Math Education: An Inconvenient Truth. How children learn (or: don't learn) math today.
posted on Sep 6, 2008 - View this thread

No gender differences found in math performance. None. Not on average, at least in countries where the sexes are treated equally. And no, not at the highest, outlier levels of mathematical ability, either, despite what some believe. And not in number of undergrad math degrees earned. And not in terms of complex problem solving ability. Just plain not.
posted on Jul 24, 2008 - View this thread

Whether you want to learn to lace shoes, tie shoelaces, stop shoelaces from coming undone, calculate shoelace lengths or even repair aglets, Ian's Shoelace Site has the answer!
posted on Jun 27, 2008 - View this thread

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology." The NY Times' John Tierney reports on new research into cognitive dissonance as examined through the famous Monty Hall Problem. [A previous MetaFilter thread about the Monty Hall Problem: Let's Make A Deal!]
posted on Apr 8, 2008 - View this thread

Fun and games with mathematics and mathematical puzzles (e.g. heart basket, Rubik's Cube, Rubik's Magic, hypercubes, and more) in both English and (with yet more content in) German.
posted on Feb 18, 2008 - View this thread

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)
posted on Dec 1, 2007 - View this thread

More than fifty selected articles from The Princeton Companion of Mathematics (username: Guest, password: PCM) — a thematically-organized compendium of mathematics and mathematicians from Fields Medal-winner Tim Gowers. [via, previously]
posted on Sep 27, 2007 - View this thread

The Marquis de Condorcet and Admiral Jean-Charles de Borda were two men of the French Enlightenment who struggled with how to design voting systems that accurately reflected voters' preferences. Condorcet favored a method that required the winner in a multiparty election to win a series of head-to-head contests, but he also discovered that his method easily led to a paradoxes that produced no clear winners. The Borda method avoids the Condorcet paradox by requiring voters to rank choices numerically in order of preference, but this method is flawed because the withdrawal of a last-place candidate can reverse the election results. Mathematicians in the 19th century attempted to design better voting systems, including Lewis Carroll, who favored an early form of proportional representation. Economist Kenneth Arrow argued that designing a perfect voting system was futile, because his "impossibility theorem" proved that it's impossible to design a non-dictatorial voting system that fulfills five basic criteria of fairness. (more inside)
posted on Aug 27, 2007 - View this thread

What is the square of 85? In an instant, a 17-year-old boy said without blinking, "7,225." Kamlesh Shetty had used a trick from a quaint concept called Vedic math, a compilation of arithmetic shortcuts believed to have been written by ancient Indians who lived centuries before Christ, during a glorious period in Indian history called the Vedic Age. More on Vedic math. Still more. And there's a similar system called the Trachtenberg system, invented in a Nazi concentration camp. Where were these guys when I was in the third grade struggling with my times tables?
posted on May 28, 2007 - View this thread

Mathematics in Movies.
posted on May 6, 2007 - View this thread

Aptitude Schmaptitude! While the state of mathematical incompetence in this country has been much lamented, most famously in Paulos's brilliant 1988 book Innumeracy, it is still tacitly accepted . . . Being incompetent in math has become not only acceptable in this widely innumerate culture, it has almost become a matter of pride. No one goes around showing off that he is illiterate, or has no athletic ability, but declarations of innumeracy are constantly made without any embarrassment or shame.
posted on May 3, 2007 - View this thread

The Narrow Road : in which a professional mathematician guides you through pure mathematics (and touches on tangential issues).
posted on May 1, 2007 - View this thread

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 E₈, a symmetrical structure whose mathematical calculation has long been considered an unsolvable problem. Yet an international team of math whizzes cracked E₈'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 on Mar 19, 2007 - View this thread

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 on Mar 10, 2007 - View this thread

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 on Feb 2, 2007 - View this thread

Mysterious number 6174. An excellent recreational math article.
posted on Jan 13, 2007 - View this thread

Riemann's Curve , Airfoils, Complex Roots, More.
posted on Dec 14, 2006 - View this thread

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 on Dec 7, 2006 - View this thread

Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks to the New Yorker.
posted on Aug 29, 2006 - View this thread

Grisha Perelman, where are you? Perelman has quite possibly solved one of mathematics biggest mysteries, Poincaré’s conjecture, but has since disappeared.
posted on Aug 15, 2006 - View this thread

