Math Overflow is the first attempt to use the Stack Exchange platform, already popular with programmers, as a scientific research tool. Founded this month by a group of young mathematicians, including Scott Morrison and Ben Webster of the Secret Blogging Seminar, the site is already wrestling with hundreds of questions, ranging from the technical ("When is a map given by a word surjective?") to the historical ("Most interesting mathematics mistake?")
posted by escabeche on Oct 17, 2009 - 40 comments

When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection [pdf] (via)
posted by brundlefly on Aug 13, 2009 - 65 comments

The Cornell Historical Math Monographs archive has a great many famous papers, including works by De Morgan, Hamilton, Descartes (warning: French) and of course Lewis Carroll. [more inside]
posted by DU on Jun 15, 2009 - 7 comments

Stephen Wolfram discusses Wolfram|Alpha: Computational Knowledge Engine - at the same time Google Adds Search to Public Data, viz: "Nobody really paid attention to the two hour snorecast" -- like a cross between designing for big data and a glossary of game theory terms -- on Wolfram|Alpha (previously), yet the veil is being lifted nonetheless: "[on] a platonic search engine, unearthing eternal truths that may never have been written down before," cf. hunch & cyc (and in other startup news...) [via] [more inside]
posted by kliuless on May 1, 2009 - 29 comments

"the scale-free network modeing paradigm is largely inconsistent with the engineered nature of the Internet..." For a decade it's been conventional wisdom that the Internet has a scale-free topology, in which the number of links emanating from a site obeys a power law. In other words, the Internet has a long tail; compared with a completely random network, its structure is dominated by a few very highly connected nodes, while the rest of the web consists of a gigantic list of sites attached to hardly anything. Among its other effects, this makes the web highly vulnerable to epidemics. The power law on the internet has inspired a vast array of research by computer scientists, mathematicians, and engineers. According to an article in this month's Notices of the American Math Society, it's all wrong. How could so many scientists make this kind of mistake? Statistician Cosma Shalizi explains how people see power laws when they aren't there: "Abusing linear regression makes the baby Gauss cry."
posted by escabeche on Apr 23, 2009 - 30 comments

Ever wondered what comes next, and why? The On-Line Encyclopedia of Integer Sequences has the answers. (Previously.)
posted by parudox on Mar 10, 2009 - 33 comments

The MacTutor History of Mathematics archive is an astounding collection of historical material on mathematics, especially biographies. (Previously: 1 2 3 4.)
posted by parudox on Feb 28, 2009 - 5 comments

"Do you like fiction and mathematics? Are you interested in what our society thinks about mathematicians?" [more inside]
posted by Minus215Cee on Feb 27, 2009 - 15 comments

Somewhere between 538 and xkcd, Ask Doctor Math is an advice column for practical math questions. [more inside]
posted by piers on Feb 16, 2009 - 25 comments

Division: Work it out! - these girls be spittin the math.
posted by madamjujujive on Jan 17, 2009 - 40 comments

Math Education: An Inconvenient Truth. How children learn (or: don't learn) math today. [more inside]
posted by davar on Sep 6, 2008 - 130 comments

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 by kyrademon on Jul 24, 2008 - 103 comments

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 by Blazecock Pileon on Jun 27, 2008 - 22 comments

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 by amyms on Apr 8, 2008 - 119 comments

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 by Blazecock Pileon on Feb 18, 2008 - 6 comments

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 by parudox on Dec 1, 2007 - 11 comments

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 by Blazecock Pileon on Sep 27, 2007 - 8 comments

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 by jonp72 on Aug 27, 2007 - 43 comments

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 by frogan on May 28, 2007 - 29 comments

Mathematics in Movies.
posted by nthdegx on May 6, 2007 - 28 comments

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 by jason's_planet on May 3, 2007 - 140 comments

The Narrow Road : in which a professional mathematician guides you through pure mathematics (and touches on tangential issues).
posted by phrontist on May 1, 2007 - 10 comments

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 by ericb on Mar 19, 2007 - 67 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

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

Mysterious number 6174. An excellent recreational math article.
posted by fatllama on Jan 13, 2007 - 34 comments

Riemann's Curve , Airfoils, Complex Roots, More.
posted by Kwantsar on Dec 14, 2006 - 19 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

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

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

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

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

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

The Dot and the Line. (by Norman Juster) Read the book. Watch the movie.
posted by jrb223 on May 20, 2006 - 20 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

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

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

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

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 by odinsdream on Sep 14, 2005 - 8 comments

Bathsheba Grossman: a geometric sculptor
posted by Gyan on Aug 26, 2005 - 11 comments

Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson
posted by Gyan on Jul 29, 2005 - 77 comments

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 by Gyan on Jun 29, 2005 - 65 comments

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 by kliuless on Jun 20, 2005 - 6 comments

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 by madamjujujive on May 30, 2005 - 26 comments

Mandelbrot explorer 20th century Dutch mathemeticians are cool. http://www.ddewey.net/mandelbrot/
posted by longsleeves on May 24, 2005 - 21 comments

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 by gleuschk on Apr 22, 2005 - 7 comments

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 by mediareport on Apr 18, 2005 - 8 comments

Mathematics Awareness Month - April 2005: Essays, DVD, Links. Prior MAMs.
posted by Gyan on Apr 1, 2005 - 7 comments

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 by bbrown on Feb 25, 2005 - 43 comments