## Anecdotes from the Archive: A ship-shooting formula

February 25th, 2011 | 2

One of the reasons I dreaded math class was the looming feeling that what I learned would turn out to be useless. No matter how hard I tried, I could not imagine a situation outside of school when I would need to know how to graph a logarithm or find the degree of an unknown [...]

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## Editor’s Selections: Myths, Shoulders, Risks, Resolutions, And Math

Part of my online life includes editorial duties at ResearchBlogging.org, where I serve as the Social Sciences Editor. Each Thursday, I pick notable posts on research in anthropology, philosophy, social science, and research to share on the ResearchBlogging.org News site. To help highlight this writing, I also share my selections here on AiP. Happy New Year! Bloggers [...]

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## The Need for Belonging in Math and Science

October 21st, 2013 | 6

From her earliest memories, Catherine Good was good at math. By second grade she was performing at the fourth grade level, sometimes even helping the teacher grade other students’ work. She was praised constantly for her “gift”, often overhearing her mother tell anyone who would listen that she was a “sponge” for anything mathematical. By [...]

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## Why Education Needs More Radioactive Spiders

September 9th, 2013 | 4

Education needs more radioactive spiders. Stay with me. Remember Peter Parker? His childhood wasn’t easy. Both of his parents– Richard and Mary– were killed on a mission as double agents. Raised by his Uncle Ben and Aunt May in Queens, Peter spent most of his childhood without an identity. Now, Peter was a good student. [...]

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## The New, New Math: A Parent’s Guide

September 6th, 2011 | 3

There are big changes underway in how kids across the country are learning math. Forty-four states plus the District of Columbia have adopted a common set of standards that detail what students should understand and be able to do at each grade level, from Kindergarten through the end of high school. Known as the Common Core State Standards, [...]

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## Benoit Mandelbrot (RIP) and the quest for a theory of really everything

October 18th, 2010 | 17

The passing of the mathematician Benoit Mandelbrot has triggered in me a wave of nostalgia for the 1980s, when Mandelbrot and other researchers seemed to be creating a scientific revolution. They hoped that sophisticated new mathematical techniques, plus increasingly powerful computers, could help them fathom a wide range of complex, nonlinear phenomena—from brains and immune [...]

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## Contemplating the end of the world, math, mystery and other things

September 6th, 2010 | 21

I suffer from eschatological obsession. That is, I spend lots of time brooding about ends. So the cover of the September Scientific American—which reads simply "the end."—made me all shivery, like when I hear the spooky sitar opening of The Doors’ apocalyptic rock poem "The End." (I’m never more Freudian than when I hear Morrison’s [...]

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## Play, Informal Learning Cultivate Kids’ Interest in STEM

When I was eight years old I couldn’t speak English. I’d been born in another country and came to the U.S. because my father’s postdoctoral medical research brought us here. Frustrated with my inability to communicate with others, I stopped trying. I didn’t want to play with the other kids anyway – at least that’s [...]

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## To What Extent Do We See with Mathematics?

November 27th, 2013 | 5

When I first became fascinated with mathematics’ tightly knit abstract structures, its prominence in physics and engineering reassured me. Mathematics’ indisputable value in science made it clear that my preoccupation with its intangible expressions was not pathological. The captivating creative activity of doing mathematics has real consequences. During my graduate school years, I began to [...]

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## Celebrations of Mind Honor Math’s Best Friend, Martin Gardner

Every fall provides a special excuse for all thinking people to celebrate recreational math, magic and rationality, some of the things that were dear to America’s greatest man of letters and numbers, former Scientific American columnist Martin Gardner (1914 – 2010), via Celebration of Mind events. While Gardner was without doubt the best friend mathematics [...]

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## Can Synesthesia in Autism Lead to Savantism?

December 4th, 2013 | 1

Daniel Tammet has memorized Pi to the 22,514th digit. He speaks ten different languages, including one of his own invention, and he can multiply enormous sums in his head within a matter of seconds. However, he is unable to hold down a standard 9-to-5 job, in part due to his obsessive adherence to ritual, down [...]

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## World Cup Prediction Mathematics Explained

June 11th, 2014 | 8

The World Cup is back, and everyone’s got a pick for the winner. Gamblers have been predicting the outcome of sporting contests since the first foot race across the savannah, but in recent years a unique type of statistical analysis has taken over the prediction business. Everyone from Goldman Sachs to Bloomberg to Nate Silver’s [...]

