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Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]

posted by kliuless on Sep 17, 2014 - 28 comments

posted by kliuless on Sep 17, 2014 - 28 comments

[more inside]How did something as loud as a bell—something which is experienced so much more often, and more powerfully, by hearing than by sight—become dumb?

posted by tykky on Aug 30, 2014 - 20 comments

Mathematician Zachary Abel builds impressive Mathematical Sculptures from office supplies and other household objects. [more inside]

posted by We had a deal, Kyle on Aug 29, 2014 - 12 comments

posted by We had a deal, Kyle on Aug 29, 2014 - 12 comments

Bees & Bombs is a tumblr of hypnotic GIF animations programmed by Dublin-based physics student Dave Whyte

posted by Mr. Six on Aug 26, 2014 - 19 comments

posted by Mr. Six on Aug 26, 2014 - 19 comments

Middle East Peace Potential through Dynamics in Spherical Geometry: Engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks. * This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism...Mathematically these patterns cannot be readily combined. This issue is described in mathematics in terms of tiling...A set of hexagons and pentagons can however be uniquely fitted together as a particular three-dimensional polyhedron, namely the truncated icosahedron. * [more inside]

posted by leahwrenn on Aug 21, 2014 - 32 comments

posted by leahwrenn on Aug 21, 2014 - 32 comments

The Peg Solitaire Army is a problem spun off from a classic recreation, and yet another example of the golden ratio turning up where you least expect it. If you want to look at the game more deeply, George Bell's solitaire pages are the ne plus ultra: There's more about the solitaire army (and variants), ... [more inside]

posted by Wolfdog on Aug 15, 2014 - 6 comments

posted by Wolfdog on Aug 15, 2014 - 6 comments

Welcome to Al Zimmermann's Programming Contests. *You've entered an arena where demented computer programmers compete for glory and for some cool prizes.* The current challenge is just about to come to an end, but you can peruse the previous contests and prepare for the new one starting next month.

posted by Wolfdog on Aug 14, 2014 - 11 comments

posted by Wolfdog on Aug 14, 2014 - 11 comments

The 2014 Fields Medals have been awarded to Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani. Mirzakhani, a professor at Stanford, is the first woman to win math's highest prize, and Avila is the first South American. Erica Klarreich at Quanta Magazine has profiles of all four winners. [more inside]

posted by escabeche on Aug 12, 2014 - 35 comments

posted by escabeche on Aug 12, 2014 - 35 comments

The Minimal Superpermutation Problem - *Imagine that there is a TV series that you want to watch. The series consists of n episodes, with each episode on a single DVD. Unfortunately, however, the DVDs have become mixed up and the order of the episodes is in no way marked (and furthermore, the episodes of the TV show are not connected by any continuous storyline – there is no way to determine the order of the episodes just from watching them). Suppose that you want to watch the episodes of the TV series, consecutively, in the correct order. The question is: how many episodes must you watch in order to do this?* [more inside]

posted by Wolfdog on Aug 10, 2014 - 34 comments

posted by Wolfdog on Aug 10, 2014 - 34 comments

The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short video shows its beauty [alternating English and German audio]. PDFs with pictures.
"The Crochet Coral Reef is a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. [more inside]

posted by travelwithcats on Aug 10, 2014 - 7 comments

posted by travelwithcats on Aug 10, 2014 - 7 comments

Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again) - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named Claude Shannon." [more inside]

posted by kliuless on Jul 11, 2014 - 12 comments

posted by kliuless on Jul 11, 2014 - 12 comments

Trio for Three Angles (1968) is one of many beautiful acclaimed visually-oriented short films with music by mathematical filmmakers Bruce and Katharine Cornwell, some animated by hand and some using early digital technology. It inspired three sequels: Similar Triangles (1975), Congruent Triangles (1976), and Journey to the Center of a Triangle (1978) (previously). [more inside]

posted by beryllium on Jul 6, 2014 - 5 comments

posted by beryllium on Jul 6, 2014 - 5 comments

Let's Talk About Science is a blog devoted to discussing the world of science and technology communication with clear, beginner-friendly language, written and compiled by nanoscientist/physicist Jessamyn Fairfield and science educator ErinDubitably. [more inside]

posted by divined by radio on Jul 3, 2014 - 4 comments

posted by divined by radio on Jul 3, 2014 - 4 comments

How To Marry The Right Girl: A Mathematical Solution

posted by paleyellowwithorange on Jun 21, 2014 - 67 comments

posted by paleyellowwithorange on Jun 21, 2014 - 67 comments

Math or Maths? A few minutes with Dr Lynne Murphy (an American linguist in England) should clear this right up. Via Numberphile.

