Providence, RI---"Mathematics links Art and Science in one greatenterprise, the human attempt to make sense of the universe."
So writes Abel Prizewinner and Fields Medalist Sir Michael F. Atiyahin the January 2010 Notices of the American Mathematical Society. Thetheme of the issue is creativity in mathematics.
Mathematicians have always felt a strong creative aspect in theirsubject, but only in recent years has the flowering of connectionsbetween mathematics and the arts made this aspect apparent to thegeneral public. The collection of three articles in the Notices,together with Atiyah's short introductory piece, explore some of thevarious ways in which art and beauty appear in mathematics.
Mathematics and Mime
In "Envisioning the Invisible", Tim Chartier describes how theperforming arts can be used to capture mathematical concepts in avisceral way that audiences can really connect with. Chartier is amathematician and also a mime; he trained with the legendary MarcelMarceau. In one of Chartier's mime sketches, he gets the audience tovisualize the one-dimensional number line as a rope of infinitelength. The sketch begins with the lone mime walking toward theaudience and suddenly stumbling. Peering down, he sees an (invisible)object on the floor and proceeds to slowly pick it up. Examining it,he discovers a rope of infinite length in both directions. He thenengages in a tug-of-war with the rope and eventually cuts it into two,prompting the audience to ponder questions about the nature ofinfinity. In addition to describing several such mime pieces heperforms (some of them together with his wife, who is also a trainedmime), Chartier discusses the work of other mathematicians who work insuch performing arts as dance, theater, juggling, and magic.
Mathematics and Music
The strong affinity between mathematics and music is the subject of"Music: Broken Symmetry, Geometry, and Complexity", by Gary W. Don,Karyn K. Muir, Gordon B. Volk, and James S. Walker. Among thequestions explored in the article are: Does Louis Armstrong's voicesound like his trumpet? What do Ludwig van Beethoven, Benny Goodman,and Jimi Hendrix have in common? How does the brain sometimes fool uswhen we listen to music, and how have composers used such illusions?Is it possible to objectively describe the connection between pitchand rhythm in melodies? Is it possible to objectively describe thecomplexity of musical rhythm? How can math help create new music?
Mathematics and Visual Art
In "The Life and Survival of Mathematical Ideas", Michael F. Barnsleydiscusses how a specific mathematical topic, that of iterated functionsystems, can be viewed as a "creative system": The forms emerging fromthis system are fractals. His article is illustrated with manyarresting computer-generated pictures that are true works of art,including some he has sold in art shows. Barnsley explains his notionof a "creative system", which is a system that possesses a core stableform (DNA), a fertile environment, a determination to survive, andrandom stimuli. "The mind of a mathematician", he argues, "provides alocus for creative systems, a place where mathematical structures liveand evolve." He makes a parallel between biological forms, such asplants, and mathematical forms. An example of mathematical forms arethe geometric building blocks of points, lines, and planes; their"DNA" consists of the equations that describe points, lines, andplanes. The forms evolve and adapt as they are passed on throughgenerations of mathematicians' minds.
By serendipity, the article on music by Don et al employs some ofBarnsely's work on fractal images to produce new music. UsingBarnsley's Iterated Function Systems formulas, the authors createdfractal images of a fern and of Sierpinski's triangle and used theseimages to create notes for musical compositions---so the "scores" werecomputer images rather than the usual musical scores. This connectionbetween the two articles shows how the power of abstraction inmathematics makes it a fertile source for artistic expression.
Source: American Mathematical Society