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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]
posted by kliuless on Dec 1, 2012 - 19 comments

Math Publishing for Dummies!

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

The strange case of The Pigeon-hole Principle

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

Ein Beitrag zur Optik der Farbanstriche

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

The Fifth problem: Math & Anti-Semitism in the Soviet Union

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

Factor Conga

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

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]
posted by Rhaomi on Oct 27, 2012 - 14 comments

no stairway?

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

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]
posted by escabeche on Oct 18, 2012 - 119 comments

Smoothlife

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

weee eigenvectors

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

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."
posted by escabeche on Sep 18, 2012 - 61 comments

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.
posted by escabeche on Sep 12, 2012 - 5 comments

Making Math Fun

Is your elementary school youngster struggling with math? Are they a visual person? Would math games and videos help them learn? Enter Math Playground, to assist with problem solving and real world math. Try the enticing logic game Sugar, Sugar or beef up your math word problem skills. There are plenty of games to help educate while entertaining.
posted by netbros on Sep 4, 2012 - 14 comments

I ♥ Cardioids

I ♥ Cardioids, Vi Hart's condensed awesome tackles parabolas, cardioids, circles and more. Related: Part 1 of Rolling Circles and Balls.
posted by odinsdream on Aug 31, 2012 - 24 comments

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

Cliff Stoll makes glass Klein bottles. He also sells imported portraits of Gauss.
posted by madcaptenor on Aug 29, 2012 - 26 comments

To Infinity and Somewhat Past That!

Are there as many odd numbers as there are all numbers? Can one infinity be bigger than another? TED Ed and Minute Physics both take a look at some of the mind boggling realities of Infinity.
posted by quin on Aug 28, 2012 - 148 comments

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]
posted by escabeche on Aug 22, 2012 - 32 comments

The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer’s Law

Einstein described the "Tea Leaf Paradox" (more) to explain Baer's Law of erosion. [more inside]
posted by Algebra on Aug 19, 2012 - 9 comments

bons mots, poems, math, knitting and logic

Entertaining, collected bon mots and surprisingly interesting, collected poems by various authors. From a likable math brainiac's site, Dr T.E. Forster, a Cambridge University lecturer. He also knits and writes about Buddhist logic [pdf]. Bonus, there's a fun gif.
posted by nickyskye on Aug 16, 2012 - 4 comments

Fun with kinematics!

Racetrack is a game with very simple rules which nonetheless does a surprisingly good job of simulating the acceleration, braking, and handling of a race car. It can teach not only about inertia and kinematics, but also about optimal racing lines. Racetrack can be played with nothing more than a piece of graph paper and a pen, but there is also an online implementation called Vector Racer.
posted by 256 on Aug 11, 2012 - 42 comments

"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.
posted by Rory Marinich on Jul 31, 2012 - 17 comments

Win with mathb.in!

"MathB.in is a website meant for sharing snippets of mathematical text with others on the web. This is a pastebin for mathematics… The post can be composed in a mixture of plain text, LaTeX and HTML."
posted by grouse on Jul 26, 2012 - 5 comments

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]
posted by kliuless on Jul 21, 2012 - 78 comments

Piaget Beer Gauge

The Piaget Beer Gauge - a product to clear up visual misunderstandings about height and volume in American bars.
posted by Greg Nog on Jul 19, 2012 - 193 comments

Why Johnny Can’t Add Without a Calculator

Slate: Technology is doing to math education what industrial agriculture did to food: making it efficient, monotonous, and low-quality. [more inside]
posted by beisny on Jun 30, 2012 - 70 comments

The Art of π, φ and e

The Art of π, φ and e [more inside]
posted by Blazecock Pileon on Jun 26, 2012 - 24 comments

Linear Programming Will Save Us From the Invisible Hand

As part of Crooked Timber's Seminar on Francis Spufford's work of speculative fiction "Red Plenty." Cosma Shalizi has posted "7800 words about optimal planning for a socialist economy and its intersection with computational complexity theory."
posted by JPD on May 30, 2012 - 24 comments

Big (and small) Numbers

FatFonts creates numerical fonts where the amount of ink/pixels for each number is in direct proportion to its value.
posted by fearfulsymmetry on May 14, 2012 - 23 comments

Cool Math Conundrums

In Russian roulette, is it best to go first? | The Mathematics of Tetris | What is the result of infinity minus infinity? [more inside]
posted by Foci for Analysis on May 14, 2012 - 30 comments

Sure it's irrational! Just look!

