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Posts Tagged "mathematics"

The Artful Amoeba

Origin of Mysterious Portuguese Mathematical and Geographical Tiles Revealed

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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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Beautiful Minds

The Neuroscience of Mathematical Beauty

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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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Beautiful Minds

Talent on the Sidelines: The Widening Gap in Excellence

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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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Beautiful Minds

The Need for Belonging in Math and Science

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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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Cross-Check

For Pi Day: A Reminiscence on “The Death of Proof”*

The 1993 article "The Death of Proof" argued that "the doubts riddling modern human thought have finally infected mathematics."

In 1993, when I was a full-time staff writer for Scientific American, my boss, Jonathan Piel, asked, or rather, commanded me to write an in-depth feature on something, anything, mathematical. Fercrissake, I was an English major! I whined. I could fake math knowledge for little news stories about the Mandelbrot set or Fermat’s last theorem, [...]

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Cross-Check

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

"The mathematical intelligibility of nature is evidence for a rational spirit behind the universe." John Lennox.

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, who has debated Richard Dawkins, Christopher Hitchens, Michael Shermer and other prominent non-believers–emailed me the following response: It was a great pleasure [...]

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Cross-Check

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

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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Guest Blog

John Conway Reminiscences about Dr. Matrix and Bourbaki

John H. Conway holds an advance copy of a forthcoming biography. (Photo: Colm Mulcahy)

Last week, life took me through Princeton, and I seized the opportunity to drop in to see resident English mathematician John Horton Conway. He was in particularly good form despite health issues that come with aging, and proudly showed me an advance copy of a forthcoming biography of his life by Siobhan Roberts. “Being the [...]

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Guest Blog

How Many Digits of Pi Do You Really Need to Know? Find Out with This Bar Bet

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A physicist or engineer who uses π (pi) in numerical calculations may need to have access to 5 or 15 decimal place approximations to this special number, but most of us—mathematicians included—don’t need to know more (decimal-wise) than the fact that it’s roughly 3.14. Yet there is an inexplicable nerdy subculture far removed from real [...]

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Guest Blog

To What Extent Do We See with Mathematics?

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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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Life, Unbounded

In Defense Of Metaphors In Science Writing

(James Gillray)

“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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MIND Guest Blog

Can Synesthesia in Autism Lead to Savantism?

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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Observations

World Cup Prediction Mathematics Explained

Brazil vs. England in a "friendly" in Rio de Janeiro

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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Observations

Mathematical Patterns in Sea Ice Reveal Melt Dynamics

Melt ponds on the surface of Arctic sea ice. Credit: Karen Frey

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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Observations

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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Observations

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

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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Observations

“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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Observations

Fractal Kitties Illustrate the Endless Possibilities for Julia Sets

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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Observations

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

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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Observations

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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Observations

Metrocard Mathematics: Are Unlimited Subway Passes a Good Deal?

Metrocards subway bike

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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Observations

Abandoning Algebra Is Not the Answer

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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Roots of Unity

In Praise of Fractals and Poetry

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This year for Math Poetry month, I read Proportions of the Heart: Poems that Play with Mathematics, a collection of poems by Emily Grosholz. Grosholz is both a philosophy professor at Penn State and a poet. She does research in the philosophy of math, and her poems are peppered with references to both mathematics and [...]

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Roots of Unity

A Few of My Favorite Spaces: The Cantor Set

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Last month, I wrote about the π-Base, a website that serves a similar function to the book Counterexamples in Topology. I’m teaching a topology class this semester, and it’s been fun to revisit some good counterexamples. As a new series on the blog, I’ll be writing about some of these strange and interesting mathematical spaces. [...]

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Roots of Unity

What’s so Great about Continued Fractions?

The continued fraction expansion for the number pi.

The more I learn about continued fractions, the more enamored I am with them. Last week, when I wrote about how much better continued fractions are than the arbitrary decimal digits we usually use to describe numbers, I mentioned that continued fractions tell us the “best approximations” of irrational numbers. Continued fractions are just fractions [...]

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Roots of Unity

Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead.

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The digits of pi reciting contest is an all-too-common Pi Day event. And as this year is a once-in-a-century confluence of month/day/year with the first few decimal digits of pi, we might be in for more of those than usual. Our 10 fingers make decimal digits a natural choice, but if we were capybaras or [...]

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Roots of Unity

Uber, but for Topological Spaces

Cantor's Leaky Tent, one of the many lovely, perplexing, and colorfully named counterexamples available at the π-Base.

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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Roots of Unity

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

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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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Roots of Unity

Gauss and Germain on Pleasure and Passion

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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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Roots of Unity

The Media and the Genius Myth

Not many of us can be Serena Williams. Does that keep us from playing tennis? Image: Yann Caradec, via Flickr.

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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Roots of Unity

Understand the Measles Outbreak with this One Weird Number

A man sneezes, possibly transmitting measles or other airborne diseases. Image: James Gathany, CDC.

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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Roots of Unity

Learn to Count like an Egyptian

Count Like an Egyptian by David Reimer. Image: Princeton University Press.

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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SA Visual

Math Is Beautiful, But Is It Art?

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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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Symbiartic

The Symbiartic SciArt Roundup: Exhibits On View Now

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Our recent effort to galvanize people around great #sciart on Twitter was a raging success, proving to us that science art is growing by leaps and bounds. These scienceart exhibits are ones you can see in the flesh and are popping up all around the country. Get out and see them while you can! EXHIBITS: [...]

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Symbiartic

The Long Shadow of Fungal Networks

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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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Symbiartic

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

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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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