History Of Negative And Imaginary Numbers

1578 words - 7 pages

Mathematics is either loved or hated by those who are charged with mastering it. In a world that has such strong feelings about mathematics, negative and complex numbers have been considered erroneous throughout most of history. It is understandable that many young students have dread in their hearts about new and unknown topics like negative and complex numbers, especially when mathematicians for thousands of years have had those same feelings. In Tennessee, according to state standards, negative numbers are introduced in sixth grade as an extension of the rational number system and complex numbers are introduced in high school Algebra. Some middle and high school teachers look back on their years as math students with dislike for such topics and create more anxiety than is necessary for their own learners. Historically speaking, these students and teachers are actually in the company of many great mathematicians who had strong feelings about or denied the existence of negative and imaginary numbers altogether. These numbers were largely a stepchild of mathematics until modern times. Even the etymology is, for lack of a better word, negative. Words like false, fictitious, sophistic, and absurd have been traditionally common descriptors, but the modern terminology does not put one’s mind at ease. The word imaginary might cause a person to think of unicorns and fairies rather than numbers and the term complex just makes the concept seem more difficult. The influence of history could be related to the way this mathematical topic has caused and is still causing anxiety in classrooms. Negative and complex numbers have always existed even though they may not have been accepted, and because of the work of the nineteenth century mathematicians, they should not be feared.
The earliest evidence of the use of negative numbers was in China sometime between 475 B.C. and 221 B.C. The Chinese number rod system represented negative quantities with black rods and positive quantities with red rods, where the black cancelled out the red. These rods were used for practical purposes, such as buying and selling goods. Nine Chapters, a historically famous mathematical text from ancient China, mentions negative numbers in its eighth book. It includes a sign rule for adding and subtracting positive and negative numbers with the rods. With such an early start, it might seem that negative numbers would have flourished, but the ancient Chinese mathematicians had no contact with the Greek mathematicians who have influenced western mathematics so greatly (Katz 7). The Greek mathematicians, however, completely disregarded negative quantities. These great minds thought of numbers in terms of magnitude or length and therefore, gave no indication of working with negative quantities. Lengths, areas, and volumes were all positive results from geometric constructions. The first suggestion of negative numbers from the Greeks was in the third century by...

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