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Calculus of Averages - *Newton and Archimedes did not possess this knowledge. No mathematics professor today can provide this knowledge and depth of understanding.* Author John Gabriel maintains a blog, Friend of Wisdom, and contributes articles such as Are real numbers uncountable? to Google's Knol project.

posted by Wolfdog on Jan 8, 2010 - 78 comments

posted by Wolfdog on Jan 8, 2010 - 78 comments

The beauty of roots. From Dan Christensen and Sam Derbyshire via John Baez. If you like algebra: these are plots of the density in the complex plane of roots of polynomials with small integral coefficients. If you don't: these are extravagantly beautiful images produced from the simplest of mathematical procedures. Explore the image interactively here.

posted by escabeche on Jan 4, 2010 - 29 comments

posted by escabeche on Jan 4, 2010 - 29 comments

Chisenbop - a tool for doing simple math on your fingers, invented by Sung Jin Pai in the '40s, it uses the same principles as the abacus. Tutorial 1 and 2, and a cute kid.

posted by serazin on Jan 3, 2010 - 34 comments

posted by serazin on Jan 3, 2010 - 34 comments

A gathering of puzzles including many old chestnuts but also perhaps one or two you haven't met before.

posted by Wolfdog on Dec 16, 2009 - 29 comments

posted by Wolfdog on Dec 16, 2009 - 29 comments

Way to overthink a plate of ~~beans~~ pizza. [more inside]

posted by jonathanstrange on Dec 11, 2009 - 58 comments

posted by jonathanstrange on Dec 11, 2009 - 58 comments

"Center the bagel at the origin, circling the Z axis. A is the highest point above the +X axis. B is where the +Y axis enters the bagel. C is the lowest point below the -X axis. D is where the -Y axis exits the bagel."

posted by william_boot on Dec 7, 2009 - 44 comments

posted by william_boot on Dec 7, 2009 - 44 comments

Eminem's "Lose Yourself" re-envisioned as a high school math course. The math and film departments of Madison East High School collaborate on a video, starring math teacher Philip Galarowicz. Not to be confused with The Rappin' Mathematician (hear "The Number Line Dance" here), or these high school math rappers, or the rap battle of TI-83 and Fitty Slope. The quadratic formula, rapped. The quadratic formula, rapped again. The quadratic formula, rapped, strangely compellingly, by a teacher in a tie.

posted by escabeche on Dec 5, 2009 - 28 comments

posted by escabeche on Dec 5, 2009 - 28 comments

How should math be taught? The Kumon Math curriculum provides a simple and clear description of one possible sequence of skills. Hung-Hsi Wu decries the bogus dichotomy of basic skills versus conceptual understanding (PDF, Google Docs). David Klein provides a detailed history of US K-12 math education in the 20th century. The NYT describes the 2008 report of the National Mathematics Advisory Panel (full text as PDF). [more inside]

posted by russilwvong on Nov 15, 2009 - 71 comments

posted by russilwvong on Nov 15, 2009 - 71 comments

posted by twoleftfeet on Nov 9, 2009 - 19 comments

We all wish we had a teacher like this

posted by Christ, what an asshole on Nov 5, 2009 - 50 comments

posted by Christ, what an asshole on Nov 5, 2009 - 50 comments

SAGE is a free, open-source computer algebra system. [more inside]

posted by kaibutsu on Oct 30, 2009 - 37 comments

posted by kaibutsu on Oct 30, 2009 - 37 comments

"Pynchon, postmodern author, is commonly said to have a non-linear narrative style. No one seems to have taken seriously the possibility, to be explored in this essay, that his narrative style might in fact be *quadratic*." Number theorist Michael Harris on Pynchon and conic sections.

posted by escabeche on Oct 25, 2009 - 60 comments

posted by escabeche on Oct 25, 2009 - 60 comments

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

posted by escabeche on Oct 17, 2009 - 40 comments

The eyeballing game: compare your best attempts at several instinctive everyday tasks - determining a point of convergence, bisecting an angle, finding the midpoint of a line - against mathematical certainty. In a more financial mood? Play Chartgame: given a random historical stock chart of an unnamed S&P 500 company, choose to buy and sell as time advances to see if you can beat the market.

