stoolpigeon writes "The O'Reilly School of Technology is teaming up with Wolfram Research to provide on-line math courses using an AJAX version of Mathematica. O'Reilly has posted an and interview with Scott Gray, the director of OST, that has more details on the program (named Hilbert after David Hilbert) itself as well as the classes they will be offering."

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?"

Lucas123 writes "A study performed at the Free University Berlin on human free will has produced some unexpected results showing that fruit flies may have a spark of free will in their tiny brains." From the article: "Their behavior seemed to match up with a mathematical algorithm called Levy's distribution ... Future research delving further into free will could lead to more advanced robots, scientists added. The result, joked neurobiologist Björn Brembs from the Free University Berlin, could be "world robot domination."

An anonymous reader writes "Stephen Wolfram, creator of Mathematica and author of A New Kind of Science, is offering a prize of $25K to anyone who can prove or disprove his conjecture that a particular 2-state, 3-color Turing machine is universal. If true, it would be the simplest universal TM, and possibly the simplest universal computational system. The announcement comes on the 5-year anniversary of the publication of NKS, where among other things Wolfram introduced the current reigning TM champion — 'rule 110,' with 2 states and 5 colors."

Ed Pegg writes "Wolfram Research has just released Mathematica 6. That link, in addition to the usual 'dramatic breakthrough' material, has an amazing flash banner that simultaneously shows a thousand mathematical demonstrations all at once. The animations came from the Wolfram Demonstrations Project, a free service with 1200+ dynamically interactive examples of math, science, and physics, all with code. For the product itself, much is new or improved, with built-in math databases, improved visualizations, and more."

Joe Lau writes to mention a story running on the Xinhua News Agency site, reporting a proof for the Poincare Conjecture in an upcoming edition of the Asian Journal of Mathematics. From the article: "A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman have laid foundation on the latest endeavors made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrization conjecture. Yang, member of the Chinese Academy of Sciences, said in an interview with Xinhua, 'All the American, Russian and Chinese mathematicians have made indispensable contribution to the complete proof.'"

Lester67 writes "Business 2 put a bunch of big brains together to give us a peek at Google from 2015 to 2105. "Will it succumb to hubris and flame out like so many of its predecessors? Or will it grow into an omnipresent, omnipotent force--not just on Wall Street or the Web, but in society? We put the question to scientists, consultants, former Google employees, and tech visionaries like Ray Kurzweil and Stephen Wolfram. They responded with well-argued, richly detailed, and sometimes scary visions of a Google future." "

gslin writes to tell us MathWorld News is reporting that RSA-640 has been factored. F. Bahr, M. Boehm, J. Franke, and T. Kleinjung, memebers of the German Federal Agency for Information Technology Security (BSI) announced they had cracked the 193-digit number last Friday using the General Number Field Sieve. The team purportedly used 80 opteron CPUs and 5 months to achieve victory.

waynegoode writes "Stephen Wolfram's Wolfram Research has produced an new application: WolframTones-- 'An Experiment in A New Kind of Music'. It combines the principles in Stephen's book, 'A New Kind of Science' and Mathematica to 'instantly create unique music' in many different styles. They describe it as pretty neat as well as being scientifically interesting, and useful. After listening to some compositions and creating a few random ones myself, I must agree that it is. And anyone who has listen to the radio the last few years could certainly use some unique music."

Jazzer_Techie writes "The possible Mersenne Prime discovered last week has now been confirmed. This prime has 7,816,230 digits, which makes it not only the largest Mersenne Prime, but also the largest prime of any kind ever discovered. For those who don't want to take time to read the article, the prime is 2^25,964,951 - 1."

RTKfan writes "Chalk up another achievement for distributed computing! MathWorld is reporting that the 42nd, and now-largest, Mersenne Prime has probably been discovered. The number in question is currently being double-checked by George Woltman, organizer of GIMPS (the Great Internet Mersenne Prime Search). If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered."

Tangurena writes "Emergence is a field that is trying to come to grips with how new behavior emerges out of smaller units. There is no gene that determines the behavior of a hive of bees or colony of ants, but the behavior of the nest emerges from the individuals within. Some people are using cellular automata as a means of explaining higher order behavior (like Wolfram in A New Kind of Science )." Read on for Tangurena's review of Steven Johnson's 2002 book Emergence: the Connected lives of Ants, Brains, Cities and Software.

Rui Carmo writes "Now here's something you don't get asked every day, but which a friend happens to need for her kids: If you had to suggest Open-Source software for mathematics - somewhere from high-school to freshman level, and not merely for 'pure' mathematics, but also applicable to physics and statistics (the kids are considering going into Applied Maths and Engineering), what would you point people toward, assuming they have access to both Linux and Windows? I know this is a niche thing and that there is nothing out there that even comes close to Wolfram's excellent Mathematica (which I used on my old NeXTCube), but surely something along the lines of (or simpler than) Calculation Center exists?" The Knoppix-based Quantian might be a good place to start; what math software do you recommend?

mekkab writes "The Wall Street Journal reports (yet again) that despite knowing better, users do dumb things to compromise security. Is seven different 8 character passwords (with numbers and mixed cases) really too much to ask? Do people need training on how to make well known phrase (to them) into a perfect password acronym, or other memory boosting techniques? Or is it that the entire business culture needs to change from within to take digital security seriously?" If you require unmemorizable passwords, you've effectively changed the security requirement from "something you know" to "something you have", and if the required dongle is a note under your keyboard...

HateBreeder writes "Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many Prime Twins, it seems that a hole has recently been found in the proof, however mathematicians remain hopeful that the proof can be corrected."

neutron_p writes "The so-called "falling paper" problem has long intrigued scientists. James C. Maxwell pondered the tumbling motions of playing cards in 1853. Why don't flat things fall straight down? Pieces of paper fall down, then rise into the air, then glide along, then again rise... It occurs in a seemingly chaotic manner. Now researchers at Cornell University have solved the falling paper problem by calculating the motions of a scientific journal page in flight and there were a few surprises." There's also a story in the Cornell Sun.

colonist writes "Tit for Tat, the reigning champion of the Iterated Prisoner's Dilemma Competition, has been defeated by a group of cooperating programs from the University of Southampton. The Prisoner's Dilemma is a game with two players and two possible moves: cooperate or defect. If the two players cooperate, they both have small wins. If one player cooperates and the other defects, the cooperator has a big loss and the defector has a big win. If both players defect, they both have small losses. Tit for Tat cooperates in the first round and imitates its opponent's previous move for the rest of the game. Tit for Tat is similar to the Mutual Assured Destruction strategy used by the two nuclear superpowers during the Cold War. Southampton's programs executed a known series of 5 to 10 moves which allowed them to recognize each other. After recognition, the two Southampton programs became 'master and slave': one program would keep defecting and the other would keep cooperating. If a Southampton program determined that another program was non-Southampton, it would defect." Update: 10/14 15:08 GMT by J : If anyone wants to try writing their own PD strategy and see how it fares in a Darwinian contest, I'll host a tournament of Slashdot readers. Here are the docs, sample code, notes on previous runs, and my email address.