posted by R. Mutt on Apr 30, 2014 - 116 comments

posted by R. Mutt on Apr 30, 2014 - 116 comments

Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)

posted by kliuless on Apr 12, 2014 - 24 comments

posted by kliuless on Apr 12, 2014 - 24 comments

Did you know there's a direct correlation between the decline in Spirograph popularity and the rise in gang activity? Reverse this deplorable trend by playing around with the Guilloché spiral pattern generator! [more inside]

posted by Iridic on Mar 28, 2014 - 34 comments

posted by Iridic on Mar 28, 2014 - 34 comments

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)

posted by kliuless on Mar 9, 2014 - 15 comments

posted by kliuless on Mar 9, 2014 - 15 comments

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of *understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)

posted by kliuless on Mar 2, 2014 - 17 comments

posted by kliuless on Mar 2, 2014 - 17 comments

Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, has collected them all in one place. [more inside]

posted by escabeche on Feb 26, 2014 - 33 comments

posted by escabeche on Feb 26, 2014 - 33 comments

A/B testing has become a familiar term for most people running web sites, especially e-commerce sites. Unfortunately, most A/B test results are illusory (PDF, 312 kB). Here's how not to run an A/B test. Do use this sample size calculator or this weird trick.

posted by Foci for Analysis on Feb 23, 2014 - 38 comments

posted by Foci for Analysis on Feb 23, 2014 - 38 comments

The emotional experience of mathematical elegance. A new study by the perceptual neurobiologist Semir Zeki and the great mathematician (& Fields Medalist) Sir Michael Atiyah examines fMRI scans of mathematicians viewing formulae which they'd previously rated as beautiful or ugly, and reports that mathematical beauty elicits activity in the same brain regions as great art or music.

posted by Westringia F. on Feb 21, 2014 - 36 comments

posted by Westringia F. on Feb 21, 2014 - 36 comments

Random necktie knot generator [more inside]

posted by prize bull octorok on Feb 19, 2014 - 33 comments

posted by prize bull octorok on Feb 19, 2014 - 33 comments

Open warfare erupts in the world of mathematical biology, as Lior Pachter of UC-Berkeley writes three blog posts attacking two papers in Nature Bioscience, accusing one of them of being "dishonest and fraudulent": The Network Nonsense of Albert-Laszlo Barabasi, The Network Nonsense of Manolo Kellis, and Why I Read the Network Nonsense Papers. Kellis (MIT) and his co-authors respond (.pdf.)

posted by escabeche on Feb 12, 2014 - 53 comments

posted by escabeche on Feb 12, 2014 - 53 comments

While the concept of shunya or "zero", both as place holder in the decimal system and as "null" or "nothingness" has been historically attributed to the Indian mathematician/astronomer Aryabhata, it was when I went to search for its history and impact that whole new world was revealed. From culture and art to spiritual practice, the concept of zero has captured the imagination of many throughout the ages. Books have been written, its origins debated while the etymology of the word itself sometimes replaces understanding. From a disconcerting concept of nothingness to the ubiquitous misspelling of the one followed by a hundred zeros, Shunya today is more than just the gaping void it originally represented.

posted by infini on Feb 7, 2014 - 55 comments

posted by infini on Feb 7, 2014 - 55 comments

The pressure of a human bite is about 1/9th of the atmospheric pressure on Venus. The fastest bacterium on earth is just outstripping the fastest glacier. A square meter of sunshine in the spring imparts about 1 horsepower. [more inside]

posted by kagredon on Dec 7, 2013 - 20 comments

posted by kagredon on Dec 7, 2013 - 20 comments

Headlines from a Mathematically Literate World [more inside]

posted by Blasdelb on Dec 4, 2013 - 32 comments

posted by Blasdelb on Dec 4, 2013 - 32 comments

Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]

posted by kliuless on Dec 1, 2013 - 16 comments

posted by kliuless on Dec 1, 2013 - 16 comments

posted by Iridic on Nov 19, 2013 - 43 comments

...to leave a smile on your face, by Helder Guimarães: Individual vs Crowd | Chaos | Freedom | Trick [more inside]

posted by Blazecock Pileon on Nov 8, 2013 - 12 comments

posted by Blazecock Pileon on Nov 8, 2013 - 12 comments

The Washington Post reports on a ridiculous mathematics test for first graders administered under New York's Common Core standards initiative. [Common Core previously.]

