Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers
Joseph Mazur
Language: English
Pages: 312
ISBN: 0691173370
Format: PDF / Kindle (mobi) / ePub
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.
Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.
From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
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Brahmasphutasiddhanta, and wrote a textbook on arithmetic using the new Indian numbers.1 In around 820 AD, al-Khwārizmī wrote The Book of Restoration and Equalization, a book on how to solve equations (in particular, solving for the positive roots of quadratic equations).2 Its title in Arabic is Hisab aljabr w’almuqabala, from which we get the word “algebra.” It was translated into Latin sometime during the middle of the twelfth century under the title Algebra et Almucabala, and that is how the
century earlier than Fibonacci’s Liber abbaci.5 FIGURE 6.1. Al-Khwārizmī. Al-Khwārizmī’s On the Calculation with Hindu Numerals, written sometime near 825 AD, may have been responsible for spreading the Indian system of numeration throughout the Arab world in the ninth century, and then to Europe after a series of Latin translations were made available in the twelfth century.6 The years between 786 and 809 in Persia were endowed with scientific and artistic richness. Sometime just before the
these letters also could be confused with their corresponding numerical equivalents—namely, 40, 4, and 20. To avoid such a confusion, Diophantus must have added the second letter of each of the Greek words, µονάδων, δύναµιc, and κύβοc. But then µο, δύ, and κύ could be confused with the numerical equivalents 4,070, 4,400, and 20,400, respectively.7 To avoid that confusion, the second letter of each word was superscripted. The abbreviations became µο, δύ, and κύ. Applied to the word ἀριϑµός, the
over a problem, would not be aware of a live gorilla in the room. How many times have I denied that I ever heard something my wife told me? The gorilla might be in the room and I wouldn’t know it, but should she walk across the problem I am working on, she wouldn’t need to thump on her chest for me to know she is there. The Invisible Gorilla experiment applies only to inattentional blindness of unexpected objects in visual fields. What about gorillas in mathematical problems? Return to the
The first involves the parietal cortex when visually received information is processed and an image representation is transformed. The second involves the prefrontal cortex when it receives a transformed representation and brings in the retrieval of mathematical facts that interact with the processed representation of the problem. This two-step process continues in a back and forth sequence. For example, when the stimulus was to solve equations such as , the mathematical knowledge comes in after
