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Found Functions. An elegant demonstration of beauty in mathematics (and landscape). Nikki Graziano is a math and photography student at Rochester Institute of Technology; some of her photographs were recently featured in Wired. Graziano "overlays graphs and their corresponding equations onto her carefully composed photos. ... Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph."

posted by jokeefe on Feb 8, 2010 - 32 comments

posted by jokeefe on Feb 8, 2010 - 32 comments

"Back in 1993 I was tutoring my sister in algebra. Her quizzes and tests were always made of word problems with a running storyline involving many recurring places and characters. I tied the fate of the main characters to how well she did on the previous quiz, so a good performance brought them good fortune. Unfortunately, one test she completely bombed, and, well, this is a transcription of the quiz she got next." [more inside]

posted by Iridic on Feb 3, 2010 - 40 comments

posted by Iridic on Feb 3, 2010 - 40 comments

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a 1960 essay by Eugene Wigner. Via Steve Strogatz.

posted by jjray on Jan 31, 2010 - 30 comments

posted by jjray on Jan 31, 2010 - 30 comments

posted by albrecht on Jan 28, 2010 - 56 comments

The Calculus Lifesaver lectures -- videos available here in streaming (Real Player), mp4 and wmv formats -- were originally given as "review sessions for the Princeton introductory calculus courses MAT103 and MAT104 during the 2006/7 academic year". Each lecture is about 2 hours.

posted by AceRock on Jan 12, 2010 - 8 comments

posted by AceRock on Jan 12, 2010 - 8 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

Alice's adventures in algebra: Wonderland solved "Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid's proofs, reductio ad absurdum, he picked apart the "semi-logic" of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice's Adventures in Wonderland."

posted by dhruva on Dec 16, 2009 - 30 comments

posted by dhruva on Dec 16, 2009 - 30 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 Anatomy of Spiral Arms, *shows how galaxies naturally evolve to form grand-design two-arm spirals.* The Hubble Ultra Deep Field in 3D. [more inside]

posted by nickyskye on Aug 28, 2009 - 18 comments

posted by nickyskye on Aug 28, 2009 - 18 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

Durango Bill's Home Page. With topics that include: 3D end-to-end tour of the Grand Canyon, the origin and formation of the Colorado River, and examples of river systems that cut through mountain ranges instead of taking easier routes around them in Ancestral Rivers of the World. [more inside]

posted by netbros on Jul 22, 2009 - 5 comments

posted by netbros on Jul 22, 2009 - 5 comments

"*I can see the audience tonight, so I can see also from the size of it that there must many of you here who are not thoroughly familiar with physics, and also a number that are not too versed in mathematics- and I don't doubt that there are some who know neither physics nor mathematics very well.
That puts a considerable challenge on a speaker who is going to speak on the relation of physics and mathematics- a challenge which I, however, will not accept: I published the title of the talk in clear and precise language, and didn't make it sound like it was something it wasn't- it's the relation of physics and mathematics - and if you find that in some spots it assumes some minor knowledge of physics or mathematics, I cannot help it. It was named."*
The Feynman Messenger series at Cornell has been made available online for the first time thanks to Bill Gates.

posted by hindmost on Jul 15, 2009 - 125 comments

posted by hindmost on Jul 15, 2009 - 125 comments

The principles of Harmonics were discovered by Pythagoras c.587-c.507 B.C. during travels to Egypt and throughout the ancient world. Hans Kayser made a profound philosophic study of harmonics in the 20th century. Algorithmic composition is the technique of using harmonic algorithms to create music. Drew Lesso has been creating algorithmic music since 1975. Samples like *Crystal, Constellations, or Planet Earth* demonstrate the math behind the music. Over the years, Lesso has collaborated with many other musicians and poets to create an airy, evolutionary legacy.

posted by netbros on Jul 5, 2009 - 19 comments

posted by netbros on Jul 5, 2009 - 19 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

posted by TheophileEscargot on Jun 8, 2009 - 59 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

Logicomix: An Epic Search for Truth by Apostolos Doxiadis, Christos H. Papadimitriou, Alecos Papadatos, and Annie Di Donna.
Covering a span of sixty years, the graphic novel Logicomix was inspired by the epic story of the quest for the Foundations of Mathematics. This is another kind of epic battle that does not quite lead where the characters thought it would take them. Featuring Bertrand Russell as narrator and the awesome might of the villain (of sorts) Incompleteness. Themes include the high personal price paid for knowledge.

posted by incompressible on Apr 29, 2009 - 24 comments

posted by incompressible on Apr 29, 2009 - 24 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

Joe Palca, a science correspondent for NPR's Morning Edition, was meditating on the best way to convey the magnitude of the world's largest known prime number, 2^{43112609}-1. He contacted H&FJ at Typography.com to discuss the implications of typesetting a number with more than twelve million digits. Crunching of numbers and fonts ensued.

posted by netbros on Apr 22, 2009 - 21 comments

posted by netbros on Apr 22, 2009 - 21 comments

NYT Guesstimation Quiz. Enrico Fermi estimated the yield of the Trinity A-bomb test by dropping some shredded paper. He also asked his students to estimate unusual quantities like the number of piano tuners in Chicago - to show that just about anything can be estimated without detailed knowledge.

posted by Electric Dragon on Apr 1, 2009 - 54 comments

posted by Electric Dragon on Apr 1, 2009 - 54 comments

Oxford Professor & Fellow of the Royal Society James Murray uses mathematical modelling to predict whether a marriage will survive or end in divorce, with 94% accuracy.
His lecture to the Royal Society will be available for view on demand within two days.

