To refine search, see subtopics Germany in the 1800s, Austria in the 1800s, and Hungary in the 1800s. Laterally related topics: The Neolithic Era, The Stone Builders, The Middle Ages, The Renaissance, The 1600s, The 1700s, The 1400s, The 1500s, The Paleolithic Era, The 1900s, and The Late Bronze Age.
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.
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.
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: Applied Mathematics (General), Archimedes, Isaac Newton (1642-1727), Karl Friedrich Gauss (1777-1855), Religion, and Philosophy. Also possibly relevant: Literature.
Hargittal, István and Lengyel Györgi. The seventeen two-dimensional space-group symmetries in Hungarian folk needlework. Journal of Chemical Education 62 (1985), 35--36.
The Hungarians of the late 1800s may be among the earliest people known to have "discovered" all 17plane patterns. The authors give an example of each pattern from Hungarian needlework. For the related article on frieze patterns, see Hargittal, István and Lengyel Györgi, The seven one-dimensional space-group symmetries illustrated by Hungarian folk needlework. Closely related topics: Frieze Patterns, Hungary in the 1800s, and Needlework.
Nagy, Dénes. Symmet-origami (symmetry and origami) in art, science, and technology. Symmetry Cult. Sci. 5 (1994), no. 1, 3--12. SC: 00A69 (01A99), MR: 1 309 239.
Discusses the history and philosophy of origami and then (in a little more depth) discusses some of its applications. The author discusses applications in math and science education, and also in art, design, and technology. A particularly interesting application of paper-folding and the theory of polyhedra is in music education, where one researcher devised "a 'tower' of five octahedra, to illustrate some basic concepts in musicology. His inspiration was from a work by Möbius written in 1861. Ganter's compound polyhedron illustrates geometrically the following concepts and their connections: the vertices correspond to the notes of the chromatic scale, the edges corresponds to the thirds and fifths, and the triangular faces correspond to the triads." He mentions that M. C. Escher was interesting in construction paper models (though it is not really clear how deep that interest lay). It is interesting that the well-known book by T. Sundara Row entitled Geometric Exercises in Paper Folding seems to be independent from the Japanese traditions. Closely related topics: Origami, Symmetry, Japan, Education, Music, M. C. Escher, and August Ferdinand Möbius (1790-1868).