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 on Aug 3, 2006 - View this thread

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 on Jul 19, 2006 - View this thread

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 on Jun 4, 2006 - View this thread

The Dot and the Line. (by Norman Juster) Read the book. Watch the movie.
posted on May 20, 2006 - View this thread

"...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 on Mar 28, 2006 - View this thread

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 on Feb 16, 2006 - View this thread

Beyond Discovery - illustrations of the path from research to human benefit
posted on Oct 22, 2005 - View this thread

A View from the Back of the Envelope - approximations and the fun behind them.
posted on Oct 18, 2005 - View this thread

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 on Sep 25, 2005 - View this thread

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.
posted on Sep 14, 2005 - View this thread

Bathsheba Grossman: a geometric sculptor
posted on Aug 26, 2005 - View this thread

Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson
posted on Jul 29, 2005 - View this thread

Godel's theorems have been used to extrapolate a great many "truths" about the world. Torkel Franzen sets the record straight in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse. Read the introduction (PDF). If you want, check out his explanation of the theorems.
posted on Jun 29, 2005 - View this thread

The Logic of Diversity "A new book, The Wisdom of Crowds [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)
posted on Jun 20, 2005 - View this thread

Whether its crocheted hyperbolic models or Lorenz manifolds, a lace pi shawl or knit Fibonacci socks, some math geeks find expression in the fiber arts.
posted on May 30, 2005 - View this thread

Mandelbrot explorer 20th century Dutch mathemeticians are cool. http://www.ddewey.net/mandelbrot/
posted on May 24, 2005 - View this thread

Saunders Mac Lane, mathematician, has died, age 95. Winner of the National Medal of Science, Vice-President of the National Academy of Science, President of the American Mathematical Society, author of three of the canonical texts in algebra [reg. maybe req., here's a local copy], Mac Lane was also mathematical ancestor to over a thousand mathematicians, father of category theory and homological algebra, and expert in topology, topos theory, group cohomology, logic, and applied mathematics. He was one of the towering figures of postwar mathematics. Remembered by his students and all of us who were affected by his work and his life.
posted on Apr 22, 2005 - View this thread

The Mathematical Fiction Homepage is a collaborative attempt to "collect information about all significant references to mathematics in fiction." Feel free to add classic or recent works in any medium to the collection, or rate existing entries on their mathematical content and literary quality.
posted on Apr 18, 2005 - View this thread

Mathematics Awareness Month - April 2005: Essays, DVD, Links. Prior MAMs.
posted on Apr 1, 2005 - View this thread

Danica McKellar —the former star of The Wonder Years—has her own web site. It's got a great feature where she answers your math questions. No, really. She's got a degree in mathematics and co-authored a paper on percolation and Ashkin-Teller models. No, really.
posted on Feb 25, 2005 - View this thread

Hypothesis as thought-crime ...Now, however, a new brouhaha has erupted [at Harvard]and it seems impossible that Summers [the president]will emerge from this one without serious erosion of his moral authority. The trigger was a statement he made at a conference, suggesting that the reason there are more men than women in the mathematical sciences at top-flight institutions has to do with a small statistical difference in inate ability, which becomes a pretty large disparity when one looks at the 'high end' of the respective distribution curves... The fatal words did not set forth his main theme, but merely constituted a brief aside, thoroughly hedged and qualified. Nonetheless, they touched off a firestorm of indignation, the most striking aspect of which was the intemperate response of a number of feminist scientists, who offered no counter-arguments, but simply declared the whole idea misogynistic and therefore forbidden intellectual territory.
posted on Jan 31, 2005 - View this thread

The Mathematics Genealogy Project. A service of the Department of Mathematics at North Dakota State University, the project intends to "compile information about ALL the mathematicians of the world. [...] It is our goal to list all individuals who have received a doctorate in mathematics." Seven generations from one of my recent professors back to Gauss, six back to Felix Klein (of Erlangen Program and bottle fame), eight back to Jacobi, and nine back to Poisson and Fourier, then Lagrange, then Euler, then the Bernoulli brothers, then Leibniz, and then it blew up at infinity.
posted on Dec 21, 2004 - View this thread

Thinking Machine 4 explores the invisible, elusive nature of thought. Play chess against a transparent intelligence, its evolving thought process visible on the board before you.

