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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.
Chandrasekhar, S. Shakespeare, Newton and Beethoven or patterns of creativity. Current Sci. 70 (1996), no. 9, 810--822. SC: 01A99, MR: 1 387 202.
Discusses the creative lives of Shakespeare, Newton, and Beethoven. The example of Newton contrasts with the other two, particularly in how old they were when they did their most creative work. While the best work of poets is often later in life, G. H. Hardy tells us that the best work of mathematicians is generally when they are young. Chandrasekhar gives the additional examples of the mathematicians or scientists James Clerk Maxwell, George Gabriel Stokes, and Albert Einstein. Lord Rayleigh's example is different, and gives us a possible explanation of the differences we've seen. In the words of J. J. Thomson, "There are some great men of science whose charm consists in having said the first word on a subject, in having introduced some new idea which has proved fruitful; there are others whose charm consists perhaps in having said the last word on the subject, and who have reduced the subject to logical consistency and clearness. I think by temperament Lord Rayleigh belonged to the second group." Chandrasekhar then discusses the importance of beauty to mathematics and science, and concludes with statements of scientists and poets on one or the other of the two disciplines (some comments are more favorable than others). Closely related topics: Creativity, Shakespeare, Isaac Newton (1642-1727), and Beethoven.
Evans, Brian. Number and form and content: a composer's path of inquiry. The Visual Mind, 113--120, Leonardo Book Series, MIT Press, Cambridge, Mass., 1993.
The author shows how the golden ratio occurs in music and art. His examples include Mozart's Symphony in G Minor, Grant Wood's American Gothic, Piet Mondrian's Composition with Blue, and some of his own musical and visual compositions. More controversial examples include the Great Pyramid in Egypt and Stonehenge, where the author shows how approximate values of both pi and the golden ratio can be found. The author mentions Luca Pacioli's statements on the golden ratio in De Divina Proportione and discusses other aspects of the philosophy of number and art as well. Closely related topics: Proportion and the Golden Ratio, Music, Art, Wolfgang Amadeus Mozart (1756-1791), Luca Pacioli, The Egyptian Pyramids, and The Stone Builders.
Grattan-Guinness, I. Mozart 18, Beethoven 32: hidden shadows of integers in classical music. History of mathematics, 29--47, Academic Press, San Diego, CA, 1996. SC: 01A99 (00A69), MR: 97a:01075.
Discusses number symbolism in the works of Mozart and Beethoven. With Mozart, discusses in particular Die Zauberflöte and the last three symphonies (and particularly the Symphony in g of 1788). There is also some evidence that Mozart used gematria. Literary sources also attest to Mozart's interest in numerology. With Beethoven, focuses primarily on Piano Sonata op. 111 (no. 32), the Diabelli Variations, and the Missa Solemnis. The choice of opus numbers themselves appear to show an interest in numerology. The author suggests that some knowledge of the history and conventions of numerology would be useful before reading this article. The author's own article in the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences may be useful in this regard. The author also suggests some avenues for future research. Closely related topics: Music, Numerology, Gematria, Wolfgang Amadeus Mozart (1756-1791), and Beethoven.
Grattan-Guinness, I. Some numerological features of Beethoven's output. Ann. of Sci. 51 (1994), no. 2, 103--135. SC: 01A99 (00A69), MR: 1 278 119.
The author discusses possible occurrences of number symbolism in Beethoven's compositions. A large number of examples are used to buttress his arguments, and some prior familiarity with Beethoven's work might be useful. In some cases, numbers occur as the number of measures or notes of a them or motif, and in other cases in Beethoven's choice of opus numbers. (In contrast with the common practice of the time, Beethoven chose his opus numbers himself, and the numbers chosen could at times be seriously at variance with the order of composition.) The author's conclusions have been controversial, partly because Beethoven has often been regarded as being quite poor at arithmetic. The author discusses this objection and aspects of methodology in some detail. Closely related topics: Numerology, Music, and Beethoven.