Book Review: The Universal History of Numbers

A review I wrote 20 years ago.

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!