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Tony Phillips' Take on Math in the Media A monthly survey of math news |

- Bernhard Riemann's contribution to modern mathematics
- Studies on the teaching of mathematics
- Things that go bump - oscillons

Why does a negative times a negative equal a positive? Why do you ``invert and multiply'' when dividing fractions? These questions and more are addressed in the Fall 1999 issue of the *American Educator*, a publication of the American Federation of Teachers. This issue features substantial articles by Richard Askey and H. Wu, both distinguished mathematicians who have helped focus the attention of the research community on problems in mathematics education. Askey's article refers to the study *Knowing and Teaching Elementary Mathematics* by Liping Ma (Lawrence Erlbaum Associates, Inc., 1999). Ma's work, which emphasizes the ``profound understanding of fundamental mathematics'' as the goal toward which the education of elementary-school teachers should be directed, was reviewed by Roger Howe in the July 1999 *Notices*, with a survey of its implications for American schools.

Things that go bump. The September 28, 1999 *New York Times* carried an article by James Glanz entitled ``Scientists Discover New Clues to Earthquakes' Deadly Vibrations.'' He is referring to the similarity between the surface manifestation of certain tremors and the phenomenon of ``oscillons.'' Oscillons were named and first studied by Paul Umbanhowar (now at Northwestern University) and colleagues in 1996. They studied the behavior of spherical copper beads in a vibrating tray, and found, at certain frequencies, stable repeating patterns, as in this figure

An oscillon in a vibrating tray of copper beads. Image courtesy of Paul Unbanhowar, Northwestern University Physics Department. |

The oscillation of oscillons in a saucer-full of a suspension of potters' clay. Scale: frame width = 4cm. Time interval between pictures = 32 msec. Image courtesy of Jay Fineberg, Hebrew University of Jerusalem. |

* -Tony Phillips SUNY at Stony Brook*