posted by Bora Horza Gobuchul on Oct 14, 2009 - 22 comments

posted by Bora Horza Gobuchul on Oct 14, 2009 - 22 comments

42.7 percent of all statistics are made up: After Strategic Visions refused to share the methodology behind some of their polling, Nate Silver of fivethirtyeight analyzed the firm's poling results and found evidence of fraud. Strategic Visions responds to The Hill. More amusingly, Nate went on a look at an even more questionable study by the same company claiming that only 23 percent of Oklahoma students know that George Washington is the first president. [more inside]

posted by The Devil Tesla on Sep 27, 2009 - 76 comments

posted by The Devil Tesla on Sep 27, 2009 - 76 comments

For math geeks. How to Draw the Voronoi Diagram. Voronoi diagrams, as a geometric model are fascinating because they can be used to describe almost literally everything: from cell phone networks to radiolaria, at every scale: from quantum foam to cosmic foam. See also the Wallpaper Group: there are only 17 ways to fill a plane with a regular 2 dimensional pattern. Fred Scharmen [weblog home] is known as 765 and also produces a number of shapes, textures and patterns.

posted by netbros on Sep 16, 2009 - 35 comments

posted by netbros on Sep 16, 2009 - 35 comments

Photographer Mariana Cook has a new book of portraits of well-known mathematicians. Here's a slideshow with some interesting audio, and more of the photographs.

posted by Frobenius Twist on Sep 10, 2009 - 10 comments

posted by Frobenius Twist on Sep 10, 2009 - 10 comments

The Status of the P Versus NP Problem *It's one of the fundamental mathematical problems of our time, and its importance grows with the rise of powerful computers.* (via mr)

posted by kliuless on Aug 27, 2009 - 116 comments

posted by kliuless on Aug 27, 2009 - 116 comments

When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection [pdf] (via)

posted by brundlefly on Aug 13, 2009 - 65 comments

posted by brundlefly on Aug 13, 2009 - 65 comments

Why bureaucracy, like gas, fills up all available space. From the archive of *The Economist*, 1955 [via ArchiveDigger.]

posted by digaman on Jul 31, 2009 - 11 comments

posted by digaman on Jul 31, 2009 - 11 comments

"This day may be celebrated in a variety of ways. Pause and give thought to the role that the number pi has played in your life. Imagine a world without pi. Attempt to memorise pi to as many decimal places as you can. If you're feeling creative, devise alternative values for pi. Go to a party (I will). Or just celebrate in the time-honoured fashion of ignoring Pi Approximation Day altogether."

Happy Pi Approximation Day. [more inside]

posted by swift on Jul 23, 2009 - 55 comments

Happy Pi Approximation Day. [more inside]

posted by swift on Jul 23, 2009 - 55 comments

The Free Will Theorem - "If there exist experimenters with (some) free will, then elementary particles also have (some) free will." (previously)

posted by kliuless on Jun 28, 2009 - 229 comments

posted by kliuless on Jun 28, 2009 - 229 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

posted by DU on Jun 15, 2009 - 7 comments

Douglas Hofstadter's *Gödel, Escher, Bach: An Eternal Golden Braid* has been recorded as a series of video lectures for MIT's Open Courseware project.

posted by loquacious on May 30, 2009 - 74 comments

posted by loquacious on May 30, 2009 - 74 comments

Theory versus Statistics, Financial Economics Edition. "You can almost here the lament of this quant that the real math theory has been dead since 1980, and that it has all been applied and statistics ever since. It’s like Fischer Black was Kool Herc and Myron Scholes was Afrika Bambaataa, and they’d all go plug in their computers into lamp posts and do martingale representations in the streets and at house parties. And, of course, it was all ruined in 1979 when it went commercial." A response to The Last Temptation of Risk by Barry Eichengreen.

posted by chunking express on May 4, 2009 - 8 comments

posted by chunking express on May 4, 2009 - 8 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

posted by kliuless on May 1, 2009 - 29 comments

Following the recent uproar over Texas and the possibility of its secession (previously), Fivethirtyeight.com puts forward a theoretical division of Texas into five states: Plainland, Trinity, Gulfland, New Texas, and El Norte.

posted by aerotive on Apr 24, 2009 - 52 comments

posted by aerotive on Apr 24, 2009 - 52 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

posted by escabeche on Apr 23, 2009 - 30 comments

MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.

posted by Brian B. on Mar 21, 2009 - 8 comments

posted by Brian B. on Mar 21, 2009 - 8 comments

Dolphins at SeaWorld Orlando make and play with bubble rings. Others learn by watching. (SLYP) via [more inside]

posted by Toekneesan on Mar 18, 2009 - 17 comments

posted by Toekneesan on Mar 18, 2009 - 17 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

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

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

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

posted by piers on Feb 16, 2009 - 25 comments

Sal Khan likes explaining things, and he's really good at it. Here he is on CNN giving an excellent explanation of the financial crisis. And here's a great explanation of Newton's Law of Gravitation. His YouTube channel has over 700 lectures and you leave understanding everything he talks about no matter the subject.

