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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

posted by motty on Jun 27, 2013 - 42 comments

Is there any point to the 12 times table? [more inside]

posted by Cat Pie Hurts on Jun 27, 2013 - 159 comments

posted by Cat Pie Hurts on Jun 27, 2013 - 159 comments

How To Use Math To Crush Your Friends At Monopoly Like You've Never Done Before

posted by Renoroc on Jun 21, 2013 - 82 comments

posted by Renoroc on Jun 21, 2013 - 82 comments

Avogadro Project - The International Avogadro project relates the kilogram to the mass of a fixed number of atoms by measuring the number of atoms in a sphere of silicon.
I'll leave this here.

posted by hypersloth on Jun 8, 2013 - 26 comments

posted by hypersloth on Jun 8, 2013 - 26 comments

The series of Project Mathematics tapes regularly brought the house down at the annual SIGGRAPH video show; these mathematical animations were glowing jewels among the over-produced, techy-commercial animations usually shown at SIGGRAPH. -- Edward Tufte via edwardtufte.comI wonder where these jewels might be found ... [more inside]

posted by tarpin on May 23, 2013 - 8 comments

This afternoon, Yitang Zhang of the University of New Hampshire gave a special seminar at Harvard, in which he announced that he had proved that there are infinitely many pairs of prime numbers separated by no more than 70,000,000, a result differing only by a constant factor from the venerable twin prime conjecture. Dan Goldston, who together with Yildirim and Pintz made the last major advance on prime gaps, said, ""I was doubtful I would ever live to see this result." Not enough excitement for one day? Harald Helfgott has just posted to the arXiv a proof of the ternary Goldbach conjecture: every odd number is the sum of three primes.

posted by escabeche on May 13, 2013 - 54 comments

posted by escabeche on May 13, 2013 - 54 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

Division of labor in child care: A game-theoretic approach The analysis shows that it is difficult to achieve the equilibrium of equal sharing of child care, even when this is the preference of the parents. This leads to a discussion of alterations and meta-strategies for couples who want to share care equally. Gender differences between parents are also modeled, including the impact these have on outcomes and equilibria.Full text PDF

posted by bq on May 6, 2013 - 14 comments

posted by bq on May 6, 2013 - 14 comments

"One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis."

posted by cthuljew on May 5, 2013 - 31 comments

Every Noise At Once. A map of musical genres, built by Glenn McDonald of The War Against Silence and the Echo Nest. Click on a genre name to hear a sound sample, or pop it open to see a map of bands within that genre.

posted by escabeche on Apr 30, 2013 - 51 comments

posted by escabeche on Apr 30, 2013 - 51 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

"Each prime number is represented by a bright, white square, whereas a non-prime ("composite") is grey. Visitors can select difference spatial arrangements of these numbers, ranging from several variants of the well-known Ulam Spiral, over the Archimedian spiral, to the more sophisticated 3D Hilbert curves." [more inside]

posted by jquinby on Apr 22, 2013 - 28 comments

posted by jquinby on Apr 22, 2013 - 28 comments

Do you need to know math to do science? Harvard professor emeritus E. O. Wilson says, "no." Jeremy Fox, an Associate Professor of Population Ecology at the University of Calgary disagrees.

posted by Obscure Reference on Apr 8, 2013 - 74 comments

posted by Obscure Reference on Apr 8, 2013 - 74 comments

The Circle Drawing Experiment. You've seen competitive circle drawing (previously). Now try your own hand (mouse?) at drawing a freehand circle. Bonus: cats.

posted by Wulfhere on Mar 27, 2013 - 57 comments

posted by Wulfhere on Mar 27, 2013 - 57 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

Three professors at Harvey Mudd College wanted to do something special to mark the final lecture of Math 40: Linear Algebra that their students could relate to. The result: they transformed themselves into The Three Directions and performed "That Makes It Invertible!" for their class, complete with choreography and bad math puns. (SLYT)

posted by zachlipton on Mar 14, 2013 - 27 comments

posted by zachlipton on Mar 14, 2013 - 27 comments

The facebook question that has everyone stirred up... I got 9. I am a fifty-one year old white guy. Did new math f-ck me up? [more inside]

posted by shockingbluamp on Mar 13, 2013 - 237 comments

posted by shockingbluamp on Mar 13, 2013 - 237 comments

Ahead of Pi Day (March 14), Matt Parker tries to accurately calculate pi using pies. [SLYT] An extended version of the video will be uploaded on Pi Day, but here's your chance to go out and buy pies before that.
(Video runs 3 minutes, 14 seconds.)

posted by Room 641-A on Mar 13, 2013 - 14 comments

posted by Room 641-A on Mar 13, 2013 - 14 comments

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."

posted by spbmp on Mar 12, 2013 - 30 comments

posted by spbmp on Mar 12, 2013 - 30 comments

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]

posted by zarq on Mar 8, 2013 - 40 comments

posted by zarq on Mar 8, 2013 - 40 comments

Trippy animated GIFs generated by Mathematica code. via

posted by OmieWise on Feb 28, 2013 - 20 comments

posted by OmieWise on Feb 28, 2013 - 20 comments

Surely you've heard of the physicist Maxwell, but what about Oliver Heaviside? Oliver Heaviside: A first-rate oddity.

posted by Evernix on Feb 14, 2013 - 14 comments

posted by Evernix on Feb 14, 2013 - 14 comments

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

posted by ocherdraco on Feb 8, 2013 - 5 comments

posted by ocherdraco on Feb 8, 2013 - 5 comments

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]

posted by jeffburdges on Jan 19, 2013 - 11 comments

posted by jeffburdges on Jan 19, 2013 - 11 comments

"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]

posted by bluefly on Jan 16, 2013 - 12 comments

posted by bluefly on Jan 16, 2013 - 12 comments

New research can detect five different emotions with 81 percent accuracy. [Additional project information].

posted by Evernix on Jan 8, 2013 - 21 comments

posted by Evernix on Jan 8, 2013 - 21 comments

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)

posted by BitterOldPunk on Dec 29, 2012 - 20 comments

posted by BitterOldPunk on Dec 29, 2012 - 20 comments

What do you get if you slice a Menger Sponge on a diagonal plane?

