Growth of Mathematics Term Paper

Pages: 2 (615 words)  ·  Bibliography Sources: 0  ·  File: .docx  ·  Level: College Senior  ·  Topic: Education - Mathematics

Growth of Mathematics

Mathematics Hard and Soft

Mathematical truth is time-dependent, although it does not depend on the consciousness of any particular live mathematician," (p. 415). In other words, mathematics grows as the body of human knowledge grows; each generation gleans new wisdom from the environment, experimentation, or personal experience and transmits that knowledge to contemporary and future generations either orally or in writing. Noted mathematicians may get their names printed in textbooks or permanently etched on the name of their theorems but the greater body of mathematics grows whether or not momentous discoveries warrant an individual mathematician's fame. One of the primary ways mathematics changes over time is through the transformation of soft sources of information such as common knowledge, intuition, or hunch, into hard information in the form of proof.

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In fact, mathematicians have accepted hunches and other soft sources of information to be "true" even before formal proof has been established. Number theory is especially full of instances in which mathematicians can rely fairly well on assumptions without demanding full proof: "in Number theory, there may be heuristic evidence so strong that it carries conviction even without rigorous proof," (p. 411). For example, mathematicians do not know for sure whether or not an infinite number of twin prime number pairs exist and yet we still act as if there are an infinite number of twin prime pairs. Mathematicians take some ideas for granted, unless of course the ideas are proven wrong. In any case, proofs often take generations or even centuries to manifest. Prime number theory was first postulated in 1792 by a fifteen-year-old Gauss, but the theory remained unproven until 1896. Mathematicians rely on soft information that can be best described as working knowledge until hard information becomes available.

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Similarly, mathematicians permit the existence of underlying beliefs, biases, and ideology that may influence… [END OF PREVIEW] . . . READ MORE

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APA Style

Growth of Mathematics.  (2006, August 7).  Retrieved August 4, 2021, from

MLA Format

"Growth of Mathematics."  7 August 2006.  Web.  4 August 2021. <>.

Chicago Style

"Growth of Mathematics."  August 7, 2006.  Accessed August 4, 2021.