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The Universal History of Numbers: From Prehistory to the Invention of the Computer

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Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.


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Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.

30 review for The Universal History of Numbers: From Prehistory to the Invention of the Computer

  1. 4 out of 5

    Carlos

    This book covered everything I was looking for and more. Ifrah does a magnificent and herculean job at sharing with the reader the wonderful path taken by those numbers that we can’t help but take for granted. He takes us through the evolution of arithmetic from the biological concepts of “one-two-many” to the great and intricate counting systems designed by many pre-literate societies. He similarly devotes ample time to explain the fascinating origin of the various bases used throughout history This book covered everything I was looking for and more. Ifrah does a magnificent and herculean job at sharing with the reader the wonderful path taken by those numbers that we can’t help but take for granted. He takes us through the evolution of arithmetic from the biological concepts of “one-two-many” to the great and intricate counting systems designed by many pre-literate societies. He similarly devotes ample time to explain the fascinating origin of the various bases used throughout history (base 10, 20, 60 or even 100!). Then, by taking apart the counting systems of several civilizations, from the Assyro-Babylonian to the Chinese and Mayan, Ifrah shows us the logic behind them and the great purposes for which many of those cultures used them. Likewise, in was is perhaps the crowning achievement of this book, Ifrah uses the vast amounts of detail given on the case studies to show the reader the evolving path of our numerical system and the key advantages along the continuum of improvements made by all human cultures. He also takes pains to dispel the theories that seek to preserve the racist myths of the superiority of the Greeks and Romans (and by extension the West, as their intellectual heirs) by implying that our current number system was neither Arabic nor Indian. He fills pages with point by point refutations of the claims against the Indian origin of our number system and with excruciating details of the evolution of the modern writing system through the ancient history of Indian civilization. He dedicates equal time to the vital role played by Islamic science in bring this great achievement to the attention to the western world. Although it is undeniable that the book is more than what the casual reader might choose to pick up, Ifrah manages to make all his discussions completely accessible to the mathematical layman and constantly manages to link the evolution of writing system to the increasing achievements of our species in a way that manages to keep the reader through this leviathan.