Watch this video to find out.

posted by thatwhichfalls on Dec 26, 2012 - 44 comments

Watch this video to find out.

posted by thatwhichfalls on Dec 26, 2012 - 44 comments

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.)

posted by escabeche on Dec 13, 2012 - 24 comments

posted by escabeche on Dec 13, 2012 - 24 comments

He is not the only one. Computer rankings are proliferating, said Kenneth Massey, a professor of math at Carson-Newman in Jefferson City, Tenn., who has been ranking teams since 1995. “When I started, there were six or seven,” he said. “But every year, it gets bigger and bigger.” Massey currently tracks more than 100 college football rankings.

With so many competitors, what is the appeal of creating one’s own rankings?

“It’s kind of a nerdy hobby,” Massey said. “It combines sports with math and computers, three things that don’t ordinarily go together.” [more inside]

posted by DynamiteToast on Dec 7, 2012 - 20 comments

With so many competitors, what is the appeal of creating one’s own rankings?

“It’s kind of a nerdy hobby,” Massey said. “It combines sports with math and computers, three things that don’t ordinarily go together.” [more inside]

posted by DynamiteToast on Dec 7, 2012 - 20 comments

"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]

posted by ocherdraco on Dec 3, 2012 - 65 comments

posted by ocherdraco on Dec 3, 2012 - 65 comments

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]

posted by kliuless on Dec 1, 2012 - 19 comments

posted by kliuless on Dec 1, 2012 - 19 comments

Mathgen is a program to randomly generate professional-looking mathematics papers, including theorems, proofs, equations, discussion, and references. Try Mathgen for yourself! (PDF example) It’s a fork of SCIgen, a program which generates random papers in computer science. Surprisingly, Mathgen has already had it's first randomly-generated paper accepted by a "journal".

posted by DynamiteToast on Nov 20, 2012 - 51 comments

posted by DynamiteToast on Nov 20, 2012 - 51 comments

It's Saturday; why not think about the pigeonhole principle? Here are problems and more problems and what you might call a problem with the principle itself as it is often stated.

posted by Wolfdog on Nov 10, 2012 - 41 comments

posted by Wolfdog on Nov 10, 2012 - 41 comments

For years now, the primary way of representing and storing color on a computer display has been to define it as existing in three dimensions: Red, Green, and Blue. What if that's wrong? “While the appearance of a color on a screen can be described in three dimensions, the blending of color actually is happening in a six dimensional space,” How Fifty-Three, developers of the iPad painting app Paper, used a theory of paint optics from 1931 to develop a better color mixer.

posted by gauche on Nov 9, 2012 - 28 comments

posted by gauche on Nov 9, 2012 - 28 comments

The Fifth Problem: "If this were a boxing match, with one of the boxers pressed in the corner, bloodied, desperately trying to hold his own against the barrage of punches falling on him (many of them below the belt, I might add), that would be the equivalent of the final, deadly, blow. The problem looked innocent enough at first glance: given a circle and two points on the plane outside the circle, construct another circle passing trough those two points and touching the first circle at one point." Edward Frenkel, now Professor of Mathematics at the University of California, Berkeley, details the curiously baroque way Moscow State University chose to discriminate against talented Jewish math students: By quizzing them with fiendishly difficult math problems with deceptively simple solutions that are nearly impossible to find. [more inside]

posted by flug on Nov 5, 2012 - 41 comments

posted by flug on Nov 5, 2012 - 41 comments

Animation of prime factorization of the integers based on Brent Yorgey's factorization diagrams, described here. [via Data Pointed, previously.]

posted by albrecht on Nov 1, 2012 - 35 comments

posted by albrecht on Nov 1, 2012 - 35 comments

posted by Rhaomi on Oct 27, 2012 - 14 comments

Q: How many miles is it to the crab nebula? How does one even figure this out?
A: The cosmic distance ladder! Here's a talk by Fields medalist Terrence Tao on methods for indirect calculation of distances to astronomical objects. Here's Tao's blog post on the subject, including the slides for the talk. And here's a Wikipedia page. [more inside]

posted by kaibutsu on Oct 22, 2012 - 17 comments

posted by kaibutsu on Oct 22, 2012 - 17 comments

"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]

posted by escabeche on Oct 18, 2012 - 119 comments

posted by escabeche on Oct 18, 2012 - 119 comments

SmoothLife is a continuous version of John Conway's Game of Life. When you tire of watching the hypnotic video you can read a technical description of SmoothLife on the arXiv. Then you can watch more videos of SmoothLife.

posted by escabeche on Oct 10, 2012 - 30 comments

posted by escabeche on Oct 10, 2012 - 30 comments

Eigenfaces for facial recognition. (*This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces.*)

posted by Evernix on Oct 6, 2012 - 18 comments

posted by Evernix on Oct 6, 2012 - 18 comments

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."

posted by escabeche on Sep 18, 2012 - 61 comments

posted by escabeche on Sep 18, 2012 - 61 comments

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.

posted by escabeche on Sep 12, 2012 - 5 comments

posted by escabeche on Sep 12, 2012 - 5 comments