a read. ( )

As others have noted this book is partly a memoir and travelogue, and partly a review of the history of mathematics and its interrelation with religion. I found the latter theme most interesting. The concepts of zero and infinity, as they developed in both East and West, are for me the heart of this book. ( )

Amir D. Aczel gives us an excellent account of the development of our system of numbers, and the special function played by the number "0." Specifically, Aczel spent a substantial portion of his professional life searching for physical proof of the first use of "0" (as signifying "nothing", and as a placeholder in large numbers - like 104 for 'one hundred and four').

Along the way, Aczel gives us an intriguing history of numbers, an interesting history of the search for zero, and a usually interesting account of his search and the people he encountered. Some parts of the book almost read like an adventure story, rather than a history, and it is easy to get quite caught up in the hunt for zero.

At the same time, Aczel does succumb to the temptation to make things a bit melodramatic, and some parts of the book are a bit over-long and/or repetitive. Whether some choice editing and excision would have helped the book is a moot point, however - what you see is what you get.

I am fascinated by math, and this book was a lot more interesting than I thought it would be. You don't have to know math to appreciate what the search is about, and discovering the ultimate conclusion of the search makes the book well worth reading. ( )

Science, religion, history, and travelogue combined into an interesting story of the search for the origin of our modern day number system, particularly zero. Although this is a book about mathematics, it is written in an easy, approachable style that makes for a quick read. The bits about the author's past travels are especially enjoyable.

Note: this review is based on an ARC received from the publisher ( )

This was an Early Reviewers copy. The title intrigued me since I am fascinated by numbers and a history buff -- what more could I ask?

Other reviewers have thoroughly detailed the contents of the book much more competently than I could so I'll just say I found the book enjoyable.

The author managed to hold my attention throughout the book although, as another reviewer noted, I found his disparagement of other researchers a bit off-putting. ( )

There's little question that the use of positional notation for numbers is one of the most useful human inventions. I mean, can you imagine trying to do calculus with Roman numerals? And in our modern mathematical notation, the most important idea is that of the zero - representing nothing!

Sometime in the early Renaissance, these concepts migrated to Europe through the Arabic world, initially through the work of Fibonacci. And the merchants and business people loved the efficiency of accounting using this new system.

What we don't know is who invented our numbers, especially introducing the concept of zero. Many think they came out of the East - India, or perhaps the Middle East - hence we call them Hindu-Arabic numerals. But the evidence for this is skimpy and the history of our numerals isn't known. Finding Zero is Aczel's memoir of his years-long search for that evidence. It's well-written, and an interesting story. I wish Aczel had given us more on ancient numbering systems and arithmetic - what was there was great, but more would have been better!

Recommended, even for the non-mathematically inclined. The level of expertise needed is absolutely minimal while still a fun story! ( )

This book is a little hard to review. It is part memoir/travelogue - I normally dislike those, but found this one somewhat charming. I like the stories from his younger days, and he gave just the right amount of flavor and detail on his travels. It was also part philosophical, which I did not like as much. The crux of it was that eastern cultures are not as tied to true/false, black/white forms of logic, which is what enabled them to be able to conceive of the concept of zero when western cultures did not. It's a somewhat compelling argument, but it takes far too may turns in to hippyish fuzzy headed philosophy. Just because a guy with a beard in robe says weird stuff doesn't mean he has any idea what he is talking about. It's not a proof or evidence of anything, and felt out of place.

The math was interesting, but there wasn't a whole lot of it. There was some really basic number theory that I think most people could understand, and some set theory. I think there could have been a little more on just why zero was so odd & took so long to be "discovered". This is one of those things that SEEMS obvious until you start to think about why it might NOT be. It's obvious what the difference between 3 apples and 2 apples and 1 apple is, but it is not obvious that the absence of apples is the same thing as a quantity of apples. The one is concrete, and the other IS a bit philosophical, i.e., can something used to represent the presence of something also be used to denote its absence. Today the answer to that is obvious, but why did it take so long to figure out, and why does it have to be that way?

