FRANK A. WILCZEK
School of Natural Sciences
Institute for Advanced Study
Recently there have been dramatic developments in the theory of knots. Methods of statistical mechanics and quantum field theory have been discovered to yield new, practical ways of distinguishing knots. The new invariants have been used to resolve a number of long-standing mathematical problems. They also have been used in amazing analyses of knotted DNA and 2+1 dimensional gravity, among other cases. V. Jones, "Knot theory and statistical mechanics," Scientific American, 263, 98-103, November 1990. (University of California, Berkeley)
Close looks inside several galaxies have revealed very singular mass distributions near their centers. These observations are probably best interpreted as indicating the existence of extremely massive black holes. The existence of such objects also plausibly explains indications (from quasars) of violent activity in the universe early on. This activity would result from the formation of giant black...