G1ASOC -- Mathematics and Society

from Copernicus to Hawking

This document is accessible from the G1ASOC home page.

First, some very general references:
- John O'Connor and Edmund Robertson of St Andrews have constructed an archive of articles about mathematicians. All famous, most infamous, and some downright unfamous mathematicians are there, together with more general articles. Most articles include pictures and cross-references, and most are aimed at a reasonably general audience.
- David Wilkins of Trinity College, Dublin maintains a page of references to sites of relevance to the history of mathematics. This is pretty comprehensive, but many of the articles mentioned are quite advanced.
- The George Green Library has the books mentioned in the introductory page, and many, many others [of course!].
Series A
Kepler and Copernicus: There are articles on Kepler, Brahe and Copernicus in the St Andrews archive. All three include cross-references to other Web sites. Also at St Andrews there is a more general article on orbits. I used M Caspar, Kepler, (New York, 1993) as a source about Kepler, as well as the more general information in Kline and elsewhere.
Galileo: The St Andrews archive has an article on Galileo, with plenty of links. The Galileo room of the Florence Institute and Museum of the History of Science contains some interesting exhibits, and their Web page includes many links to relevant articles produced by the Museum. The series mentioned below in connexion with Brunelleschi on the art of Renaissance science includes biographical material on Galileo, some animations of his mechanics experiments, and many further links. The George Green Library catalogue lists 35 books by or about Galileo; his own writing is very readable. In addition, every book on the history of mathematics includes material on the Copernican revolution and the role in it played by Galileo.
Newton: As usual, the St Andrews archive article on Newton is informative and has a number of links, though Newton is not [yet] actually all that well served by Web sites. Again, every book on the history of mathematics includes material on Newton; the George Green Library has dozens of specialist books in this area. Newton's Principia is mostly rather heavy going, even for a specialist mathematician, but some parts are readable, and give an insight into the mathematics of the period and of Newton's contributions. Of the many biographies, I commend R. S. Westfall's Never at rest: a biography of Isaac Newton [QC16.N7 WES] as very comprehensive [but not easy reading], and Let Newton be!, a compilation edited by John Fauvel of articles on many aspects of Newton's life [QC16.N7 LET].
Euler:
Lagrange, Laplace:
Gauss:
For these, one primary source has been the St Andrews archive articles on Euler, Lagrange, Laplace and Gauss. All of these also get extensive mention in Hollingdale and other books on the great mathematicians. The St Andrews archive also includes some relevant articles, notably one on orbits, and one primarily on the discovery of Neptune.
Green, Maxwell: The St Andrews article on Maxwell is reasonably comprehensive. His equations are dealt with in most textbooks on electromagnetism, though never in such cavalier fashion as in this lecture! In addition to the St Andrews article on Green, there is a suite of Web pages on his life and works, including material about Green's Mill [see below] and the science centre there, produced by our own, our very own, School of Physics and Astronomy. A biography, George Green: mathematician and physicist 1793-1841, by local historian Mary Cannell is in the George Green Library at QA29.G7 CAN, and of course every student on this module should visit Green's Mill in Sneinton. The Mill was restored through a committee initiated jointly by us and Physics, and is now a working mill, worth a visit in its own right, together with a science centre and a playground. Those with an historical bent can also visit the nearby church, where Green is buried, and the Bendigo pub, and the Salvation Army museum, all within easy walking range.
Einstein: There can be little doubt that Einstein is the single most famous scientist in history. Even people who are completely ignorant of Newton or Darwin or Galileo or Archimedes have heard of Einstein and can tell you that he has something to do with relativity. He looks like the archetypical scientist. Only Stephen Hawking has comparable iconic status. So there are zillions of Web articles on him and his work, and many books in the Library likewise, including a number of attempts to explain his work to the layman. The St Andrews article on Einstein will give you an adequate start for all of this.
That article refers to an Oxford `Einstein blackboard'; this University too has an Einstein blackboard, kept by the School of Physics and Astronomy [and last seen in C13]. Scurrilous rumour hath it that the board was once cleaned, and the current writing inscribed by some professor; I expect all EBs have similar rumours!
Feynman, Hawking: As you will expect, there are St Andrews articles on Feynman and Hawking, but Professor Hawking has his own home pages, including his life story and two of his lectures.
Series B
Art:
