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.
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: 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, Social Science, and Proof.
Gupta, R. C. Why study history of mathematics? Ga\d nita-Bh\=arat\={\i} 17 (1995), no. 1-4, 10--28. (Reviewer: C. J. Scriba.) SC: 01A99 (00A30 01-01), MR: 97e:01025.
Discusses a wide variety of reasons for studying the history of mathematics. We will only give a few short excerpts, with the goal of suggesting the breadth of the article. Quotes the saying "History makes a man wise" (p. 10). Mathematics is "a great cultural heritage. A study of the history of mathematics will help us to understand this cultural heritance. It will also help us in knowing the relation of mathematics to other varied elements of culture such as art, architecture, crafts, religion, philosophy, etc." (p. 11). Mathematics "is called the mirror of civilization" (p. 11). "History of Mathematics can humanize Mathematics" (p. 13). Quotes George Sarton as saying "the main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men" (p. 14). "We can know as to why and how new branches of mathematics were born. One can find as to how the unified approaches often integrate various apparently divergent branches. Mathematical revolutions sometimes revolutionized not only mathematics, but other sciences and even society" (p. 15). The author also notes the advantages of knowledge of the history of mathematics in education. He notes a parallel with the biological maxim "Ontogeny parallels phylogeny" (p. 17). It can also "grab the attention of students and spark their interest" (p. 17). With regard to problems once solved or found to be unsolvable, notes "those who are ignorant of history are condemned to repeat it" (p. 20). He concludes with the note about mathematics that "Its international appeal illustrates that mathematics has been a unifier of human experience and a vehicle for better global understanding. It thus helps to cultivate the noble idea of a world family (Vasudhaiva Kutumbakam)" (pp. 22-23). There is much more as well--an article to recommend to anyone interested in teaching at any level. The bibliography includes a number of sources that may not be widely known; S. Buchman's book Poetry and Mathematics may be a good example. There appear to be quite a few useful references to articles on mathematics education as well. Closely related topic: Education.
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: Education, Applied Mathematics (General), and India.