From Martin Wattenberg (with Marek Walczak); they have been noted here before.
posted on Oct 27, 2004 - View this thread

Maths puzzles and more problems. Found whilst searching for the fiendish the Monty Hall Problem. A Tangled Tale, indeed.
posted on Sep 24, 2004 - View this thread

Famous Curves. Safe for work.
posted on Aug 20, 2004 - View this thread

64=65? there must be some kind of trick to this, right?
posted on Aug 18, 2004 - View this thread

The Shapes of Space [note : pdf, sciam, poincaré conjecture]
posted on Aug 1, 2004 - View this thread

The House With Too Many Perpundiculars
posted on Jul 13, 2004 - View this thread

Coincidence or contortion? Ivan Panin deciphered a numeric code in the Bible. Known as Gematria, the 'code' implies the Bible could not have been written without Holy assistance. Panin offered an open challenge for someone to create text using a similar pattern, yet no one was able to create one(nor tried).

However many people doubt the authenticity of the code though. The code is found in the same verses using different translations. It is also claimed that Panin manufactured his own translations to create this mathematical phenomenon.

Whether or not you believe, you can determine how good or evil any text or website is.
posted on Jun 25, 2004 - View this thread

Number Spirals: Coincidences of order. "In mathematics you don't understand things. You just get used to them."
posted on Apr 15, 2004 - View this thread

Cut the Knot. Interactive mathematics miscellany and puzzles.
posted on Jan 6, 2004 - View this thread

The MacTutor History of Mathematics archive from the University of St. Andrews' School of Mathematics and Statistics.
posted on Dec 30, 2003 - View this thread

Algorithmic Obscenity [maybe nsfw?] Who knew math could be this much fun? [via BoingBoing]
posted on Nov 15, 2003 - View this thread

Fun with Fibonacci numbers. So you say you scored 130 on yesterday's IQ test, did ya?
posted on Oct 28, 2003 - View this thread

The Lizzie Method : 16-year-old Elizabeth Seagle figured out a better way of factoring quadratic equations. What do the Me-Fi mathematicians think? Will it be taught in future textbooks? Personally, I never touch the stuff.
posted on Jul 9, 2003 - View this thread

13-year-old Gregory Robert Smith graduates from Randolph-Macon College this month. He has yet to find the vaccine for the brutal Atomic Wedgie.
posted on Jun 1, 2003 - View this thread

A Hypercube is "One of the simplest four-dimensional structures that we can imagine...[Google cache]. It is the four-dimensional analogue of an ordinary cube."
It's confusing, but Drew's words and pictures here will probably wrap your head around the concept. If you're already a Math-Head, you may find this more interesting, and it leads us to this fun interactive tesseract. Or you can draw your own.
Want even more fun?: This Hypercube is just out on video (in the US; 3/03 in the UK), this tesseract has been around since '62, and this one is has just been released.
[Yes, tesseracts & h-cubes were previously discussed here & even waaay back here.]
posted on May 8, 2003 - View this thread

planetmath.org. I'd say more but there's just too much here. Browse around.
posted on May 2, 2003 - View this thread

Paul Bourke of Auckland has an excellent set of elegant and informative webpages for the kind of math you look at. Even if math perplexes you, his pages are still quite pretty and often make for interesting reading regardless. Every place I've worked between college and now, Paul has given me pages that nicely explained how to do somthing I needed to do and even personal help on occasion. Here's to you, Paul!
posted on Oct 28, 2002 - View this thread

The man who wrote 10,000 Grooks (grooks, grooks, grooks), Piet Hein, was also the inventor of Hex and the creator of the Soma Cube. In the design world, he is most famous for the SuperEllipse, a figure that rivals Buckminster Fuller's geodesics in ingenuity, an aesthetic balance between a circle and a square, and a mathematical figure which has been used to design a square in Stockholm. From the SuperEllipse, you can get the SuperEgg, a strange solid which will unexpectedly balance on one end and has been mistaken for an alien artifact.
posted on Oct 28, 2002 - View this thread

Women Mathematicians. With numerous biographies and photographs, this website indexes the many contributions that women have made to the field of mathematics. From Pythagoras' wife Theano and martyr Hypatia, also notable are the first female computer programmer and the first female Ph.D. recipient.
posted on Oct 9, 2002 - View this thread