posted by Westringia F. on Nov 1, 2013 - 197 comments

posted by Westringia F. on Nov 1, 2013 - 197 comments

GaMuSo is an application of BioGraph-based data mining to music, which helps you get recommendations for other musicians. Based on 140K user-defined tags from last.fm that are collected for over 400K artists, results are sorted by the "nearest" or most probable matches for your artist of interest (algorithm described here). [more inside]

posted by Blazecock Pileon on Oct 2, 2013 - 17 comments

posted by Blazecock Pileon on Oct 2, 2013 - 17 comments

Unleashing Genetic Algorithms on the iOS 7 Icon - In the pursuit of something just a bit tighter than Marc Edwards' superellipse approximation, Mike Swanson applies genetic algorithms to the task of making a better button-making script.

posted by Blazecock Pileon on Sep 26, 2013 - 19 comments

posted by Blazecock Pileon on Sep 26, 2013 - 19 comments

Paper Matrix is a blog that gives instructions for cool papercraft objects, "reinterpreting the Danish tradition of woven paper hearts and ornaments." Cut paper in the prescribed ways and weave it together carefully to make a mobile of colorful hot air balloons, gorgeous and complex boxes; simple but satisfying pennants and much more... including a full theater for performances by paper dolls.

posted by LobsterMitten on Sep 23, 2013 - 18 comments

posted by LobsterMitten on Sep 23, 2013 - 18 comments

Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe.
The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions.
**More:** The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)

posted by Rhaomi on Sep 18, 2013 - 128 comments

posted by Rhaomi on Sep 18, 2013 - 128 comments

The Movie Math Quiz: Can you figure out which movies are being described by these mathematical equations?

posted by schmod on Sep 10, 2013 - 13 comments

posted by schmod on Sep 10, 2013 - 13 comments

Wonkblog has a new advice column called "Dear Dylan" where Dylan Matthews answers the usual advice column staples using game theory, mathematics and charts.

posted by reenum on Aug 25, 2013 - 30 comments

posted by reenum on Aug 25, 2013 - 30 comments

Making Music with a Möbius Strip : "It turns out that musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip."

posted by dhruva on Aug 15, 2013 - 16 comments

posted by dhruva on Aug 15, 2013 - 16 comments

tholman.com is the playground and folio of interactive developer Tim Holman, where he has posted 15 different projects, both interactive (fizzy cam [info/demo]; ZenPen; Texter; and Image Nodes) and passive (Meet the Ipsums, more than 30 text generators, from corporate to batman; the useless web; dripping paint). [more inside]

posted by filthy light thief on Aug 7, 2013 - 8 comments

posted by filthy light thief on Aug 7, 2013 - 8 comments

The regular polygons have been kidnapped by ninjas. Are you a bad enough dude/tte to construct the regular polygons with nothing but a virtual compass and straightedge? [more inside]

posted by Iridic on Jul 3, 2013 - 67 comments

posted by Iridic on Jul 3, 2013 - 67 comments

This Simple Math Puzzle Will Melt Your Brain

"Adding and subtracting ones sounds simple, right? Not according to the old Italian mathematician Grandi—who showed that a simple addition of 1s and -1s can give three different answers."

posted by andoatnp on Jul 2, 2013 - 61 comments

"Adding and subtracting ones sounds simple, right? Not according to the old Italian mathematician Grandi—who showed that a simple addition of 1s and -1s can give three different answers."

posted by andoatnp on Jul 2, 2013 - 61 comments

You Are Not So Smart: Survivorship Bias, demonstrated through Abraham Wald's work at the Statistical Research Group in World War 2. [more inside]

posted by the man of twists and turns on Jun 6, 2013 - 48 comments

posted by the man of twists and turns on Jun 6, 2013 - 48 comments

In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (previously on Metafilter). Almost a year later, no one else knows whether he has succeeded. No one can understand his proof.

posted by painquale on May 10, 2013 - 59 comments

posted by painquale on May 10, 2013 - 59 comments

Mathematician Kenneth Appel has died at the age of 80. He is best known for having proved, with Wolfgang Haken, the four-color theorem, which states that only four colors are needed to have a map in which no two adjacent countries have the same color. [more inside]

posted by Cash4Lead on Apr 29, 2013 - 21 comments

posted by Cash4Lead on Apr 29, 2013 - 21 comments

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear, three linked gears in space that can rotate together. A short writeup of the topology and geometry behind the triple gear on the arXiv.

posted by escabeche on Apr 26, 2013 - 36 comments

posted by escabeche on Apr 26, 2013 - 36 comments

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]

posted by kliuless on Mar 16, 2013 - 25 comments

posted by kliuless on Mar 16, 2013 - 25 comments