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Math Team Solves the Unsolvable E8

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E_{8}, a symmetrical structure whose mathematical calculation has long been considered an unsolvable problem. Yet an international team of math whizzes cracked E_{8}'s symmetrical code in a large-scale computing project, which produced about 60 gigabytes of data. If they were to show their handiwork on paper, the written equation would cover an area the size of Manhattan."

posted by ericb on Mar 19, 2007 - 67 comments

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E

posted by ericb on Mar 19, 2007 - 67 comments

"This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries - such as square, hexagonal and triangular - and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a "quasicrystal," was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials...."

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.

posted by parudox on Mar 18, 2007 - 11 comments

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.

posted by parudox on Mar 18, 2007 - 11 comments

Alain Connes has a blog. Terry Tao also has a blog. Two Fields medalists blog on open problems, their views on mathematics, and Tomb Raider. Timothy Gowers doesn't have a blog, but does have a compendium of informal essays on topics like Why is multiplication commutative? If you prefer pictures to words: Faces of Mathematics.

posted by escabeche on Mar 10, 2007 - 15 comments

posted by escabeche on Mar 10, 2007 - 15 comments

The Integrator is Mathematica's integration capabilities, available over the web. Other online resources from Wolfram include Tones, an automatic music generator, and the venerable Mathworld, an extensive collection of math terms and theorems. (which, yes, has been mentioned previously.)

posted by Upton O'Good on Feb 27, 2007 - 29 comments

posted by Upton O'Good on Feb 27, 2007 - 29 comments

Seb Przd's photos specialising in delightful and mind-bending spherical panoramas and conformal mappings.

posted by MetaMonkey on Feb 15, 2007 - 10 comments

posted by MetaMonkey on Feb 15, 2007 - 10 comments

PhET - Physics Education Technology offers this astoundingly large library of online physics simulations. Play orbital billiards. Land on a cheesy moon. Experiment with sound. Or try more advanced quantum physics simulators. Still bored? Try the "cutting edge" catagory. Here's the complete index. (Warnings: Frames, Flash, Javascript, Java applets, graphics, sound, quantum timesuck.)

posted by loquacious on Feb 3, 2007 - 7 comments

posted by loquacious on Feb 3, 2007 - 7 comments

Dr. Jeannine Mosely finishes building a level-3 Menger sponge from business cards. You can also build your own, though Dr. Mosely warns, "[a] level 4 sponge would require almost a million cards and weigh over a ton. I do not believe it could support its own weight — so a level 3 is the biggest sponge we can hope to build." (related)

posted by Blazecock Pileon on Feb 2, 2007 - 19 comments

posted by Blazecock Pileon on Feb 2, 2007 - 19 comments

Pioneering electronic artist Ben Laposky began creating his “Oscillons” – abstract artworks created by photographing Lissajous figures off a cathode-ray oscilloscope – in the early 1950’s. Some consider him the father of computer art, and the beauty and clarity of his work is astonishing.

posted by Chinese Jet Pilot on Jan 23, 2007 - 12 comments

posted by Chinese Jet Pilot on Jan 23, 2007 - 12 comments

How to boil the perfect egg. vs. How to perfectly opposite-boil an egg.

posted by loquacious on Jan 23, 2007 - 36 comments

posted by loquacious on Jan 23, 2007 - 36 comments

Mysterious number 6174. An excellent recreational math article.

posted by fatllama on Jan 13, 2007 - 34 comments

posted by fatllama on Jan 13, 2007 - 34 comments

Math skills are not Verizon's strong point. A man tries to resolve a simple problem with Verizon for 22 minutes. Listen, and despair.

posted by Drunken_munky on Dec 9, 2006 - 174 comments

posted by Drunken_munky on Dec 9, 2006 - 174 comments

Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even taught it to high school students [via Digg]. You just have to work with a new number he calls Nullity (RealPlayer video). According to Anderson's site The Book of Paragon, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of transreal arithmetic (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies? identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.

posted by treepour on Dec 7, 2006 - 63 comments

posted by treepour on Dec 7, 2006 - 63 comments

A talk with Benoît Mandelbrot, entitled Fractals in Science, Engineering and Finance (Roughness and Beauty) [video, 80mins, realplayer] about fractals as A Theory of Roughness.

posted by MetaMonkey on Dec 3, 2006 - 5 comments

posted by MetaMonkey on Dec 3, 2006 - 5 comments

Geek Logik is Garth Sundem's book & blog about equations for every day living, including how many cups of coffee you require to be functional, who to vote for, and others.

posted by xmutex on Nov 7, 2006 - 9 comments

posted by xmutex on Nov 7, 2006 - 9 comments

Raft to the Future: An article about the weirdness of physical models of the universe, how that weirdness correlates to the inherent incompleteness of mathematical systems, and how time itself can *emerge* at the fringes of these incomplete models.