  2. 5 out of 5

    Omar Ali

    Georges Ifrah is a Frenchman of Moroccan origin who was an ordinary schoolteacher of mathematics before his students sparked one of the great intellectual quests of our time (or, indeed, of any time). His students asked him where numbers came from? Who invented them and why? How did they take their modern form? When he tried to answer these simple questions, he found that the information found in standard textbooks was highly unsatisfactory and frequently contradictory. Not content with passing Georges Ifrah is a Frenchman of Moroccan origin who was an ordinary schoolteacher of mathematics before his students sparked one of the great intellectual quests of our time (or, indeed, of any time). His students asked him where numbers came from? Who invented them and why? How did they take their modern form? When he tried to answer these simple questions, he found that the information found in standard textbooks was highly unsatisfactory and frequently contradictory. Not content with passing on half-truths and conjectures, Mr. Ifrah abandoned his job and embarked on a ten-year quest to uncover the history of numbers. He traveled to the four corners of the world, read thousands of books, visited hundreds of libraries and museums and asked questions of countless scholars. All this research was supported by odd jobs as delivery boy, chauffer, waiter, night watchman and so on. The result was a book called FROM ONE TO ZERO A Universal History of Numbers, (published in English translation in 1985 ). The book was a hit and brought fame and fortune and the chance to do more research. This led to a much larger book, The Universal History of Numbers: From Prehistory to the Invention of the Computer, which was translated into English in 1998 (after initial publication in French in 1994) and is now available in either one or two volumes. These books have earned Mr. Ifrah the title of “Indiana Jones of numbers” and worldwide celebrity. After reading the book, I can only add that he deserves every superlative that has been used, and more. To quote a reviewer from “The Guardian”: "Georges Ifrah is the man, and this book, quite simply, rules.” This is not just a history of numbers, it is universal history disguised as the history of numbers. Mr. Ifrah starts with the most basic questions; what kind of “counting sense” do animals possess? What do we know about the number sense of our pre-human ancestors? When we evolved into Homo sapiens sapiens, what kind of numerical ability was “hard-wired” into our brains? He presents fascinating information about the most primitive counting systems, using tally marks, fingers, body parts etc. from these simple beginnings, we move to the abstract concepts of number and its notations. The detail provided is astounding. We learn about the earliest systems of numbers used in the Middle East, India, china, and the ancient Maya etc.etc. And not only do we learn about the numbers, Mr. Ifrah slips in his humanistic, sensitive and very very detailed knowledge of history so smoothly that we hardly notice that we are learning, not just the history of numbers, but the history of mankind; told by a very fair, very balanced and deeply sympathetic observer. The book is designed to be a reference work and thus contains more detail than the casual reader may require, but unlike most reference works, it is written in an accessible style and every concept is beautifully explained from the bottom up. You can read it from beginning to end (and enjoy every minute) or just jump to the matter that interests you and learn about that. If you have ever wondered how “primitive” people added and multiplied on their fingers, look no further, if you want to know how the abacus is used and how the Roman numerals can be (or cannot be!) manipulated, step right in. Mr. Ifrah has the answers. He will also tell you all about the use of letters to represent numbers and the number values of every letter in Hebrew, Greek, Arabic etc. I learned for the first time why the huroof-e-abjad are in an order different from the order of letters in the modern Arabic alphabet (aleph, bey, geem; rather than aleph, bey, tey) and how and when these changes came about. The section on magic and mystery tells us about the occult significances of numbers and arcane topics like chronograms (words that express a particular date). E.g. the chronogram “zaatish murd” literally means “died of burns” but when the abjud values are added together, gives us the date 952…. the hijrah year in which king Sher of Bihar died in a fire! Mr. Ifrah tackles the question of where our modern number system came from and gives an unambiguous answer: from India. Somewhere between the second and fifth century CE, Indian mathematicians worked out the revolutionary system of using 9 numbers and a zero that we still use in the same form today. This system traveled from India to the Middle East, as did the nine Indian numerals. In the course of their travels, the numerals were gradually modified into their current forms, and Mr. Ifrah provides detailed (and graphic) evidence of how this happened. This chapter also puts to rest the theory that the number forms have anything to do with counting the lines or angles to equal their value. The forms are modifications of the original Indian “Brahmi” forms and nothing more. The Arabs who took up these numerals made no attempt to hide their origin and writers like Khwarizmi gave full credit to the Indians for these discoveries, but by the time the news reached Europe in another two hundred years, the Indian origin had become obscured and thus we still call our numerals “Arabic” numerals. It’s interesting that the first attempt to introduce these to Europe was made by the progressive pope Sylvester the second in 1000 CE but failed due to resistance from conservative elements. It was only after the crusades and the work of the famous Italian mathematician Fibonacci that the new system started to take hold, even then, it was several hundred years before the church fully accepted the new invention. In fact, resistance from the church led to the zero based system being used in secret. A bit of history from which we get the word “cipher” – which originally meant zero, but took on connotations of code and secrecy because the zero based system was used in secret! At the end to the book, Mr. Ifrah provides a brilliant after word, where he incidentally demolishes all the theories of prehistoric alien invaders with the simple question: if ancient invaders came to teach us the secrets of how to build the pyramids, why didn’t they teach us about zero and place value notation? Is it conceivable that any advanced civilization that flew around in spaceships did not have the zero? The evidence is very clear that it took mankind a very long time and many failed experiments before our Indian ancestors finally solved this riddle. If arithmetic was invented slowly and painfully, with no outside help; then so was everything else, because, before any other science there is the science of numbers!

  3. 4 out of 5

    David

    This is truly the definitive of the history of numbers. Ifrah has done a huge amount of research, and this encyclopedic treatment is the result. Among the many fascinating findings is that our modern system of decimal arithmetic, complete with positional notation, zero, and the usual algorithms for +-*/, was first discovered in India, not "Arabia", and much earlier than is often believed: Ifrah cites a large number of references that indicate that place the origin at least by 458 AD. One other v This is truly the definitive of the history of numbers. Ifrah has done a huge amount of research, and this encyclopedic treatment is the result. Among the many fascinating findings is that our modern system of decimal arithmetic, complete with positional notation, zero, and the usual algorithms for +-*/, was first discovered in India, not "Arabia", and much earlier than is often believed: Ifrah cites a large number of references that indicate that place the origin at least by 458 AD. One other very interesting finding is how that the modern decimal system met such stern opposition in Europe. In the year 999, Pope Sylvester went to Spain to learn about this new scheme first-hand from Moorish scholars, but that when he returned he met only the stiff resistance, and in fact acquired a reputation of having communed with Satan himself. The scheme was practiced "underground" for centuries in Europe, but was not widely accepted until the 18th and 19th century. Our modern word "cipher", which means "mystery" and "secret code" as well as "zero", is a linguistic memory when acknowledging that one used this system could have resulted in your execution by the Inquisition!

  4. 5 out of 5

    David Tagliaferri

    It is amazing how such a book can be so interesting. Just being what it is, a catalog of numbers.

