## The Art of Learning

Visualizing the Riemann zeta function and analytic continuation (slyt)
posted by kliuless on Dec 10, 2016 - 10 comments

## Animated math

Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary."
posted by kliuless on Sep 11, 2016 - 17 comments

## xEuclidx

Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods.
posted by jedicus on Sep 8, 2016 - 20 comments

## Monumental Proof to Torment Mathematicians for Years to Come

Nearly four years after Shinichi Mochizuki (previously, previously, previously) unveiled an imposing set of papers (1, 2, 3, 4) that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity — although they have made modest progress.
posted by stinkfoot on Aug 5, 2016 - 46 comments

## So, the unknowable kicks in

Logic hacking - "Writing shorter and shorter computer programs for which it's unknowable whether these programs run forever, or stop... the winner of the Busy Beaver Game for N-state Turing machines becomes unknowable using ordinary math - somewhere between N = 5 and N = 1919."
posted by kliuless on Jul 30, 2016 - 17 comments

## What else have we missed about the primes?

Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them.
posted by Proofs and Refutations on Mar 14, 2016 - 37 comments

## “may someday help in a more objective assignment of books...”

Scientists find evidence of mathematical structures in classic books. [The Guardian] James Joyce’s Finnegans Wake has been described as many things, from a masterpiece to unreadable nonsense. But it is also, according to scientists at the Institute of Nuclear Physics in Poland, almost indistinguishable in its structure from a purely mathematical multifractal.
“The absolute record in terms of multifractality turned out to be Finnegans Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals,” said Professor Stanisław Drożdż, another author of the paper, which has just been published in the computer science journal Information Sciences.
posted by Fizz on Jan 28, 2016 - 28 comments

## The likelihood that there's interesting or important math is pretty high

Shinichi Mochizuki and the impenetrable proof - "Fesenko has studied Mochizuki's work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof. (The other three mathematicians who say they have corroborated it have also spent considerable time working alongside Mochizuki in Japan.) The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light — leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse." (previously: 1,2; via)
posted by kliuless on Oct 16, 2015 - 33 comments

## Learning common core math with a check written by an upset father

When the father of a second grader got annoyed by common core math tools (namely, ten frame cards), his annoyance went viral when he wrote a check to his student's school using common core numbers. Then the Friendly Athiest on Patheos used that check to teach how common core math works at the second grade level.
posted by filthy light thief on Sep 23, 2015 - 208 comments

## Famous Fluid Equations Are Incomplete

The Singular Mind of Terry Tao - "Imagine, he said, that someone awfully clever could construct a machine out of pure water. It would be built not of rods and gears but from a pattern of interacting currents." (via)
posted by kliuless on Jul 29, 2015 - 17 comments

## Loop - Pool on an elliptical table

Loop - Pool on an elliptical table. The ellipse has two significant points, called focuses, which have a remarkable geometrical property that is almost always explained using the example of an imaginary pool table. "If a pool table is the shape of an ellipse, then a ball shot from one focus will always rebound to the other focus no matter in which direction the ball is shot." That sounded interesting! Wouldn’t it be fun, I thought, if I could build one of these imaginary tables? So I did.
posted by dng on Jul 26, 2015 - 22 comments

## HoTT Coq

Univalent Foundations Redefines Mathematics - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics." (previously)
posted by kliuless on Jun 9, 2015 - 13 comments

## 3Blue1Brown: Reminding the world that math makes sense

Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously)
posted by kliuless on Jun 6, 2015 - 28 comments

## Arithmeticfilter

Nothing but an endless supply of mental arithmetic problems. Five levels of difficulty, from "10 - 6" to "√370881."
posted by Iridic on Jan 26, 2015 - 20 comments

## No Pentagons

Imperfect Congruence - It is a curious fact that no edge-to-edge regular polygon tiling of the plane can include a pentagon ... This website explains the basic mathematics of a particular class of tilings of the plane, those involving regular polygons such as triangles or hexagons. As will be shown, certain combinations of regular polygons cannot be extended to a full tiling of the plane without involving additional shapes, such as rhombs. The site contains some commentary on Renaissance research on this subject carried out by two renowned figures, the mathematician-astronomer Johannes Kepler and the artist Albrecht Dürer.
posted by Wolfdog on Jan 14, 2015 - 16 comments

## How we came to know the first dwarf planet

So if you had been reading about all this 200 years ago, there would have been at least two important differences from now. One is that your Internet connection would have been considerably slower. The other is that you might have learned in school or elsewhere that Ceres was a planet.
As the Dawn probe is only months away from reaching Ceres, chief engineer and mission director Marc Rayman provides a brief history of the discovery and study of Ceres. Bonus: The maths behind the discovery of Ceres
posted by MartinWisse on Dec 31, 2014 - 15 comments

## "Science is when you think a lot."

Two enjoyable chapters [PDF, 33 pages] from the book Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers. "This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children."
posted by Wolfdog on Dec 29, 2014 - 11 comments

How do we determine distances between the earth, sun, and moon, and from the sun to other planets, stars, and distant galaxies? We can't measure these directly, but indirect methods, combined with some basic high school math, can provide convincing and accurate results. A public lecture by Fields medalist Terry Tao (SLYT)
posted by Another Fine Product From The Nonsense Factory on Nov 4, 2014 - 26 comments