posted by knave on Nov 6, 2006 - 46 comments

posted by knave on Nov 6, 2006 - 46 comments

Fractran. A Turing complete programming language expressed in prime numbers from John Conway. (Interpreter here.) More pathological programming. Via Good Math, Bad Math.

posted by loquacious on Oct 30, 2006 - 14 comments

posted by loquacious on Oct 30, 2006 - 14 comments

what happens if you assign a colored pixel to each decimal of pi?

posted by petsounds on Oct 26, 2006 - 99 comments

posted by petsounds on Oct 26, 2006 - 99 comments

The Navier-Stokes equations constitute the fundamental equations that describe fluid mechanics, and are used everywhere from atmospheric science to airplane design. Proof of the existence of a smooth solution to the Navier-Stokes equations in 3-dimensions is considered a challenging problem, so challenging that the Clay Math Institute has offered a million dollars to anyone who can do so. Has it been done? (More detailed explanation). (via)

posted by onalark on Oct 5, 2006 - 17 comments

posted by onalark on Oct 5, 2006 - 17 comments

The Institute for Figuring presents the Crocheted Hyperbolic Coral Reef Project and Hyperbolic Crocheted Cacti and Kelp (more at this flickr gallery). If you secretly spend your evenings crocheting mathematical models, help build the coral reef or send a photo of your other creations to The People's Hyperbolic Gallery. (via Wonderland)

posted by madamjujujive on Sep 15, 2006 - 11 comments

posted by madamjujujive on Sep 15, 2006 - 11 comments

Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks to the New Yorker.

posted by Gyan on Aug 29, 2006 - 17 comments

posted by Gyan on Aug 29, 2006 - 17 comments

Please pick a random number between 1 and 100 (Explanation follows after filling out a short form.)

posted by kika on Aug 28, 2006 - 146 comments

posted by kika on Aug 28, 2006 - 146 comments

Grigory Perelman becomes first to reject Fields Medal: *"I do not think anything that I say can be of the slightest public interest. I have published all my calculations. This is what I can offer the public."* Perelman was to be awarded the medal due to his solution of the Poincaré Conjecture. More on the other winners. Via.

posted by Captaintripps on Aug 22, 2006 - 31 comments

posted by Captaintripps on Aug 22, 2006 - 31 comments

Bending a soccer ball - mathematically. Found via Ivars Peterson's short exposition on Braungardt and Kotschick's The Classification of Football Patterns [pdf, technical].

posted by Wolfdog on Aug 17, 2006 - 18 comments

posted by Wolfdog on Aug 17, 2006 - 18 comments

"Most people use passwords. Some people use passphrases. Bruce Schneier uses an epic passpoem, detailing the life and works of seven mythical Norse heroes."

posted by chunking express on Aug 16, 2006 - 46 comments

posted by chunking express on Aug 16, 2006 - 46 comments

Grisha Perelman, where are you? Perelman has quite possibly solved one of mathematics biggest mysteries, Poincaré’s conjecture, but has since disappeared.

posted by kliuless on Aug 15, 2006 - 32 comments

posted by kliuless on Aug 15, 2006 - 32 comments

The Zero Saga contains a great deal of information about the concept of zero, and its relation to other numbers and concepts in mathematics. It was linked in Good Math, Bad Math; which contains a variety of other informative articles on the numbers that capture our imaginations. (**Note:** You may want to skip past part 4 of the Zero Saga, as it contains replies to the site, and as such should probably be at the bottom of the page. But, to compensate, the comments on Good Math are better than most blogs I've read.)

posted by Eideteker on Aug 3, 2006 - 11 comments

posted by Eideteker on Aug 3, 2006 - 11 comments

Minimum Sudoku. It is believed (though not proven) that the minimum number of entries in a Sudoku grid that will lead to a unique solution is 17. Gordon Royle of the University of Western Australia has collected 36,628 "minimum Sudoku" grids. Additional reading: an article in American Scientist on determining the difficulty of a Sudoku problem; Wikipedia article on the mathematics of Sudoku; the Sudoku Programmers' Forum on Sudoku mathematics.

posted by Prospero on Jul 19, 2006 - 29 comments

posted by Prospero on Jul 19, 2006 - 29 comments

Sphere and circle arrangements, the Droste effect, and more: mathematical imagery by Jos Leys. The Droste effect article is informative, too.

posted by Wolfdog on Jun 29, 2006 - 8 comments

posted by Wolfdog on Jun 29, 2006 - 8 comments

The Pianolina - an addictive flash game - is something like a cross between Pong and WolframTones. Brought to you by Grotrian, piano manufacturers since 1835, the pianolina visualizes musical notes as little squares that chime when they bounce against each other or against a wall. Its sophisticated interface lets you add chords, gravity, or start with the basic notes of well known compositions like Beethoven's "Für Elise".