Geometrically the irrationality of the square root of 2 means that there is no integer-by-integer square whose area is twice the area of another integer-by-integer square. A visual proof that the square root of 2 is irrational (not found in previous visual proof post.)
posted by Obscure Reference on May 9, 2012 - 39 comments

My Prime Factorization Sweater

This is the sweater that proves that I am a Certified Math Nut.
posted by Foci for Analysis on Apr 29, 2012 - 54 comments

Why Netflix Never Implemented The Algorithm That Won The Netflix $1 Million Challenge

Why Netflix never implemented the algorithm that won the Netflix $1 Million Challenge.
posted by reenum on Apr 18, 2012 - 45 comments

Ice

Ice
posted by jjray on Apr 15, 2012 - 33 comments

How to quantify all aspects of society

"Samuel Arbesman is a senior scholar at the Ewing Marion Kauffman Foundation and author of the forthcoming book 'The Half-Life of Facts'. His research and essays explore how to quantify all aspects of society." [more inside]
posted by knile on Apr 10, 2012 - 4 comments

The mathematical modelling of popular games by Nick Berry

H _ _ _ m _ n, Y a _ _ _ e e, _ _ t t _ _ _ h i p, _ h u t _ s & L a _ _ e r _ , R _ _ k , _ _ n d y _ _ _ _ , and _ _ r t s.
posted by Jasper Friendly Bear on Apr 7, 2012 - 28 comments

A snack of classical mechanics

What is the Dzhanibekov effect? Known as the Tennis Racket theorem in English and documented by Vladimir Dzhanibekov in 1985 space, it is the result of unstable rotation about a principle axis.
posted by Algebra on Apr 6, 2012 - 21 comments

A Shory Biography of Emmy Noether

Amalie Noether: The Mighty Mathematician You’ve Never Heard Of
posted by jjray on Mar 27, 2012 - 49 comments

Machines vast and sinister

We've discussed subblue/Tom Beddard and Mandlebulbs before, but two months ago L'Eclaireur Sévigné asked him to create a few animations for their 147-screen exhibition. And here are the hypnotic, terrifying results.
posted by The Whelk on Mar 23, 2012 - 11 comments

Solve for Professor X

Pop Culture Math: Artist Matt Cowan breaks down pop-culture icons into basic formulas. [more inside]
posted by quin on Mar 22, 2012 - 11 comments

"As you can probably imagine, this took some effort to make."

"The calculator itself is just over 250x200x100 blocks. It contains 2 6-digit BCD number selectors, 2 BCD-to-binary decoders, 3 binary-to-BCD decoders, 6 BCD adders and subtractors, a 20 bit (output) multiplier, 10 bit divider, a memory bank and additional circuitry for the graphing function." Yes, someone built a working scientific calculator, in Minecraft.
posted by jbickers on Mar 21, 2012 - 46 comments

So that's why they call 'em fractals!

What is a fractional dimension?
posted by Obscure Reference on Mar 17, 2012 - 63 comments

WHAT TIME IS IT?!

Do you like Adventure Time? (previously) Do you like 8-Bit Game intros? Then you'll like the 8-bit Adventure Time Video Game Intro.
posted by The Whelk on Mar 3, 2012 - 34 comments

The Angel Problem

The Angel Problem. The Angel and the Devil play a game on an infinite chess board...
posted by Wolfdog on Feb 16, 2012 - 37 comments

Newton and Leibniz invent calculus.

There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.
posted by Obscure Reference on Feb 10, 2012 - 17 comments

Number A Day

NumberADay - Every working day, we post a number and offer a selection of that number’s properties.
posted by Wolfdog on Jan 11, 2012 - 30 comments

Morpion Solitaire

Morpion Solitaire is a very simple pencil-and-paper, line-drawing game for which the best possible score is not known! New records are still being set.
posted by Wolfdog on Jan 8, 2012 - 21 comments

What is it like to have an understanding of very advanced mathematics?

What is it like to have an understanding of very advanced mathematics? A naive Quora question gets a remarkably long, thorough answer from an anonymous respondent. The answer cites, among many other things, Tim Gowers's influential essay "The Two Cultures of Mathematics," about the tension between problem-solving and theory-building. Related: Terry Tao asks "Does one have to be a genius to do maths?" (Spoiler: he says no.)
posted by escabeche on Dec 24, 2011 - 56 comments

Monte Carlo

The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF). -N. Metropolis
Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).
posted by JoeXIII007 on Dec 17, 2011 - 13 comments

Two PDFs about PDFs

An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)
posted by JoeXIII007 on Dec 15, 2011 - 17 comments

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