- The St Andrews archive includes an article on Dürer. The versions of Melancolia that I have found on the Web are not of good enough quality to see the real details. The version shown in lectures was taken from Andrews, Magic Squares, but it is a very famous picture, and it should not be hard to track down a better copy in the Library. See also Kline.
- There is quite a lot about perspective in Kline. See this article on Brunelleschi for an excellent idea of what he contributed to the theory. That article contains links to a whole series. A Web search on Brunelleschi will easily find a great deal about his architecture. There is also plenty of relevant material in the Library. See, for example Martin Kemp, The science of art: optical themes in western art from Brunelleschi to Seurat, in the Hallward Library under [oversize] ND1475.K4, or I. Hyman, Brunelleschi in perspective under NA1123.B78. Books on projective geometry are in the George Green Library around QA471.
- There are many Web sites about Escher, easily found by a Web search, including one with many other links, a more general resource site and a collection of pictures. The Hallward Library has Escher's own book, The world of M.C. Escher in NE670.E75 [Oversize], and perhaps surprisingly the George Green Library has his The graphic work of M.C. Escher in Q231 ESC [also Oversize]. See also D. R. Hofstadter's book Gödel, Escher, Bach. You will find reference to Escher in many other books. Escher himself refers to the geometrical and similar aspects of his work.
- There is much else that you could investigate in Mathematics and Art, including Penrose tiling, Arabic art [which could not use the human form, so very often had geometric or patterned motifs], and modern Op art.
Puzzles: The St Andrews site has articles on Dudeney and Loyd, and a survey article on mathematical games and puzzles. For specific puzzles, there are many sites. There is a nice site for Solitaire, which includes explanatory text and references as well as a Java-based version of the puzzle, and another that has sound and a fastest solvers list! Sliding block puzzles can be found at this site, again with many further references. One of many good sites for Rubik's cube is this site. Mario Velucchi maintains a very useful collection of resources to do with games and puzzles, as long as you don't mind the wretched cookies.
Literature: The St Andrews site has articles on `Lewis Carroll' and Pascal. For `Lewis Carroll', there is a website devoted entirely to various aspects of his life, and an Encylopaedia Britannica article with further references. For Pascal, there is another biography at the History of Mathematics site at Trinity College, Dublin, and there are some references at the similar Clark University site. Don't forget that Galileo was also a considerable writer.
For the use of mathematics in attribution, see the work of Fiona Tweedie, also this conference, with further references in both cases.
For more general comments on mathematics and literature, see first the general course texts, Kline and Hollingdale. I found Barbara Parkin's home page interesting; she is an educator trying to integrate mathematics into literature. You may also find useful a collection of references made by JoAnne Growney, a poet who incorporates mathematics into her work. Her home page includes references to her own work. Not exactly literature, but Tom Lehrer is a mathematician/satirist who occasionally allowed maths to intrude into his songs, including Lobachevsky, NewMath, There's a delta for every epsilon and others.
Music:
- For stochastic and aleatoric (random) music, there is much on the Web about Cage, Xenakis and Ligeti [for example].
- So-called twelve-tone music, and the related theories of tone-rows ought to contain mathematical elements! Other classical music such as Bach's Goldberg Variations obviously includes a lot of structure, especially when canons, rounds, fugues or sonatas are involved. There's probably a whole project there just in deciding what mathematics, if any, is part of that structure! The same may apply to `pop' music or jazz or gamelans, etc., but this is somewhat beyond my personal experience.
- There is said to be a site that produces Mozart's dice music, but it doesn't work on my own computer. If you want to write some aleatoric music you could try the FAQ site maintained by Karl McCollester.
- Kyle Gann has a good page on the history of different tunings; see also the pages of the Just Intonation Network, which contain much information and further links.
- For bellringing [campanology], here is a brief introduction; there is much more information in this glossary, but it helps to know something about the subject already. Clearly, there is much elementary group theory involved, but this does not seem to loom large among bell-ringers.
- The St Andrews site has a page about Pythagoras, but it does not seem to know anything about his contributions to music.
Chaos: There is any amount of stuff available by surfing! Meanwhile, here is a rather disorganised page of some of the fractal pictures that I've grabbed off the Net, in full colour to compensate for the black-and-white of OHP slides.

E-mail: [my initials] [at] cuboid.me.uk, home page: http://cuboid.me.uk/anw.