posted by jann on Jun 16, 2006 - 21 comments

posted by jann on Jun 16, 2006 - 21 comments

Mapping the StarMaze A tale of mathematical obsession: "Before I can explain my decades-long quest to map the starmaze I must acquaint you with a small puzzle...I have a habit of seeing everything (cities, organizations, computers, networks, brains) as a maze, so I named this puzzle the starmaze....The first problem I ran into was that there were a lot of rooms...I invented wacky names for each room...But something funny happened...In that instant I finally grasped that the starmaze was arranged on the edges of a nine-dimensional hypercube..."

posted by vacapinta on Jun 4, 2006 - 38 comments

posted by vacapinta on Jun 4, 2006 - 38 comments

The Dot and the Line. (by Norman Juster) Read the book. Watch the movie.

posted by jrb223 on May 20, 2006 - 20 comments

posted by jrb223 on May 20, 2006 - 20 comments

Condoleezza holds a watermelon just over the edge of the roof of the 300-foot Federal Building, and tosses it up with a velocity of 20 feet per second. Using the formula provided, when the watermelon will hit the ground? Bellevue Community College President Jean Floten asked the Pluralism Steering Committee to take the lead on this, and to complete their task quickly.

posted by three blind mice on Apr 13, 2006 - 214 comments

posted by three blind mice on Apr 13, 2006 - 214 comments

Gregory Chaitin's Meta Math! The Quest For Omega

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

posted by MetaMonkey on Apr 13, 2006 - 17 comments

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

posted by MetaMonkey on Apr 13, 2006 - 17 comments

This Week's Finds in Mathematical Physics. A geek's paradise. Reminiscent of Scientific American's *Mathematical Games.*

posted by five fresh fish on Apr 1, 2006 - 11 comments

posted by five fresh fish on Apr 1, 2006 - 11 comments

"...the answer to Life, the Universe, and Everything is..." "Yes? Yes!?" "...42."

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

posted by loquacious on Mar 28, 2006 - 41 comments

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

posted by loquacious on Mar 28, 2006 - 41 comments

Who can name the bigger number? I guarantee you will lose to the Busy Beavers. (No, infinity is not allowed, the bigger infinity is a different game.) The author also debunks in very simple terms the recent story that quantum computers perform calculations without being turned on. My first post and disclaimer: I know the author from our mutual field of quantum information.

posted by gregv on Mar 16, 2006 - 113 comments

posted by gregv on Mar 16, 2006 - 113 comments

The Sarong Theorem Archive is the premier online repository for pictures of mathematicans in sarongs proving theorems.

posted by Wolfdog on Feb 28, 2006 - 24 comments

posted by Wolfdog on Feb 28, 2006 - 24 comments

The Value of Algebra: "*Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers.*"

posted by daksya on Feb 16, 2006 - 190 comments

posted by daksya on Feb 16, 2006 - 190 comments

Ripple Tank Simulation is a delightful, mesmeric java applet simulation of a ripple tank. It demonstrates two dimensional wave phenomena such as interference, diffraction, refraction, resonance, phased arrays, and the Doppler effect (do try the 3D view). From Paul Falstad's fantastic collection of Math, Physics and Engineering Applets.

posted by MetaMonkey on Jan 25, 2006 - 14 comments

posted by MetaMonkey on Jan 25, 2006 - 14 comments

Oddly obsessive statistical analysis of the rates paid by customers of legal Nevada prostitutes, broken down by sex act, attractiveness, body type and presence or absence of a jacuzzi, among other topics. [via Cynical-C, who swears he found it by accident]

posted by mediareport on Jan 9, 2006 - 32 comments

posted by mediareport on Jan 9, 2006 - 32 comments

Significance of numbers. Not to be confused with the concept of "significant figures," this page lists the significance of numbers 0 through 1000.
*See!* "2 is the only even prime."
*Hear!* "24 is the largest number divisible by all numbers less than its square root."
*Thrill!* "3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways." Whoa!

posted by scarabic on Nov 11, 2005 - 43 comments

posted by scarabic on Nov 11, 2005 - 43 comments

Flash Animations for Physics. Animations and interactive demos available in many varieties, such as classical mechanics, nuclear, quantum, and relativistic. There's even a nice explanation of the forces at work in Curling. And if that doesn't wet your geek whistle, then take a peek at the patterns of Visual Math.

posted by Gamblor on Nov 11, 2005 - 7 comments

posted by Gamblor on Nov 11, 2005 - 7 comments

Beyond Discovery - illustrations of the path from research to human benefit

posted by Gyan on Oct 22, 2005 - 7 comments

posted by Gyan on Oct 22, 2005 - 7 comments

A View from the Back of the Envelope - approximations and the fun behind them.

posted by Gyan on Oct 18, 2005 - 25 comments

posted by Gyan on Oct 18, 2005 - 25 comments

Norman Wildberger's New Trigonometry Dr Norman Wildberger has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. The First chapter of his new book, Divine Proportions, is online (.pdf).

posted by Kwantsar on Sep 25, 2005 - 21 comments

posted by Kwantsar on Sep 25, 2005 - 21 comments