## √2N

At the Far Ends of a New Universal Law
The law appeared in full form two decades later, when the mathematicians Craig Tracy and Harold Widom proved that the critical point in the kind of model May used was the peak of a statistical distribution. Then, in 1999, Jinho Baik, Percy Deift and Kurt Johansson discovered that the same statistical distribution also describes variations in sequences of shuffled integers — a completely unrelated mathematical abstraction. Soon the distribution appeared in models of the wriggling perimeter of a bacterial colony and other kinds of random growth. Before long, it was showing up all over physics and mathematics. “The big question was why,” said Satya Majumdar, a statistical physicist at the University of Paris-Sud. “Why does it pop up everywhere?”
posted by the man of twists and turns on Oct 28, 2014 - 17 comments

## Take that, Keanu Reeves.

Privilege and oppression explained through math - specifically, matrices and Venn diagrams.
posted by divabat on Oct 1, 2014 - 89 comments

## Poor man's bitcoin mining

So you wanna join this bitcoin thing but can't afford the processing cycles to actually mine stuff? Now you can earn bitcoins using pencil and paper!
posted by Foci for Analysis on Sep 29, 2014 - 25 comments

## Calculus without limits

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 :)
posted by kliuless on Sep 17, 2014 - 34 comments

## Datagenetics

DataGenetics is "a technology consultancy specializing in unlocking the value stored in large databases" and which runs an interesting blog.
posted by alby on Jul 28, 2014 - 2 comments

## 21st Century Wiener

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."
posted by kliuless on Jul 11, 2014 - 12 comments

## Math or Maths?

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

## A SAT Attack on the Erdos Discrepancy Conjecture

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

## Visually stunning math concepts...

...which are easy to explain.
posted by Foci for Analysis on Apr 7, 2014 - 27 comments

## there is no soundtrack

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

## John Baez on the maths of connecting everyone (and everything) on earth

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

## The dangers of A/B testing

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

## Wondering What to Get with That Gift Card?

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.
posted by GenjiandProust on Dec 28, 2013 - 1 comment

## 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."
posted by kliuless on Dec 1, 2013 - 16 comments

## Twelve Tones

"It's just one of those days where you wake up thinking that if you jazzed up Stravinsky's Owl And The Pussycat it'd be awesome..." [SLYT]
posted by motty on Jun 27, 2013 - 42 comments

## Is there any point to the 12 times table?

Is there any point to the 12 times table?
posted by Cat Pie Hurts on Jun 27, 2013 - 159 comments

## This looks legit

Eric Weinstein has a PhD in mathematical physics from Harvard, but has spent most of the last 10 years outside academia working as an economic consultant for a New York hedge fund. Now he apparently has a new theory of everything that claims to be able to explain quantum gravity, dark matter and dark energy. Actual details have not yet been provided and some physicists are dismissive. But his work has received enthusiastic endorsement from Oxford's Simonyi Professor of Public Understanding Marcus du Sautoy, with whom he has been discussing the theory over the last two years.
posted by leibniz on May 24, 2013 - 105 comments

## 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.
posted by painquale on May 10, 2013 - 59 comments

## England's pleasant pastures recreated

The British countryside generator uses Voronoi diagrams to recreate the patchwork quilt look of your stereotypical UK landscape of rolling meadows, woodlands and crop fields, enclosed by hedgerows and drystone walls.
posted by MartinWisse on May 1, 2013 - 21 comments

## 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."
posted by kliuless on Mar 16, 2013 - 25 comments

## the power and beauty of mathematics

An eternity of infinities (via)
posted by kliuless on Feb 2, 2013 - 23 comments

## 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]
posted by ocherdraco on Dec 3, 2012 - 65 comments

## 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)
posted by kliuless on Dec 1, 2012 - 19 comments

## 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]
posted by vidur on Nov 20, 2012 - 16 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..."
posted by kliuless on Jul 21, 2012 - 78 comments

## When the carrot is too distant, and there is no stick

Beeminder provides an interesting and novel solution to the problem of akrasia. Got a long term goal or habit you'd like to change or develop (like losing weight or writing every day), then set out your targets, record your progress every day and pay cold hard cash the day you fall off the 'yellow brick road'.
posted by grahamspankee on Jul 19, 2012 - 38 comments

## The Art of π, φ and e

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

## Because Print Is Not Yet Dead

Free online graph paper generators: variations of squares, triangle, rhombus, and hexagonal, circular and polar, for drawing, gaming, writing, note-taking and much more. Blank Sheet Music (Flash) for all arrangements (PDF). Create and edit your own grids, probability and logarithmic graphs, petri-dish inserts and storyboards. Also, multilingual  monthly and yearly calendars. Plus, more than you ever wanted to know about ISO paper dimensions and printable paper models of polyhedra. Prev-ious-ly.
posted by Bora Horza Gobuchul on May 28, 2012 - 36 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?
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 best known work is in game theory

"I hope my handwriting, etc. do not give the impression I am just a crank or circle-squarer."
posted by vidur on Feb 22, 2012 - 22 comments

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