Mathematician Henrik Lenstra was intrigued by a blank space in he middle of a drawing by MC Escher. Over two years he managed to describe the mathematical structure of the drawing, project what should go in the missing space and produce an extraordanary animation of the result.
posted on Aug 6, 2002 - View this thread

Math owie! Was math in distress during its awareness month? Discuss. [Inspired by moz of TPK.]
posted on Apr 28, 2002 - View this thread

The End of equations? Paul Dirac and Albert Einstein thought equations were things of beauty, Stephen Wolfram, by contrast thinks they are antiquated.
posted on Jan 27, 2002 - View this thread

The Paso Doble is an eerie little puzzle game, something like a De Chirico painting come to life.
Oh yeah, a new Mersenne prime was discovered today by a 20-yr old.
Both links courtesy of mathpuzzle.com
(will i ever beat joseph devincentis?!)
posted on Dec 6, 2001 - View this thread

Laws of Form In 1969, George Spencer-Brown published a mathematical book called Laws of Form, which has inspired explorations in philosophy, cybernetics, art, spirituality, and computation. The work is powerful and has established a passionate following as well as harsh critics. This web site explores these people, their ideas and history, and provides references for further exploration. I read this then, didn't understand much of the math due to my innumeracy, but was struck by a passage in passing... I especially am curious to see what the numerate in MetaFilter have to say.
posted on Nov 11, 2001 - View this thread

MathWorld is back online. And what a nightmare the experience has been. (And still is? New entries now require filling out this permissions form.)
posted on Nov 6, 2001 - View this thread

What Color is My Hat? I [heart] these mathematical conundrums -- simple, easy-to-state, seemingly obvious logic problems that have solutions that completely defy common sense. Here's another you can spring on a friend: "You want to fry up three pieces of french toast. You have a frying pan that is just large enough to accomodate two pieces of bread at a time. If it takes you 30 seconds to fry one side of bread, and each piece of must be fried on both sides, how long will it take you to cook up three pieces (assuming that the act of flipping a piece or adding/ removing it to or from the pan takes no time). Think about it. Answer inside.
posted on May 25, 2001 - View this thread

LavaRand ...harnessing the power of Lava Lite® lamps to generate truly random numbers....

That's a bold statement, but who am I to doubt the power of the lava lamp. The mathematical purist may disagree with the "truely random" part, but this geek speak convinced me that LavaRand can handle all my random number needs.
posted on Apr 30, 2001 - View this thread

Mathematician Bums Out Entire Scientific Community His "Omega" number--infinite and incalculable--guts hopes for pure mathematics, physicists' hopes for a Theory of Everything, and is just in general kind of bafflingly cool. Builds on the whole Godel/Turing foundation of hopelessness!
posted on Mar 15, 2001 - View this thread

Americans suck at math. Mathematician trade deficit ensues... I only find this article interesting because of a talk with my math teacher recently about how most math teachers these days are foriegners, although she isn't, and not that foriegners are bad. But I'm curious if this a bad problem in today's economy or not? Or if this is a problem? What country is good at math? India and China? That's where most of the Silicon Valley CEO's workers are from these days. Or is that political, financial? I don't know. Do you know?
posted on Feb 7, 2001 - View this thread

Math Against Tyranny... A mathmatician discusses the virtues of the Electoral College.
posted on Nov 10, 2000 - View this thread

Hey, kids! Statistics is cool! (Amazing introduction to the concept of estimation, and error computing.)
posted on Oct 24, 2000 - View this thread

kevin bacon as math theory: properties of the kevin bacon absorbing set
posted on Oct 17, 2000 - View this thread

Mersenne Prime Search is a distributed computing project much like Seti@home, except instead of searching for aliens, you're in the running for $100,000 and a place in math history (shouldn't your computer actually be the one that goes into the math history books?).
posted on Jul 7, 2000 - View this thread

The Poincaré Conjecture: If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the the surface of the apple is ‘simply connected,’ but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out be be extraordinarily difficult, and mathematicians have been struggling with it ever since.

...but if you can prove it, [or any of six other 'millenium prize problems'] the clay mathematics institute wants to line your pockets with $1M
posted on May 24, 2000 - View this thread