51-year Old Problem of Web Geometry Solved

Wilhelm Blaschke (1885-1962)

In 1955 German mathematician Wilhelm Blaschke, a pioneer in the branch of mathematics known as web geometry, had said that it was nearly impossible to find the conditions under which a web might be transformed into a different kind of web with different numbers of non-intersecting, straight lines. To describe such a transition mathematically would require leaps of logic and multitudes of calculations that were too great, Blaschke said.

Even as economic forecasters and theoretical physicists found uses for web geometry in subsequent decades, Blaschke's riddle remained unsolved. There was, of course, one thing that was not available to Blaschke in the 1950s: a powerful computer. Now, using advanced computer software, Vladislav Goldberg of New Jersey Institute of Technology and Valentin Lychagin of The University of Tromso, Norway have successfully arrived at a solution for the problem. Their paper "On the Blaschke conjecture for 3-webs" was published in the March, 2006 issue of 'The Journal of Geometric Analysis' and have found wide acclaim from mathematicians everywhere. Here is the Abstract of the paper.