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364 posts tagged with 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.

## It's true because pictures

## In mathematics, you don’t understand things. You just get used to them.

Calculating the Speed of Light Using a Microwave and PEEPS (or other melty things) from National Geographic's Education Blog and NPR's Skunk Bear videos (showing some history of calculating the speed of light... with peeps as historical scientists, of course)

## The golden ratio has spawned a beautiful new curve: the Harriss spiral

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

## The Man Who Tried to Redeem the World with Logic

Walter Pitts rose from the streets to MIT, but couldn’t escape himself. Pitts was used to being bullied. He’d been born into a tough family in Prohibition-era Detroit, where his father, a boiler-maker, had no trouble raising his fists to get his way. The neighborhood boys weren’t much better. One afternoon in 1935, they chased him through the streets until he ducked into the local library to hide. The library was familiar ground, where he had taught himself Greek, Latin, logic, and mathematics—better than home, where his father insisted he drop out of school and go to work. Outside, the world was messy. Inside, it all made sense. [more inside]

## Islamic Astropolitik

Despite Western anxieties over Muslim conquest, traditions of Islamic astronomy and the portability of ritual space in Islam find Muslims at home among the stars. [more inside]

## 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."## Professor and the boomerang

Professor Yutaka Nishiyama is a mathematician and a boomerang enthusiast. His Boomerang International Project page contains instructions in multiple languages for making your own paper boomerang and several videos of the boomerang in action. [more inside]

## It's pretty obscure, you probably haven't--wait, what?

The mathematician who proved why hipsters all look alike

Jonathan Touboul is a mathematician and a neuroscientist. Recently, he has been thinking about hipsters. Specifically, why hipsters all seem to dress alike. In his line of work, there are neurons that also behave like hipsters. They fire when every neuron around them is quiet; or they fall silent when every neuron around them is chattering. [more inside]

Jonathan Touboul is a mathematician and a neuroscientist. Recently, he has been thinking about hipsters. Specifically, why hipsters all seem to dress alike. In his line of work, there are neurons that also behave like hipsters. They fire when every neuron around them is quiet; or they fall silent when every neuron around them is chattering. [more inside]

## 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]

## One of these things is not like the others

US News and World Report (USNWR) ranking of the top ten universities in mathematics are:
1. Berkeley ;
2. Stanford ;
3. Princeton ;
4. UCLA ;
5. University of Oxford ;
6. Harvard ;
7. King Abdulaziz University ;
8. Pierre and Marie Curie – Paris 6 ;
9. University of Hong Kong ;
10. University of Cambridge [more inside]

## Of course, everyone knows about levers...

Elementary Mechanics from a Mathematician's Viewpoint [direct link to large PDF] by Michael Spivak - notes from his eight 2004 lectures (which eventually became a book). See the quote inside to get the flavor of it. [more inside]

## Take that, Keanu Reeves.

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

## Totally Freaking Out About Peg + Cat

Peg + Cat is an Emmy award-winning cartoon from PBS, featuring the adventures of a young girl and her feline friend, using the power of math to solve Really Big Problems. The show, created by kid TV and Broadway veterans Jen Oxley & Billy Aronson, not only gives preschoolers an introduction to practical mathematics, it's also surprisingly entertaining for adults.

## 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]

## Ring the bells that still can ring

[more inside]How did something as loud as a bell—something which is experienced so much more often, and more powerfully, by hearing than by sight—become dumb?

## Hidden patterns even in the most mundane of objects

Mathematician Zachary Abel builds impressive Mathematical Sculptures from office supplies and other household objects. [more inside]

## Geometry in motion

Bees & Bombs is a tumblr of hypnotic GIF animations programmed by Dublin-based physics student Dave Whyte

## 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]

## Orchestrate Illusions (Superpermuter)

The Minimal Superpermutation Problem -

*Imagine that there is a TV series that you want to watch. The series consists of n episodes, with each episode on a single DVD. Unfortunately, however, the DVDs have become mixed up and the order of the episodes is in no way marked (and furthermore, the episodes of the TV show are not connected by any continuous storyline – there is no way to determine the order of the episodes just from watching them). Suppose that you want to watch the episodes of the TV series, consecutively, in the correct order. The question is: how many episodes must you watch in order to do this?*[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]

## I'm leaving my body to science, not medical but physics

Let's Talk About Science is a blog devoted to discussing the world of science and technology communication with clear, beginner-friendly language, written and compiled by nanoscientist/physicist Jessamyn Fairfield and science educator ErinDubitably. [more inside]

## Following your heart is another tolerable option

## 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 ;)

## Visually stunning math concepts...

## Don't be gauche—guilloche!

Did you know there's a direct correlation between the decline in Spirograph popularity and the rise in gang activity? Reverse this deplorable trend by playing around with the Guilloché spiral pattern generator! [more inside]

## 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]

## 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.

## Truth & Beauty

The emotional experience of mathematical elegance. A new study by the perceptual neurobiologist Semir Zeki and the great mathematician (& Fields Medalist) Sir Michael Atiyah examines fMRI scans of mathematicians viewing formulae which they'd previously rated as beautiful or ugly, and reports that mathematical beauty elicits activity in the same brain regions as great art or music.

## And this one's the Half Double Decaf Half-Windsor, With A Twist of Lemon

## 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.)

## How can nothing can be something?

While the concept of shunya or "zero", both as place holder in the decimal system and as "null" or "nothingness" has been historically attributed to the Indian mathematician/astronomer Aryabhata, it was when I went to search for its history and impact that whole new world was revealed. From culture and art to spiritual practice, the concept of zero has captured the imagination of many throughout the ages. Books have been written, its origins debated while the etymology of the word itself sometimes replaces understanding. From a disconcerting concept of nothingness to the ubiquitous misspelling of the one followed by a hundred zeros, Shunya today is more than just the gaping void it originally represented.

## One pill makes you nano, and one pill makes you giga...

The pressure of a human bite is about 1/9th of the atmospheric pressure on Venus. The fastest bacterium on earth is just outstripping the fastest glacier. A square meter of sunshine in the spring imparts about 1 horsepower. [more inside]

## 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]