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182 posts tagged with Math *and* mathematics.

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## 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) [more inside]

## 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) [more inside]

## The toilet seat: up or down?

"I amused myself for over a year thinking about the impacts of different toilet seat administration policies and how to measure them – doing calculations in my head, considering ratios of Standing events to Sitting events, and I slowly began to understand some of the specific differences in the basic policies that know to be administered most often. Finally, I decided to perform a probabilistic analysis". Essential Toilet Seat Analytics.

## "You blew it, and you blew it big!"

## Thanks, Common Core.

Thanks, Common Core. Physics blogger Chad Orzel writes about the way kids do math now. (Spoiler: he likes it.) [more inside]

## 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.*[more inside]## Fake 3D Until You Make 3D

Louis Gorenfeld lovingly explores the mathematics and techniques behind early, pseudo-3D games. [more inside]

## "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."## Alexander Grothendieck

Alexander Grothendieck, who brought much of contemporary mathematics into being with the force of his uncompromising vision, is dead at 86, some twenty-five years after leaving academic mathematics and retreating into a spiritual seclusion in the countryside. "As if summoned from the void," a two-part account of Grothendieck's life, from the Notices of the American Math Society: part I, part II. [more inside]

## Take that, Keanu Reeves.

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

## 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 :) [more inside]

## Middle East Peace Potential through Dynamics in Spherical Geometry

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]## It's just a jump to the ... well, in any legal direction really

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]

## do while !glory

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.## 2014 Fields Medals

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 Foehr Reef

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]

## 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." [more inside]

## musical mathematical journeys

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]

## 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.

## 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 ;)

## 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)

## 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 ;)## "What is...." from the Notices of the American Math Society

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]

## Network Nonsense

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.)

## Math with Bad Drawings

## 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]

## 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.]

## 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.

## Assume A Cylindrical Cow

## 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."

## 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.

## 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]

## 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.)

## 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]

## 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."

## 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.