I was definitely more compelled by the final part of the book. I was getting close to the end of the book & starting to drag a little with the philosophical parts, when suddenly a engaging archaeological adventure started to unfold! I don't think it has any danger of getting made in to an Indiana Jones movie, but it pulled me in on a very human level. I could feel the authors anguish and was suddenly engrossed and rooting for him in a way I hadn't been until then. And the last chapter was actually touching, and to me set the perfect tone to end the book on.

My rating system is generally:

1 star = so bad I couldn't bear to finish and gave up.
2 stars = I finished, but wish it had been worse so I would have given up.
3 stars = I liked it, but would be hesitant to recommend it to anyone who didn't have a very specific interest in the topic.
4 stars = although there were some flaws, it was a very good book and I would recommend it to anyone with a general interest
5 stars = outstanding! I stayed up late reading it every night, if you have even a slight interest buy it and read it now. ( )

Where did the number zero come from? Where did numbers in general come from? In Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, author Amir D. Aczel traces his personal interest in number origins and how it led him to a mathematical career and then along an improbable four year search to find the oldest example of the number zero. His search takes him from France to Israel to India to Thailand and Cambodia. He encounters smugglers, corrupt government officials, great mathematicians, historians, travelers and adventurers. Engaging and personal, Dr. Aczel makes what could be a dry, esoteric subject, into a great adventure of mystery, with unexpected turns.

This is a satisfying book to anyone who enjoys history, mathematics, philosophy, or different cultures. I recommend it without reservation. ( )

To begin with, I really did want to like this book. While somewhat math-phobic during my academic career, I've developed a casual interest in pop math and science bookssince finishing undergrad math requirements, and so on that account, I was curious about the source of our numbering system and the use of zero. And when it seemed that the story was told travelogue-style, I was also intrigued, as concept-driven travel narrative (a la Bill Bryson or Tony Horwitz) is also a favorite non-fiction format of mine.

After a couple chapters, though, my interest began to wane. I'm not sure who the expected audience of this story was, but surely just about anyone could be expected to understand the basic principles of, say, prime numbers that he lays out in the middle of a retelling of his childhood. While I think this is an attempt to make sure everyone's on the same page mathematically, in order to make the revolutionary quality of zero/zeroness more apparent, it feels clumsily done. If it were fiction, I'd call it random info-dumping and poor world-building.

But anyway, the travel narrative part is moderately interesting, if a little more focused on the exoticism of "Eastern" thought and religion than seems reasonable. Claiming to have no working knowledge of Hinduism and Buddhism prior to searching for the origins of zero in India, the author nonetheless makes the rather interesting claim that zero was naturally an "Eastern" idea and an obvious product of Buddhism, which the all too literal-minded "West" just couldn't have developed. Now I won't make any counterclaims, exactly, but it seems unnecessary to use stereotypical East/West claims like this and I'd have liked a more in-depth and nuanced treatment of the philosophies of religions from both hemispheres, if such a claim were to be made central.

More bothersomely, the author also appears to overeager to defame another academic with whom he clashes over the care of the earliest record of zero he ultimately rediscovers--giving both her name and a photo. While it's possible that woman was really the malevolent, greedy, would-be history-destroyer he depicts, I really doubt it very much. Besides which, the "evidences" he presents for her wickedness don't hold water for me, personally, as they don't show her doing anything immoral or damaging to the item in question; if anything, she seemed surprisingly willing to collaborate and he far too quick to suspect the worst and insist on his own importance. Anything that smacks of a vendetta is really very off-putting in any personal writing, but it feels especially egregious in this instance, and it rather colored the rest of my reading.

While I'm still interested in the topic of the book and am glad to have more background knowledge on it, I don't think I'll keep this book. I also really wish he would have went more into the origins of the "Hindu-Arabic" numbers we use today, as both the subtitle and introductory materials implied, and hope to find an accessible work on that topic in the future.

