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366 posts tagged with Mathematics.

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## binding the andat

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]

## ASCII fluid simulator

## Whoomp

*Slate's*Ben Blatt "sat in a Barnes & Noble for three hours flipping through all seven

*Where’s Waldo*books with a tape measure" and emerged with a method for finding Waldo with speed more than 50% of the time. [more inside]

## Card tricks...

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

## A number sentence for 5 cookies and 6 cups of whole milk?

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

## The sound of graph paper

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]

## Evolved design

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.

## Papercraft project blog Paper Matrix

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.

## My God, it's full of... everything

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)## A sine of the times

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

## Dear Dylan

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

## "Topics galore."

## music meets möbius

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."

## 15 ways to waste your day online with Tim Holman

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]

## Assume A Cylindrical Cow

## Ancient Greek Geometry: The Game

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]

## If that sounds like it makes no sense that's because... well, it doesn't

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."

"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."

## The Department Of War Math

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

## Proof and Community Standards

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.

## Kenneth I. Appel (1932-2013)

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]

## Triple Gear

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.

## Computerized Math, Formal Proofs and Alternative Logic

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]

## Give or take

The origins of plus and minus signs - "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse."

## Aspiring Animators & Game Designers, Study Your Calculus & Combinatorics

Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]

## Will Redshirts by (Mefi's Own) John Scalzi have to be rewritten?

Bayesian analysis shows redshirts are not most likely to die on Star Trek:TOS.

*Although Enterprise crew members in redshirts suffer many more casualties than crew members in other uniforms, they suffer fewer casualties than crew members in gold uniforms when the entire population size is considered. Only 10% of the entire redshirt population was lost during the three year run of Star Trek. This is less than the 13.4% of goldshirts, but more than the 5.1% of blueshirts. What is truly hazardous is not wearing a redshirt, but being a member of the security department. The red-shirted members of security were only 20.9% of the entire crew, but there is a 61.9% chance that the next casualty is in a redshirt and 64.5% chance this red-shirted victim is a member of the security department. The remaining redshirts, operations and engineering make up the largest single population, but only have an 8.6% chance of being a casualty.*## OMG SCIENCE!

Henry Reich of Minute Physics shares his favorite science blogs, video channels, and other resources on the web. (Minute Physics previously) [more inside]

## the power and beauty of mathematics

## Episciences Project

Tim Gowers has announced a series of arXiv overlay journals called the Episciences Project that aim to exclude existing publishers from research publication in mathematics. As arXiv overlays, the Episciences Project avoids the editing and typesetting costs that existing open-access journals pay for using article processing charges. The French Centre pour la Communication Scientifique Directe (CCSD) is backing the remaining expenses, such as developing the platform. [more inside]

## Love in the Time of Neuroinformatics

"The models we discuss belong to the class of two-variable systems with one delay for which appropriate delay stabilizes an unstable steady state. We formulate a theorem and prove that stabilization takes place in our case. We conclude that considerable (meaning large enough, but not too large) values of time delay involved in the model can stabilize love affairs dynamics." [more inside]

## Numberphile: videos about numbers and stuff

Numberphile is a website containing short videos (approx. 5-10 min.) about numbers and stuff. Mathematicians and physicists play around with the tools of their trade and explain things in simple, clear language. Learn things you didn't know you were interested in! Find out why 493-7775 is a pretty cool phone number! What's the significance of 42, anyway? What the heck is a vampire number? Why does Pac-Man have only 255 screens?
Suitable for viewing by everyone from intelligent and curious middle-schoolers to math-impaired adults. Browse their YouTube channel here. (Via)

## The Museum of Mathematics

Last night was the grand opening of the Museum of Mathematics in New York City, the only museum of its kind in North America. The video is narrated by MoMath's chief of content, mathematical sculptor George Hart (better known in some circles as Vi Hart's dad.) The sculpture of the space of three-note chords in the video is based on the work of Dmitri Tymoczko, and the lovely curved hammock of strings a visitor is sitting in at the end is a ruled quadric surface. Many more videos at the Museum of Mathematics YouTube channel. Coverage from the New Scientist. (Previously on MetaFilter.)