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## Glow Sticks Prove the Math Theorem behind the Famous Flatiron Building

December 11th, 2013 | 3

How many math lovers live in New York City? It’s a tough count to make, but the Museum of Mathematics made progress at its first anniversary celebration on Thursday, December 5. With a mission to illuminate the math that permeates our day-to-day lives, the Museum of Mathematics, or MoMath, wasn’t about to waste its birthday [...]

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## Please Play with Your Math: New Museum Opens in New York City

December 19th, 2012 | 1

Math can be a beautiful, immersive, full-body experience, according to the creators of the newly opened Museum of Math, or MoMath, in New York City. A sculpture that lights up and plays music, a touch-screen floor that turns into a maze and a square-wheeled tricycle that one can ride around a bumpy track are just [...]

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## A Presidential Pythagorean Proof

James Abram Garfield was born on this day, November 19, in 1831. Had an unstable, delusional stalker’s bullets and nineteenth-century medical “care” not cut short his life just six months into his presidency, he would be 181 today (more on that later). Garfield was an intelligent man who studied some math in college, but contemporary [...]

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## Mathematicians at Play: 3-D Printing Enters the 4th Dimension

October 31st, 2012 | 2

I was at a math conference last week, and one of the other attendees brought a puzzle. I am a pretty slow puzzle-solver, so it will be a while before I figure out how to assemble those five pieces to get this. Three views of the assembled puzzle. Saul Schleimer, a mathematician at the University [...]

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## Fractal Kitties Illustrate the Endless Possibilities for Julia Sets

September 26th, 2012 | 11

For decades, scientists have been trying to solve a tough question: if the Internet runs out of cat pictures, can we generate more using advanced mathematics?* A paper posted on the arxiv earlier this month by mathematicians Kathryn Lindsey and the late William Thurston calms fears about “peak cat.” In the paper, they describe a [...]

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## Why 167 Is a Happy Number—Besides Being *Scientific American*‘s Age

August 27th, 2012 | 3

On Tuesday, Scientific American turns 167 years old. It doesn’t exactly look like the kind of anniversary we usually celebrate, with our decimal normative number system that overvalues ending zeroes and fives, but 167 is a pretty neat number. First of all, we can insert two symbols into it to get a correct mathematical statement: [...]

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## The Mathematical Legacy of William Thurston (1946-2012)

William Thurston, whose geometrization conjecture changed the fields of geometry and topology and whose approach to mathematics and mathematics education has reverberated throughout the mathematical world, died on August 21 following a battle with cancer. He has appeared in the pages of Scientific American in the article The Mathematics of Three-Dimensional Manifolds, which he co-wrote [...]

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## Abandoning Algebra Is Not the Answer

July 30th, 2012 | 63

In an opinion piece for the New York Times on Sunday, political science professor Andrew Hacker asks, “Is Algebra Necessary?” and answers, “No.” It’s not just algebra: geometry and calculus are on the chopping block, too. It’s not that he doesn’t think math is important; he wants the traditional sequence to be replaced by a [...]

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## How Much Pi Do You Need?

July 21st, 2012 | 23

I hope you’re ready for your big Pi Approximation Day party tomorrow. You might have observed Pi Day on March 14. It gets its name from 3.14, the first three digits of the ratio of a circle’s circumference to its diameter. Always on the lookout for excuses to eat pie, some geeky math types also [...]

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## 12 Things I Had Way Too Much Fun Writing This Year

It’s the season for family, hot chocolate, and year-in-review lists. Guess which one this is! Roots of Unity has been around for two years now, and I’m so glad I have a place to share some of the weird and wonderful math I think about. In chronological order, here are 12 of my favorite posts [...]

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## What We Talk about When We Talk about Holes

December 25th, 2014 | 7

For Halloween, I wrote about a very scary topic: higher homotopy groups. Homotopy is an idea in topology, the field of math concerned with properties of shapes that stay the same no matter how you squish or stretch them, as long as you don’t tear them or glue things together. Both homotopy groups and the [...]

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## Online Game Crowd-Sources Theorems

Now is your chance to prove some theorems without knowing what they mean! Chris Staecker, a mathematician at Fairfield University, created the game Nice Neighbors to get crowd-sourced solutions to problems from a field called digital topology. Whether that means anything to you or not, you might be able to help Staecker and his colleagues prove some [...]

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## Seeing Music: What Does the Missing Fundamental Look Like?

I wrote a post yesterday about the missing fundamental effect. It’s a startling auditory illusion in which your brain hears a note that is lower than any of the notes that are actually playing. I decided to go to Desmos, an online graphing calculator, and play around with sines to see whether the missing fundamental [...]