I requested this book through Library Thing's Early Review program because I remembered enjoying the author's earlier book, "Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem."

"Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers" was written in a conversational style and incorporated much more than cut-and-dried mathematics. The personal vignettes were charming, and the historical details were interesting (if perhaps selected with a certain bias). But to this reader, the philosophical, religious, and even racist views expressed were a distraction from what I thought the story was about. So my rating of 3 stars is an average of the good parts and the not-so-good.

If you're really interested in a history of the concept of zero, try reading Charles Seife's "Zero: The Biography of a Dangerous Idea," a slim volume, engagingly written, and strictly about what its title suggests. ( )

Part popular mathematics, part memoir / travelogue, the lion's share of Finding Zero is devoted to the latter. The discussion of math concepts is intriguing but brief, related to concept of number; the balance of the book describes Aczel's travels as he tracks down anthropological evidence for the earliest appearance of zero, the numeral. Even his "search" is given short shrift, in that he largely leaves unaddressed his research into how zero was used throughout history, how math functioned without a zero, substitutes in other number systems (e.g. an empty depression in a counting board; use of multiples as with large denomination coins or in Roman numerals). Instead, Aczel describes journeys to India, Cambodia, Thailand, Laos, Viet Nam in search of artifacts which are of interest chiefly insofar as they are documentation of these historical concepts.

I benefited more from Devlin's Man of Numbers, though his concern lies with the pragmatic influence of the Arabic zero and a placeholder number system on arithmetic and commerce. I'd hoped Aczel's slant would provide a useful supplement to Devlin's account, but it doesn't.

//

Principal concepts:
• Zero (number) central to conception of negative numbers
• Zero (numeral) key to efficient notation & arithmetic: calculation of decimals / fractions of currency or other measure; placeholder function allowing numerals to cycle as numbers increase, important for higher orders of magnitude; binary code.
• Quantity expressed historically as substantives (nouns) rather than as numbers, and numerals are unnecessary in such an approach: eight Vasu, six flavours, five senses, four Veda, two eyes; and that number systems often contain numbers deriving from these earlier terms. In antiquity, Khmer knew only numbers 1, 2, 3, 4, 5, 10, 20 and then multiples of 20. In French, 80 is quatre vingt, or four twenties. [213 - 215]
• Mayan zero devised earlier but (a) did not involve a positional element in the Mayan number system, and (b) did not influence other number systems (no trade or travel) [79]
• Cantor's preliminary link of zero's origin in India or Babylon [74]; George Coedes discovery of earliest zero on steles in Cambodia (catalogued as K-127) and Indonesia, two centuries before Arab Caliphate and definitely separate from European or Arabian influence.
• Speculatively links concept of zero (sunya) to Buddhist / Hindu / Jain tradition of emptiness (sunyata) and infinite. [105, 140]
• Most intriguing here is the tradition of tetralemma (in the Greek, catuskoti in Sanskrit): Nagarjuna's logic of true / not true / both / neither. Western mathematical tradition as epitomised in Law of the Excluded Middle, allowing only true or not true, no middle ground [55]. (Note distinction between false & not true.)
• Alex Grothendieck's concept of topos, and critique of set theory. "Technically, our strict, either-or logic is necessitated by our reliance on the theory of sets as a basis for mathematics. This gives us the concept of set membership, which is unforgiving: an element is either a member of a set, or it is not; it cannot be both, or neither. What Grothendieck ... did was to free mathematics from the reliance on set theory and set membership. He employed something called category theory, in which there is no need for sets or membership laws." [58-60] Fred Linton's exploration of tetralemma in frame of Western mathematics, using topos and category theory. [57] ( )

I liked this book, but the story didn't keep my attention. I found the book to drag in the latter half - the spiritual aspect I found a bit dragging. I am not a big a fan of books about self discovery.

I was horrified at the archaeologist and their attempt at restoration. One thing - as a an American, the discoveries of non-western cultures get overlooked - and we as a society, need to start thinking as part of a global society, rather than us vs them. ( )