To refine search, see subtopic Proof by Contradiction. To expand search, see Logic. Laterally related topics: Computation and Infinity.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Altshiller-Court, Nathan. The Dawn of Demonstrative Geometry. Mathematics Teacher 57 (1964), 163--66.
The author argues that it seems unlikely that the Greeks could have invented their notion of proof so rapidly and in isolation. Instead, he suggests that the notion of geometric proof was a secret that was jealously guarded from all but the "inner sanctum" of the Egyptian priesthood. (Of course, since his argument implies by its very nature that Egyptian proofs were unlikely to have been written down, this will be a hard argument to either prove or disprove.) Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Geometry, Ancient Egypt, and Greece.Modify notes on this entry Modify bibliography entry Make comment on this entry
Court, Nathan Altshiller. Mathematics in the History of Civilization. The Mathematics Teacher 41 (1948), 104--11.
How different concerns of society influenced mathematics. How the development of the concept of number is reflected in language. How the concept of how many led to arithmetic. How the concept of how much led to geometry. (Taxation and agriculture also contributed to both.) Efforts to keep time led to trigonometry. Navigation and associated astronomical problems led to logarithms [and more trigonometry]. Problems in artillery led to graphs. Both required an understanding of motion. Analytic geometry and calculus were invented in part to better understand motion. Statistics developed to understand problems in the social sciences. Also discusses the nature of mathematics: mathematics for its own sake and the axiomatic method. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Why Study History Of Math, Mathematics in Language, Number Systems, Arithmetic, Geometry, Taxation, Agriculture, Astronomy, The Reckoning of Time, Trigonometry, Artillery, Graphing, Navigation, Dynamics, Force, and Motion, Analytic Geometry, Calculus, Statistics, and Social Science.Modify notes on this entry Modify bibliography entry Make comment on this entry
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