## Origin of Mysterious Portuguese Mathematical and Geographical Tiles Revealed

November 5th, 2014 | 4

A few months ago I wrote about some mystifying mathematical and geographic tiles I encountered at the National Tile Museum in Lisbon, Portugal. Their accompanying label gave no clue to who had made them or why. Several readers subsequently wrote to tell me what they knew about these tiles. Thank you to everyone who did [...]

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## The Neuroscience of Mathematical Beauty

May 7th, 2014 | 5

Mathematics, rightly viewed, possesses not only truth, but supreme beauty” — Bertrand Russell The latest neuroscience of aesthetics suggests that the experience of visual, musical, and moral beauty all recruit the same part of the “emotional brain”: field A1 of the medial orbitofrontal cortex (mOFC). But what about mathematics? Plato believed that mathematical beauty was [...]

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## Talent on the Sidelines: The Widening Gap in Excellence

October 22nd, 2013 | 6

An alarming report on the current state of excellence in the United States has been released today. The conclusion of the report “Talent on the Sidelines: Excellence Gaps and the Persistence of America’s Permanent Talent Underclass” is that the United States is relying on less than half of its talent, with large percentages of our brightest students [...]

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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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## Can Faith and Science Coexist? Mathematician and Christian John Lennox Responds

March 1st, 2015 | 5

My last column outlined points I made in a February 18 debate at my school, Stevens Institute of Technology, about whether religion and science are compatible. My “opponent,” Oxford mathematician John Lennox, a Christian, emailed me the following response: It was a great pleasure for me to meet and have a spirited discussion with John [...]

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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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## 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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## In Defense Of Metaphors In Science Writing

July 9th, 2013 | 19

“Science is all metaphor” Timothy Leary We live in an elegant universe. The cosmos is like a string symphony. Genes are selfish. There is an endless battle between thermodynamics and gravity. Do you love these statements, or hate them? The reading world gets pretty divided over whether or not it’s okay to apply metaphors and [...]

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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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## Mathematical Patterns in Sea Ice Reveal Melt Dynamics

March 13th, 2014 | 4

Some people call Ken Golden the “Indiana Jones” of mathematics due to his frequent excursions to remote, harsh parts of the world. Golden, a professor of mathematics at the University of Utah, studies the dynamics of sea ice, and he regularly goes out into the field to test his hypotheses. He has visited the Arctic [...]

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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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## “Wikithon” Honors Ada Lovelace and Other Women in Science

A Wikipedia edit-a-thon seems like a fitting tribute to the woman many consider to be the first computer programmer. October 16 is Ada Lovelace Day, an annual observation designed to raise awareness of the contributions of women in science, technology, engineering and math (STEM) disciplines. Groups in the U.S., U.K., Sweden and India are marking [...]

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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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## Metrocard Mathematics: Are Unlimited Subway Passes a Good Deal?

July 31st, 2012 | 6

Unlimited, or Pay-Per-Ride? That’s the question posed by the New York Times City Room blog this morning, as New Yorkers confront the great algebraic unknown of August: are unlimited subway passes still a good value even if you’re going out of town on vacation? Perhaps the author, reporter Clyde Haberman, has been reading too much [...]

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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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## Uber, but for Topological Spaces

So it’s cold and rainy, and you’re up a little too late trying to figure out why that one pesky assumption is necessary in a theorem. Wouldn’t it be nice if you could just order up a space that was path connected but not locally connected? You’re in luck, there’s an app a website for [...]

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## Things to Make and Do in the Fourth Dimension (Book Review)

Sometimes you want to learn a “new” multiplication algorithm from a general interest math book, sometimes you want to learn why voting systems are doomed to imperfection, and sometimes you just want to play with numbers, patterns, and pictures. Things to Make and Do in the Fourth Dimension by Matt Parker is the third kind of [...]

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## Gauss and Germain on Pleasure and Passion

February 13th, 2015 | 2

Sophie German, who was not allowed to attend university, was the first woman to make significant original contributions to mathematical research. Today, her story is both inspiring and heartbreaking. What might this brilliant, creative mind have done if barriers had not been thrown in her way at every step? How many others like her do [...]

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## The Media and the Genius Myth

February 5th, 2015 | 15

I’ve been thinking a lot about the genius myth, the notion that in order to be a successful in certain disciplines, you need to have a special innate talent that can’t be learned. Last month, a study in Science found that fields whose practitioners buy into the genius myth, say, mathematics, have lower proportions of [...]

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## Understand the Measles Outbreak with this One Weird Number

January 31st, 2015 | 4

15. That’s all you need to know about the measles. OK, that’s not true at all. There’s no one weird trick that will give you a flat belly (besides lying face-down on something flat), and there’s no one weird number that explains measles epidemiology. But the basic reproduction number, or R0, of a disease does [...]

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## Learn to Count like an Egyptian

January 26th, 2015 | 1

Last semester, I began my math history class with some Babylonian arithmetic. The mathematics we were doing was easy—multiplying and adding numbers, solving quadratic equations by completing the square—but the base 60 system and the lack of a true zero made those basic operations challenging for my students. I was glad that the different system [...]

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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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## Math Is Beautiful, But Is It Art?

Every so often, beauty comes up as a topic of conversation in editorial meetings at Scientific American. Surely there’s an article, or series of articles that we can develop on the topic? After all, it’s not unusual for theories and/or equations to be described as beautiful. Our conversations circle around to perception and aesthetics and [...]

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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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## 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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