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## Your Telephone Is Lying to You About Sounds

Telephones lie about sounds because odd numbers aren’t even. Once again with those integers and sound perception! Telephones can only pick up frequencies above 300 or 400 Hertz (cycles per second, also called Hz), but most adults’ speaking voices are lower than 300 Hz (approximately the D above middle C). And yet every day, people [...]

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## The Math Geek Holiday Gift Guide

November 23rd, 2014 | 1

Looking for a gift that says, “Hey, I know you like math”? Look no further. There is an embarrassment of riches when it comes to wonderful mathematical things to give to people, but here are some of the coolest items I’ve seen this year. To read I wrote reviews of Jordan Ellenberg’s How Not to Be [...]

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## A Proof of the Math Fact of Rolle in Short Words

November 17th, 2014 | 3

This proof of the math fact of Rolle, I wrote it down; here was my goal: Use just words with one part. (So it won’t sound too smart.) Please tell me if you find a hole. The math fact of Rolle: Let f be a map from a closed length of the reals (the length [...]

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## In Which Omar Khayyam Is Grumpy with Euclid

October 28th, 2014 | 7

My math history class is currently studying non-Euclidean geometry, which means we’ve studied quite a few “proofs” of Euclid’s fifth postulate, also known as the parallel postulate. I’ve written about this postulate before. There are many statements that are equivalent to the parallel postulate, including the fact that parallel lines in a plane are equidistant. This [...]

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## Beyond Emmy and Sophie: Resources for Learning about Women in Math

Today is Ada Lovelace Day, an international celebration of women in science, technology, engineering, and math. If you’d like to read about women in math for the occasion, you’re in serious danger of coming across an article about Hypatia, Emmy Noether, Sophie Germain, or Sofia Kovalevskaya. Of course, these are inspiring women with compelling stories, [...]

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## Build Your Own Fractal with MegaMenger!

October 9th, 2014 | 1

Later this month, people will be gathering at museums and schools around the world to build giant Menger sponges as part of a global fractal extravaganza called MegaMenger. A Menger sponge is a fractal that sits in three-dimensional space. To visualize one, imagine starting with a cube and splitting it into 27 sub-cubes, like a [...]

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## The Making of a Mathematical Mind: 1 Step at a Time

August 15th, 2013 | 5

One time when I was in the third grade, I got sick and missed a week of school. My dad wanted me to keep up with my schoolwork, so he brought my assignments and books home. I did the required work in the math workbook quickly, or so the story goes, and went on to [...]

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## Do Music Lessons Make You Smarter?

March 1st, 2013 | 18

Practice makes progress, if not perfection, for most things in life. Generally, practicing a skill—be it basketball, chess or the tuba—mostly makes you better at whatever it was you practiced. Even related areas do not benefit much. Doing intensive basketball drills does not usually make a person particularly good at football. Chess experts are not [...]

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## Star Filmmakers Found in Unlikely Spot

In Tyson Schoeber’s class at Nootka Elementary School in Vancouver, 15 fourth through seventh graders struggle to read, write or do math at a level near that of their peers in other classes. Ten-year-olds have entered Schoeber’s program, called THRIVE, virtually unable to read independently (see “One Man’s Mission to Save Struggling Students”). Yet Schoeber [...]

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## The Long Shadow of Fungal Networks

I’ve heard it said that if you removed everything from the forest except for fungi you would still be able to discern outlines of trees and leaves because of the vast fungal networks of pervading everything. I’ve often thought that would make a powerful illustration but never got around to acting on it. So when [...]

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## 20th-Century Math Hidden in 15th-Century Art

February 25th, 2014 | 3

Art and science are often thought of as disparate entities, drawing on different strengths and different ways of thinking. This is surely true, but the disciplines also share patterns of thought and essential characteristics. Take, for example, their inherently collaborative processes. No artist creates in a vacuum just as no scientists could perform the work [...]

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## Yes, T-Shirt Messages Matter

August 6th, 2013 | 13

Yesterday, I came across a very interesting T-shirt design during my afternoon web surfing. The Children’s Place apparently forgot about the great “I’m too pretty to do my homework, so my brother has to do it for me” T-shirt debacle of 2011, and they decided to produce a shirt that reads, “My best subjects” and [...]

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## SciArt of the Day: Hyperdimensional Suffering

As our month of SciArt of the Day winds down, I had to share this image. For me, this is a touchstone of what makes wonderful science-art: marrying metaphors from past and present, science and myth. The idea that art and science represent two cultures, as C.P. Snow described is a curious one. Art, or [...]

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