Laterally related topics: Religion, Time and Space, Mathematics in Recreation, Art, Language and Literature, Music, Measurement, Arithmetic, Mathematics and Mysticism, Geometry, Discrete Mathematics, Optimization, Philosophy, Calculus, Statistics, Social Science, Logic, Computation, Probability, Education, Algebra, Number Theory, Optics, Archaeology, Medicine, Creativity, Business, Fractals, and Science.
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.
Høyrup, Jens. Sub-scientific mathematics: observations on a pre-modern phenomenon. Hist. of Sci. 28 (1990), no. 79, part 1, 63--87. (Reviewer: David Singmaster.) SC: 01A10 (01A05 01A12 01A80), MR: 91j:01007.
Høyrup makes a distinction between scientific and subscientific mathematics. These fields correspond somewhat to pure and applied mathematics. However, by using this new terminology, the author hopes to avoid suggesting that "subscientific" mathematics is always derived from "scientific" mathematics in the way that "applied" mathematics is derived from "pure" mathematics. Høyrup discusses the distinction between scientific and subscientific mathematics and also their various kinds of relationships. His examples are drawn from Greece, Egypt, India, the Islamic World (with references to the Silk route), and from the Carolingian Propositiones ad acuendos jevenes. (The latter is traditionally associated with Alcuin.) Høyrup touches on relevant work by the mathematicians Hero, Diophantus, and al Khwarizmi. Surveying is discussed as a particularly important type of subscientific mathematics. Closely related topics: Greece, Ancient Egypt, India, The Islamic World, Alcuin, Heron, Diophantus, Surveying, and Abu Abdullah Muhammed ibn Musa al Khwarizmi.
Hansen, David W. The Dependence of Mathematics on Reality. Mathematics Teacher 64 (1971), 715--19.
Discusses how the greatest mathematicians have been vitally concerned with the real world. Uses Archimedes, Newton, and Gauss as examples. Archimedes did so much applied work that it is hard to see how he fits Plutarch's description of considering mechanical work ignoble and inferior. The case of Newton is of course well known. An interesting example is Gauss, who used the motto "Thou, nature art my goddess;to thy laws/My services are bound" from Shakespeare's King Lear. Newton and Gauss were also very interested in religion. Philosophy was very important to Gauss. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Archimedes, Isaac Newton (1642-1727), Karl Friedrich Gauss (1777-1855), Religion, and Philosophy. Also possibly relevant: Literature.
Kapur, J. N. Encounters of a working mathematician with history of mathematics. Ga\d nita Bh\=arat\=\i 11 (1989), no. 1-4, 30--37. SC: 01A99 (01A32), MR: 91i:01150.
In the process of describing his own encounters with the history of mathematics, the author makes a strong argument for its importance, particularly in mathematics education. He notes that mathematicians are too often unaware even of the history of their own research areas. For example, he mentions "a student who had written a Ph.D. thesis on Banach spaces had no idea who Banach was, to which century he belonged and of what country he was a citizen and why this concept was necessary." As the author notes, such ignorance inevitably weakens mathematics, since it separates mathematics from the applied problems that often motivated it. He discusses the quantity of research currently taking place in India in various fields of mathematics, and in the history of mathematics (and Indian mathematics) in particular. He finds room for improvement, and closes with some some recommendations for correction. Closely related topics: Why Study History Of Math, Education, and India.
Vitrac, Bernard. The Odyssey of Reason. UNESCO Courier (1989), 29--35.
The development of Greek schools, the role of mathematics in Greek thought, "pure" and "applied" mathematics, the mathematical community that existed in the Hellenistic era. Includes a passage by Proclus on Geminus' classification of mathemata (the root mathema originally meant "that which is taught", so included all branches of knowledge). Reprinted in edited form in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: History of Education and Greece.