History of Mathematics, Part 5
Question 1: Describe early number concepts.
Answer 1: Early mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common was a breakthrough in human thought. In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time—measured in days, seasons, or years. Arithmetic (addition, subtraction, multiplication and division) naturally followed. Monolithic monuments testify to knowledge of geometry.
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Question 2: Discuss the origins of mathematical notation.
Answer 2: Most of the mathematical notation in use today was not invented until the 16th century. Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed in that a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way.
Question 3: What caused early civilizations to need numerical concepts?
Answer 3: From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics into the studies of quantity, structure, space, and change.
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