DISCIPLINE BY DISCIPLINE:
Norway recently announced the creation of the Abel Prize, an annual, international award in the field of mathematics. The first Abel Prize will be given in the year 2003. Made possible by a $22 million government endowment, the prize rivals the prestige of a Nobel prize (there is no Nobel prize for mathematics).
The new prize was established in memory of famed Norwegian mathematician Niels Henrik Abel, who died in 1829 at the age of 26. Despite his short life of poverty he earned the enduring respect of fellow mathematicians, and before his death he published proof of the insolvable nature of fifth-degree algebraic equations known as quintics.
The goal of the Norwegian Academy of Science and Letters in awarding the Abel Prize is to increase awareness of the importance of mathematics in all areas of science. Until now, the only comparable award has been the Fields Medal, which is bestowed every four years and is restricted to mathematicians under the age of 40.
Mathematicians recently gained new insights into certain aspects of knot theory. In the February 2001 issue of the Journal of the American Mathematical Society, mathematicians Joel Mass of the University of California-Davis, and Jeffrey Lagarias of AT&T Labs-Research in Florham Park, New Jersey, announced a formula for the upper limit of the number n of special manipulations, known as Reidemeister moves, that are required to undo a tangle. Although the number is huge, 2100,000,000,000n, which limits its practical use, the discovery that an upper boundary even exists is considered a significant milestone.
In mathematics, knots are studied as theoretical closed curves in space, as opposed to the familiar knots with trailing ends that we see in common use. Knot theorists define the unknot, also known as the trivial knot, as a tangle with no crossings that cannot be undone without severing the closed loop. Thus, a circle and a figure eight are unknots, as is the magician’s seemingly knotted rope that simply shakes out with a single tug. The upper boundary formula as described by Hass and Lagarias applies to the unknot.
In a separate observation, published in the October 2001 issue of the European Physical Journal, Polish physicists reported their computer analysis of a knot’s writhe, a measure of how a knot twists upon itself. They discovered that, so far, these plotted values follow principles of quantum theory. That is, their results fell into discrete groupings, reminiscent of electrons moving around an atom’s nucleus. This has led some to suggest a relationship to superstring theory, which proposes that all matter is composed of time-space loops that are coiled upon themselves into strings.
Knot theorists continue to ponder the implications of these ongoing discoveries about knots and the properties that govern them. A better understanding of how knots work is already helping scientists to probe the way that some viruses interrupt coils of DNA, and is providing new insights for physicists in their quest to understand the structure of universe.
A study, published in the June 2001 issue of the Journal of Experimental Psychology, suggests that math anxiety