Richard Pritches writes in to let us know that MIT errata expert Evangelos Georgiadis has disproved 44 conjectures set by Dr. Stephen Wolfram (founder of Mathematica) in A New Kind of Science. The paper was published in the latest issue of the Journal of Cellular Automata and can be read in PDF form at Prof Edwin Clark's collection of reviews of Wolfram's ANKS. "The formulas provided by Wolfram for these [44] rules are not minimal. Moreover for 8 of these cannot be minimal even by simple inspection since minimal formula sizes for 3-input Boolean functions over this basis never exceeds 5."

Fishbat writes "In a cutting message to the Foundations of Mathematics mailing list, Stanford's Vaughan Pratt has pointed out an elementary mistake in the recently announced proof that Wolfram's (2,3) machine is universal." Update: 10/30 04:18 GMT by KD : Ed Pegg Jr. from Wolfram Research points to this response to Dr. Pratt's note, which has been submitted to the FoM mailing list but has not yet appeared there due to moderation.

Rik702 writes "Wolframscience.com have announced that an undergraduate from Birmingham, UK has proved Wolfram's 2,3 Turing Machine is universal." You can read a pdf of the proof as well as some related coverage.

ObsessiveMathsFreak writes "I'm an applied mathematician who has recently needed to obtain good numerical approximations to the classic second-order wave equation, preferably in three space dimensions. A lot of googling has not revealed much on what I had assumed would be a well-studied problem. Most of the standard numerical methods, finite difference/finite element methods, don't seem to work very well in the case of variable wave speed at different points in the domain, which is exactly the case that I need. Are any in this community working on numerically solving wave equation problems? What numerical methods do you use, and which programs do you find best suited to the task? How do you deal with stability issues, boundary/initial values, and other pitfalls? Are there different methods for electromagnetic wave problems? Finally, when the numbers have all been crunched, how do you visualize your hard-earned data?"