## "The data that we actually used."

Rosalind.info is a website with bioinformatics problems inspired by Project Euler (previously, previouslier.) [more inside]

## Making things with Maths

## An example of "order out of chaos"

"Draw some random points on a piece of paper and join them up to make a random polygon. Find all the midpoints and connecting them up to give a new shape, and repeat. The resulting shape will get smaller and smaller, and will tend towards an ellipse!" [code to make this in Mathematica] [a version which allows you to watch the process step by step, with 10 vertices or 100]

## direct realism

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

## Potatoes and Math

Maximum gravy: Vi hart, daughter of George & mathemusician at The Khan Academy, cooks mathematical potatoes to go along with a symmetrical Turduckenen. Have a delicious Thanksgiving. [more inside]

## Skill-Luck Continuum

"We have little trouble recognizing that a chess grandmaster’s victory over a novice is skill, as well as assuming that Paul the octopus’s ability to predict World Cup games is due to chance. But what about everything else?" [Luck and Skill Untangled: The Science of Success]

## Significand of the figure

From the somewhat arbitrary and dimensionful to the timeless classic, one man's subjective list of notable properties of specific numbers. [more inside]

## There is Nothing New Under the Sun

*She sat zazen, concentrating on not concentrating, until it was time to prepare for the appointment. Sitting seemed to produce the usual serenity, put everything in perspective. Her hand did not tremble as she applied her make-up; tranquil features looked back at her from the mirror. She was mildly surprised, in fact, at just how calm she was, until she got out of the hotel elevator at the garage level and the mugger made his play. She killed him instead of disabling him. Which was obviously not a measured, balanced action--the official fuss and paperwork could make her late. Annoyed at herself, she stuffed the corpse under a shiny new Westinghouse roadable whose owner she knew to be in Luna, and continued on to her own car. This would have to be squared later, and it would cost. No help for it--she fought to regain at least the semblance of tranquillity as her car emerged from the garage and turned north. Nothing must interfere with this meeting, or with her role in it.*"Melancholy Elephants," an enthralling, Hugo Award-winning short story by Spider Robinson about a disciplined operative, a powerful senator, and a crucial mission to preserve humanity's most precious resource. (some spoilers inside) [more inside]

## Boaler and the math wars

"Milgram and Bishop are opposed to reforms of mathematics teaching and support the continuation of a model in which students learn mathematics without engaging in realistic problems or discussing mathematical methods. They are, of course, entitled to this opinion, and there has been an ongoing, spirited academic debate about mathematics learning for a number of years. But Milgram and Bishop have gone beyond the bounds of reasoned discourse in a campaign to systematically suppress empirical evidence that contradicts their stance. Academic disagreement is an inevitable consequence of academic freedom, and I welcome it. However, responsible disagreement and academic bullying are not the same thing. Milgram and Bishop have engaged in a range of tactics to discredit me and damage my work which I have now decided to make public." Jo Boaler, professor of mathematics education at Stanford, accuses two mathematicians, one her colleague of Stanford, of unethical attempts to discredit her research, which supports "active engagement" with mathematics (aka "reform math") over the more traditional "practicing procedures" approach. [more inside]

## What is the smallest prime?

What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."

## The purpose of life is to keep the SF's score low.

N Is a Number: A Portrait of Paul Erdős is a 1993 documentary directed by George Paul Csicsery about the life of mathematician Paul Erdős. Paul Erdős (26 March 1913 -- 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He is also known for his "legendarily eccentric" personality. (Previously he was mostly a number)

## Robert MacPherson interviewed

Robert MacPherson interviewed as part of the Simons Foundation's Science Lives series. MacPherson is among the founders of the modern theory of

*singularities*, points like a kink in a curve where the geometry of a space stops being smooth and starts behaving badly. In the interview, MacPherson talks about cultural differences between math and music, his frustration with high school math, growing up gay in the South and life as a gay man in the scientific community, smuggling $23,000 in cash into post-Soviet Russia to help mathematicians there keep the lights on, catastrophe theory, perverse sheaves, how to be a successful graduate student, stuttering, and of course the development of the intersection homology theory for which he is most well-known.## Mathematics world abuzz with a proof of the ABC Conjecture

Shinichi Mochizuki believes that he has found a connection between prime numbers by developing a 500 page proof of the ABC conjecture [more inside]

## Knots in Spaaaaace

The fine people over at the International Guild of Knot Tyers Forum talk knots. On Mars.

## While almost unknown to Americans, many Europeans have treasured these portraits

Cliff Stoll makes glass Klein bottles. He also sells imported portraits of Gauss.

## William Thurston

"The real satisfaction from mathematics is in learning from others and sharing with others." William Thurston, one of the greatest mathematicians of the 20th century, has died. He revolutionized topology and geometry, insisting always that geometric intuition and understanding played just as important a role in mathematical discovery as did the austere formalism championed by the school of Grothendieck. Thurston's views on the relation between mathematical understanding and formal proof are summed up in his essay "On Proof and Progress in Mathematics." [more inside]

## "Your argument has to be beautiful."

Paul Lockhart, author of the famous Mathematician's Lament, has a new book coming out called Measurement, which tries to discuss mathematics "as an artful way of thinking and living". Lockhart discusses his passion for math and motives for writing the book in this video.

## noncommutative balls in boxes

Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]