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Posts Tagged "Mathematics & Modeling"

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

Reserved sign

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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Critical Opalescence

How Do You Count Parallel Universes? You Can’t Just Go 1, 2, 3, …

Cosmologists have been thinking for years that our universe might be just one bubble amid countless bubbles floating in a formless void. And when they say “countless,” they really mean it. Those universes are damned hard to count. Angels on a pin are nothing to this. There’s no unambiguous way to count items in an [...]

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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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Doing Good Science

Getting kids interested in math careers may require a hero.

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Back when I was a high school math geek, our math team would go to meets that occasionally had tables set up to encourage us to pursue various careers that would make use of our mad math skillz. The one such profession where the level of encouragement far outstripped our teenaged interest was the actuarial [...]

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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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PsiVid

Math Warriors: Season 3

Have you ever watched “Mean Girls”? It’s one of the movies before Lindsey Lohan really began to let her career slip. She plays Cady, a smart girl, homeschooled by her parents as they lived in Africa until her high school years, where, desperate to fit in AND to “get the guy”, she dumbs down her [...]

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Roots of Unity

Some Infinities Are Bigger than Other Infinities, and Some Are Just the Same Size

How to count potatoes by pairing them with numbers. Image: Yen Duong.

Warning: contains minor spoilers for The Fault in Our Stars. I recently read The Fault in Our Stars by John Green, now a major motion picture that has led to theft in Amsterdam and a shortage of dry eyes in movie theaters around the world. One of the ideas that resonates with Hazel, the 16-year-old narrator [...]

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Roots of Unity

British Objects of Constant Width

Several British objects of constant width. Image: Evelyn Lamb.

As I wrap up a trip to the UK, I reflect on the many objects of constant width I encountered here. I’ll let Numberphile tell you a little more about objects of constant width. Almost immediately after getting off the plane at Heathrow, I got some breakfast and some change in the form of metal [...]

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Roots of Unity

The Most Mathematically Perfect Day of the Year

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Whether you write it 6/28 or 28/6, today is a perfect day. A perfect number is a number that is the sum of its factors besides itself, and 6 (1+2+3) and 28 (1+2+4+7+14) are the first two perfect numbers. Hence, June 28 is a perfect day. Perfect numbers are few and far between, so don’t [...]

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Roots of Unity

2, 4, 6, 8, What Does Not Associate?

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Last month, I wrote about group theory via monkeys, and it got me thinking about the associative property. A mathematical group consists of a collection of stuff: integers, or rational numbers, or even something more abstract; and an operation that combines any two elements of your stuff into another element of stuff. One of the [...]

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Roots of Unity

How to Make “e-1″ Salad Dressing

Delicious salad not included in this dressing recipe. Image: Geoff Peters, via flickr.

What does math taste like? Andrea Hawksley recently posted a recipe for Fibonacci lemonade, a drink that is inspired by the famous Fibonacci sequence: 1,1,2,3,5,8, and so on. It is a thing of beauty to behold, and as you drink it, you actually taste successive approximations of the golden ratio due to the relationship between [...]

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Roots of Unity

How Not to Be Wrong (Book Review)

How Not to Be Wrong by Jordan Ellenberg. Image courtesy of Penguin Press.

How Not to Be Wrong by Jordan Ellenberg. Image courtesy of Penguin Press. How Not to Be Wrong, the first popular math book by University of Wisconsin-Madison math professor Jordan Ellenberg, just hit the shelves. In addition to a Ph.D. in math, Ellenberg has an MFA in creative writing and has been writing about math [...]

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Roots of Unity

A Higher Murder Rate than New York and Los Angeles Combined

Non-Violence, a sculpture by Carl Fredrik Reuterswärd in Malmö, Sweden. Image: Francois Polito, via Wikimedia Commons.

Today on the radio, I heard an announcer say, “Chicago has a higher murder rate than New York and Los Angeles combined.” The compassionate human being in me cringed, and the statistical pedant in me also cringed. What does that mean? When I heard, “New York and Los Angeles combined,” I intuitively thought of combining [...]

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Roots of Unity

MoMA to MoMath: a Mathematician’s Picks for Art in New York City

A sculpture made of matches from the Compounding Visions exhibition by Trevor and Ryan Oakes at the Museum of Mathematics. Photo: Adriana Salerno.

I was in New York City earlier this month, and in addition to finally having an excuse to ride the Staten Island Ferry (I gave a talk there), I managed to make it to a few of the excellent museums in the city. I don’t go to art museums to try to find connections with [...]

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Roots of Unity

Nothing Is More Fun than a Hypercube of Monkeys

More Fun than a Hypercube of Monkeys, a sculpture by Henry Segerman and Will Segerman. The monkeys do not all look like they are the same size, but that is due to the stereographic projection technique used to visualize a 4-dimensional object in 3-d. (Similarly, if one part of a 3-d object is closer to a surface than another part, it will appear larger when projected to that surface.) Image: Henry Segerman and Will Segerman.

Monkeys! Mathematical groups! 4-dimensional geometry! Together at last! This sculpture, called More Fun than a Hypercube of Monkeys, answers an open question: has the quaternion group ever appeared as the symmetry group of an object? Thanks to mathematician Henry Segerman and mathemusician Vi Hart, the answer is now yes. Their very readable paper about the sculpture [...]

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Roots of Unity

Happy Birthday, Evelyn Boyd Granville!

Evelyn Boyd Granville in 1997. Image: Margaret Murray, via Mathematicians of the African Diaspora by Scott W. Williams.

Evelyn Boyd Granville, the second African American woman to earn a Ph.D. in mathematics, turns 90 today (May 1, 2014). I first heard her name in a talk by Patricia Kenschaft about African American mathematicians. Of course, having an affinity for the name Evelyn, she stuck in my mind, and when I found out her [...]

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Streams of Consciousness

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

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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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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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