posted by UbuRoivas on Mar 26, 2009 - 44 comments

posted by UbuRoivas on Mar 26, 2009 - 44 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

World of Science contains budding encyclopedias of astronomy, scientific biography, chemistry, and physics. This resource has been assembled over more than a decade by internet encyclopedist Eric Weisstein with assistance from the internet community. MeFi visited Weisstein's Mathworld a couple years ago.

posted by netbros on Feb 18, 2009 - 6 comments

posted by netbros on Feb 18, 2009 - 6 comments

One night, very late, I was browsing the internet, using my current computer, Shalosh B. Ekhad, III. I was searching for "Ekhad". All of a sudden, to my amazement, I chanced on a website whose last update was Sept. 30, 2050, and found this little Elementary Geometry textbook.
This text may seem a bit strange to 2001 humans. It appears that there are no proofs, only statements, in Maple, using English-based names for the definitions and theorems. But THE STATEMENT IS THE PROOF, ready to be run on Maple, that will output "true" if the proof-statement is correct, and "false" otherwise. [more inside]

posted by orthogonality on Feb 18, 2009 - 42 comments

posted by orthogonality on Feb 18, 2009 - 42 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

On Truth and Reality. Despite several thousand years of failure to correctly understand physical reality (hence the current postmodern view that this is impossible) it is actually very simple to work out how matter exists and moves about in Space. The rules of Science (Occam's Razor / Simplicity) and Metaphysics (Dynamic Unity of Reality) require that reality be described from only one single source existing, as Leibniz wrote: *"because of the interconnection of all things with one another."* [more inside]

posted by netbros on Jan 30, 2009 - 46 comments

posted by netbros on Jan 30, 2009 - 46 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

You and Your Research was a talk given by Richard Hamming in 1986. Read it if you have an interest in doing first-class work.

posted by parudox on Jan 4, 2009 - 24 comments

posted by parudox on Jan 4, 2009 - 24 comments

MetaFilter's Eric Gjerde has just come out with a book, Origami Tessellations: Awe-Inspiring Geometric Designs. Eric also makes really unusual, complex and mathematically interesting origami. His site has all kinds of cool things to look at and explore, like Owen Jones' The Grammar of Ornament, Joel Cooper's amazing paper sculptures and Ernst Haeckel's awesome book, Kunst-Formen der Natur. [more inside]

posted by nickyskye on Dec 16, 2008 - 8 comments

posted by nickyskye on Dec 16, 2008 - 8 comments

You might have seen the Droste Effect before, perhaps even the animated version. But here's a new iteration - a music video.

posted by le morte de bea arthur on Nov 25, 2008 - 28 comments

posted by le morte de bea arthur on Nov 25, 2008 - 28 comments

Hunting the Hidden Dimension. You may be familiar with fractals, but in this PBS Nova episode, divided online into 5 parts, fractals go beyond the impossible zoom of the Mandelbrot set. Scientists are using fractals to describe complex natural occurrences, like lava, capillaries, and rain forests. In part 5, scientists measure one tree in the rain forests, and the distribution of small and large branches mirror the distribution of small and large trees. Fractals, it seems, are nature.

posted by plexi on Nov 2, 2008 - 43 comments

posted by plexi on Nov 2, 2008 - 43 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

Mathematicians create videos that help in visualizing four-dimensional objects. Science News writes about it: seeing in four dimensions.

posted by Surfin' Bird on Aug 24, 2008 - 26 comments

posted by Surfin' Bird on Aug 24, 2008 - 26 comments

Online Encyclopedia of Mathematics Edited by Michiel Hazewinkel (CWI, Amsterdam), and originaly published in dead tree form in 2002, now free to browse and poke into. [more inside]

posted by Iosephus on Aug 2, 2008 - 7 comments

posted by Iosephus on Aug 2, 2008 - 7 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

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

posted by Blazecock Pileon on Jun 27, 2008 - 22 comments

Accidental Astrophysicists: "They started with algebra and ended up learning about gravitational lensing (PDF)." [Via linkfilter]

posted by homunculus on Jun 17, 2008 - 22 comments

posted by homunculus on Jun 17, 2008 - 22 comments

The hyperbolic crochet coral reef has come to London. [more inside]

posted by chuckdarwin on Jun 17, 2008 - 14 comments

posted by chuckdarwin on Jun 17, 2008 - 14 comments

The Reality Tests. "A team of physicists in Vienna has devised experiments that may answer one of the enduring riddles of science: Do we create the world just by looking at it?"

posted by homunculus on Jun 4, 2008 - 82 comments

posted by homunculus on Jun 4, 2008 - 82 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

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

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

posted by parudox on Dec 1, 2007 - 11 comments

From Ants to People, an Instinct to Swarm. Carl Zimmer looks at the work of Iain Couzin. [Via The Loom.]

posted by homunculus on Nov 13, 2007 - 17 comments

posted by homunculus on Nov 13, 2007 - 17 comments

Gerbert D'Aurillac: mathemetician and engineer, Pope, ghost, and meddler with dark forces. [more inside]

posted by Iridic on Nov 1, 2007 - 17 comments

posted by Iridic on Nov 1, 2007 - 17 comments

An hour has 60 minutes and a minute has 60 seconds because the Sumerians used a base 60 counting system. Why *60*? A plausible explanation is that they could count to 12 with one hand, and to 60 with both hands. Alternate explanations from the MacTutor History of Mathematics archive.

posted by russilwvong on Oct 21, 2007 - 47 comments

posted by russilwvong on Oct 21, 2007 - 47 comments