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Privilege and oppression explained through math - specifically, matrices and Venn diagrams.

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]

If you live in the Boston area and would like to attend science, technology, math, or engineering lectures, you'll find Fred Hapgood's exhaustive and continually-updated list of Selected Lectures on Science and Engineering in the Boston Area very useful. (Here's his list of sources.) Perhaps you know of a list like this for lectures in your locality or field of preference?

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]

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]

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.

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]

The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]

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]

"An unusual article recently appeared in the magazine of the Royal Statistical Society and American Statistical Association.
It featured web-like diagrams of lines connecting nodes, a hallmark of research that analyzes networks. But each node, rather than being a plain dot, was the head of a burly, red-bearded Viking sporting a horned hat, his tresses blowing in the wind." [more inside]

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]

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]

Visualizing Algorithms shows you how computer algorithms can be represented visually, leading to better understanding of how the algorithms work:

"Have you ever implemented an algorithm based on formal description? It can be hard! Being able to see what your code is doing can boost productivity. Visualization does not supplant the need for tests, but tests are useful primarily for detecting failure and not explaining it. Visualization can also discover unexpected behavior in your implementation, even when the output looks correct."

"Have you ever implemented an algorithm based on formal description? It can be hard! Being able to see what your code is doing can boost productivity. Visualization does not supplant the need for tests, but tests are useful primarily for detecting failure and not explaining it. Visualization can also discover unexpected behavior in your implementation, even when the output looks correct."

Scott Aaronson on building a 'PageRank' for (eigen)morality and (eigen)trust - "Now, would those with axes to grind try to subvert such a system the instant it went online? Certainly. For example, I assume that millions of people would rate Conservapedia as a more trustworthy source than Wikipedia—and would rate other people who had done so as, themselves, trustworthy sources, while rating as untrustworthy anyone who called Conservapedia untrustworthy. So there would arise a parallel world of trust and consensus and 'expertise', mutually-reinforcing yet nearly disjoint from the world of the real. But here's the thing: *anyone would be able to see, with the click of a mouse, the extent to which this parallel world had diverged from the real one*." [more inside]

The Altgeld Math Models. Below you will find around 170 of the models that were photographed in March 2005 when the third floor model cases had to be emptied and moved. The models were carefully moved into the undergraduate lounge and arranged in a miniature "model museum" for two weeks, where each was carefully photographed and is now available for your enjoyment below. [more inside]

Who or what broke my kids? "The basic premise of the activity is that students must sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability. I thought it would be an interactive way to gauge student understanding. Instead it turned into a ten minute nightmare where I was asked no less than 52 times if their answers were “right”. I took it well until I was asked for the 53rd time and then I lost it. We stopped class right there and proceeded to have a ten minute discussion on who broke them."

I was surprised to learn that few people knew that almost all maths was written rhetorically before the 16th century, often in metered poetry. Even our wonderful symbol for equality – you know, those two parallel lines – was not used in print before 1575.

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

“I wanted to use the intermediate value theorem but it just wasn’t happening.” MIT undergrad Zach Wener-Fligner reports from this year's William Lowell Putnam Mathematical Competition, the nation's premier math contest for college students, a test so hard that the median score is often zero.

Can you ever be reasonably sure that something is random, in the same sense you can be reasonably sure something is not random (for example, because it consists of endless nines)? Even if a sequence looked random, how could you ever rule out the possibility that it had a hidden deterministic pattern? And what exactly do we mean by “random,” anyway?

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 ;)

Based on the Wheat and Chessboard problem, the Chess Board Clock is "a binary clock counting down 2 to the 63rd power in hundredths of a second". The first few squares go by super fast (a non-seizure mode is available) while the last square won't be reached for over 2 billion years. [via mefi projects]

Arthur C. Clarke, Benoit Mandelbrot, Stephen Hawking, David Gilmour and many more trip the fuck out about Fractals, the Colors of Infinity.

Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.

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)

The Teaching of Arithmetic: The Story of an experiment. *In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade. I asked the teachers if they would be willing to try the experiment.*

Discovering Free Will (Part II, Part III) - a nice discussion of the Conway-Kochen "Free Will Theorem". [more inside]

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 ;)

You Should Always Get the Bigger Pizza (SL NPR blog post w/interactive graph)

Astroblast and Overstepping Artifacts are music videos by the project Musicians with Guns, which take the viewer through detailed tours of some beauty. Relax and enjoy.

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]

Reaction-diffusion reactions used to design housewares, puzzles, and more. If you want to experiment yourself, you might get some ideas from the demos at WebGL Playground or you might use this brief intro as a jumping-off point.

Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]

Visual Patterns. Here are the first few steps. What's the equation?

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.)

The Hierarchy of Hexagons. *School geometry seems to me one of the most lifeless topics in all of mathematics.
And the worst of all? The hierarchy of quadrilaterals.*

How a Math Genius Hacked OkCupid to Find True Love

“I think that what I did is just a slightly more algorithmic, large-scale, and machine-learning-based version of what everyone does on the site,” McKinlay says. Everyone tries to create an optimal profile—he just had the data to engineer one.[more inside]

M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe.

1 + 2 + 3 + 4 + 5 ... = -1/12 -- Numberphile explains a counter-intuitive summation of an infinite series. [more inside]

"The IPython Notebook is a web-based interactive computational environment where you can combine code execution, text, mathematics, plots and rich media into a single document". It can be installed faily easily with anaconda or on Amazon EC2.
Various interesting notebooks are to be found at the official Notebook Viewer site
Another collection of interesting notebooks on many topics. [more inside]

It's a bit late for the holiday, but math(s) comedian Helen Arney sings about her Christmas wish -- the largest known Mersenne Prime, Mersenne 48. [more inside]

According to statistician Aki Vehtari of Aalto University in Finland, there is diminished 20% chance that today, December 25th, is your birthday. There is a 5% higher likelihood than chance that your birthday is actually February 14th. [more inside]

Charan Langton (blog) hosts Complex To Real: which "...offers tutorials I have written on various topics in analog and digital communications that will help you cut through this complexity." [more inside]

531 of the most interesting articles on Wikipedia covering everything from the linguistic (self-contradicting words in English) to the philosophical (The Ultimate 747 Gambit); from the only German military landing in the Americas (Weather Station Kurt) to the world's only Bigfoot Trap; to oddities both geometric (Gömböc ) and mathematical (Tupper's self-referential formula); great lists of various things (Bible errata, unsolved problems, camouflage patterns, blurred spots on Google Maps, lost art, the last monarchs of the Americas) to things that will make great band names (Orbiting Frog Otolith). [prev, shorter lists]