  5. 5 out of 5

    Andrea Hickman Walker

    I think the subtitle is rather misleading because it doesn't really discuss the invention of computers, unless one considers a computer to be any kind of calculating machine. There is a discussion of binary notation, along with the other bases. Overall the book is fascinating and incredibly detailed and informative. I was particularly interested by the fact that zero and cipher come from the same root. The knowledge that science and learning could have progressed much further much earlier is a r I think the subtitle is rather misleading because it doesn't really discuss the invention of computers, unless one considers a computer to be any kind of calculating machine. There is a discussion of binary notation, along with the other bases. Overall the book is fascinating and incredibly detailed and informative. I was particularly interested by the fact that zero and cipher come from the same root. The knowledge that science and learning could have progressed much further much earlier is a rather depressing reflection on human nature and culture, but even today there are people that are against education and the spread of knowledge. It's a position I do not understand, but presume it is a result of the desire to have power over and control of other people.

  6. 4 out of 5

    Kshitiz Uttam

    Numbers are fascinating. So is history. History of numbers, then, must be bewitching. So I thought before I read this work. I was wrong. The book has been terribly written. It reads more like a research paper than a book. Ifrah has done a terrific job researching this book. However, it seems that he has done just that, nothing more. He failed to weave a story out of the immense information he gathered. For instance, once you tell us how primitives counted, it should be enough. One does not need Numbers are fascinating. So is history. History of numbers, then, must be bewitching. So I thought before I read this work. I was wrong. The book has been terribly written. It reads more like a research paper than a book. Ifrah has done a terrific job researching this book. However, it seems that he has done just that, nothing more. He failed to weave a story out of the immense information he gathered. For instance, once you tell us how primitives counted, it should be enough. One does not need to know how all the primitives counted. Sure, there will be variation amongst them, but the basic concept is what is interesting not the details. But the book drags on such trivialities for pages. What I learned from the book? Yet again, not everyone can write.

  7. 4 out of 5

    Douglas Summers-Stay

    I assumed that this would be a history of mathematics, or perhaps arithmetic. But no, like the title says, it's a history of of numbers. Numbers and counting systems from all different cultures, from prehistoric tally marks to sheep-counting techniques, to finger counting methods from around the world. You wouldn't think it would be possible to write such a thick book about just numbers for a popular audience, but there it is. It's illustrated on almost every page, with Mayan scripts and the deve I assumed that this would be a history of mathematics, or perhaps arithmetic. But no, like the title says, it's a history of of numbers. Numbers and counting systems from all different cultures, from prehistoric tally marks to sheep-counting techniques, to finger counting methods from around the world. You wouldn't think it would be possible to write such a thick book about just numbers for a popular audience, but there it is. It's illustrated on almost every page, with Mayan scripts and the development of Arabic numerals and so forth.

  8. 4 out of 5

    Zornitsa

    Тематиката е страшно интересна, изданието е много подробно и изчерпателно. Съдържа, например, две глави за азбучните бройни системи като тази по нашите и околните земи. Ще пиша повече, като я дочета.

  9. 4 out of 5

    Kate

    I have not actually finished this behemoth of a book, nor will I probably ever finish this behemoth book. However, where I have skipped around, I have found it to be incredibly interesting. Definitive.

  10. 5 out of 5

    Eivind

    Fantastic! Always at hand

  11. 5 out of 5

    E

    Extremely dense but clear and actually quite funny.

  12. 4 out of 5

    Anna

    I treat this book as a bed time stories for mathematicians. I had problems reading it as my brain refused at some moment to take, chew and understand higher Maths.

  13. 4 out of 5

    Don M

    "Already partly read and no intention to finish" category needed.

  14. 4 out of 5

    Stephenlouis

    Quite likely the only book you will ever need to understand the history of numbers and what they really mean. I re-read this book once a year. Highly recommended.

  15. 4 out of 5

    Kyle Machulis

  16. 4 out of 5

    Robert

  17. 4 out of 5

    Antonio A

  18. 5 out of 5

    Cillian

  19. 4 out of 5

    Ma. Wendy

  20. 4 out of 5

    Mustafa Kurt

  21. 5 out of 5

    Chris C

  22. 5 out of 5

    Dean Nan

  23. 5 out of 5

    Derrick

  24. 5 out of 5

    Yasin S.

  25. 5 out of 5

    Regina Hunter

  26. 4 out of 5

    Vo

  27. 4 out of 5

    Boustrophedon

  28. 5 out of 5

    Joseph Lamarre

  29. 4 out of 5

    Paul

  30. 5 out of 5

    M

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