posted by y10k on Jan 31, 2009 - 21 comments

posted by y10k on Jan 31, 2009 - 21 comments

The sestina is an old poetic form invented by the troubadors; each of the thirty-nine lines ends with one of only six words, which gives the sestina a haunting, constricted feel. You might have read modern examples by Bishop or Auden, or the even more modern "WTF Sestina" by Meghann Marco. But you have probably never read a sestina which explains how to construct a sestina in the language of finite group theory. (.pdf link) Via excellent mathblog God Plays Dice.

posted by escabeche on Jan 20, 2009 - 24 comments

posted by escabeche on Jan 20, 2009 - 24 comments

Division: Work it out! - these girls be spittin the math.

posted by madamjujujive on Jan 17, 2009 - 40 comments

posted by madamjujujive on Jan 17, 2009 - 40 comments

Brain reorganizes to make room for math. But does math easily lead to truth? Is it really just beauty?

posted by twoleftfeet on Nov 23, 2008 - 31 comments

posted by twoleftfeet on Nov 23, 2008 - 31 comments

"...the best place to hide bulls**t is in a refereed journal that’s not open-access!" The math-physics blog n-category cafe digs into the curious case of M.S. El Naschie. El Naschie is editor-in-chief of the journal Chaos, Solitons, and Fractals, published by the well-respected scientific publisher Elsevier and sold to academic libraries for US$4,520 a year. The problem? El Naschie has published 322 of his own papers in the journal -- papers that John Baez (of "This Week's Finds in Mathematical Physics" and "The Crackpot Index") describes as "vague, dreamlike imagery," "undisciplined numerology larded with impressive buzzwords," and "total baloney." Is El Naschie a reverse Sokal? Or a Markov process for producing random publishable papers? One thing's for sure -- he knows how to cure cancer.

posted by escabeche on Nov 12, 2008 - 49 comments

posted by escabeche on Nov 12, 2008 - 49 comments

A math professor was explaining a particularly complicated calculus concept to his class when a frustrated pre-med student interrupts him. "Why do we have to learn this stuff?" the pre-med blurts out. The professor pauses, and answers matter-of-factly: "Because math saves lives." "How?" demanded the student. "How on Earth does calculus save lives?" "Because," replied the professor, "it keeps certain people out of medical school."

posted by cthuljew on Nov 9, 2008 - 82 comments

posted by cthuljew on Nov 9, 2008 - 82 comments

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

posted by mystyk on Oct 13, 2008 - 31 comments

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

posted by mystyk on Oct 13, 2008 - 31 comments

posted by cog_nate on Oct 1, 2008 - 9 comments

Quest for a true 3D Mandelbrot Fractal - a very nice exploration of Mandelbrot/Julia set fractals in various kinds of 3D space.

posted by loquacious on Sep 14, 2008 - 21 comments

posted by loquacious on Sep 14, 2008 - 21 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

posted by davar on Sep 6, 2008 - 130 comments

MEFIEach letter corresponds to a number 0-9. The solution is unique. [more inside]

META

+ ASKME

-------

FILTER

posted by Upton O'Good on Sep 3, 2008 - 27 comments

Who is Alexander Grothendieck? [PDF] *This lecture is concerned not with Grothendieck's mathematics but with his very unusual life on the fringes of human society. In particular, there is, on the one hand, the question of why at the age of forty-two Grothendieck first of all resigned his professorship at the Institut des Hautes Etudes Scientifiques (IHES); then withdrew from mathematics completely; and finally broke off all connections to his colleagues, students, acquaintances, friends, as well as his own family, to live as a hermit in an unknown place. On the other hand, one would like to know what has occupied this restless and creative spirit since his withdrawal from mathematics.*

posted by Wolfdog on Aug 17, 2008 - 31 comments

posted by Wolfdog on Aug 17, 2008 - 31 comments

How deep does the rabbit hole go? The Ultimate Fractal Video Project features animated zooms into the famous Mandelbrot Set. Some zoom in so far that, by the end of the dive, the first frame you had viewed would be as large as (or larger than) the known universe. | The animations are offered as .zip'd WMV files; lower-quality versions are viewable on FractAlkemist's YouTube page. [more inside]

posted by not_on_display on Jul 29, 2008 - 13 comments

posted by not_on_display on Jul 29, 2008 - 13 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

posted by kyrademon on Jul 24, 2008 - 103 comments

This week in mathematical physics, John Baez looks at the amazing tile patterns in the Alhambra in Granada, dividing the patterns into their characteristic Wallpaper Groups based on their symmetries. And if these patterns aren't good enough for you, try drawing your own with the Escher Web Sketch tool. [more inside]

posted by kiltedtaco on Jul 24, 2008 - 20 comments

posted by kiltedtaco on Jul 24, 2008 - 20 comments