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Posts Tagged "mathematics"

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?

Variable X

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

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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Observations

Is Pop Music Evolving, or Is It Just Getting Louder?

Classic record jukebox

Music just ain’t what it used to be. At least, that’s the stereotypical lament of each receding generation of music listeners. It’s also one way to read a new study on the evolution of pop music in the past half-century. A group of researchers undertook a quantitative analysis of nearly half a million songs to [...]

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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

Measure Yourself by the Standard of the Capybara

Are you more or less of a fish than this capybara? Image: VigilancePrime, via Wikimedia Commons.

We all know a lot of measurements about ourselves. You are some number of feet or meters tall. You weigh some number of pounds, kilograms, or stone. Your BMI is some number of kilograms per square meter, even though humans are not two-dimensional. You have some number of milligrams of cholesterol in each deciliter of [...]

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Roots of Unity

The Slowest Way to Draw a Lute

Man Drawing a Lute, by Albrecht Dürer. Public domain, via Wikimedia Commons.

Last month, I went to a talk by mathematician Annalisa Crannell of Franklin and Marshall College called Math and Art: the good, the bad, and the pretty. She talked about how mathematical ideas of perspective show up in art and how it can help us create and appreciate art. One of my favorite parts of the [...]

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Roots of Unity

Graham’s Number Is Too Big for Me to Tell You How Big It Is

Behold, Graham's number!

I was going to write an April Fool’s Day post with the title “Mathematicians Declare Graham’s Number Equal to Infinity.” Graham’s number is really big, but of course, it’s precisely 0% as big as infinity. On the other hand, everything we touch is finite, so in some sense, Graham’s number is probably “close enough” to [...]

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Roots of Unity

What T.S. Eliot Told Me about the Chain Rule

T.S. Eliot, who probably never thought about the chain rule while he was writing poetry. Photograph by Lady Ottoline Morrell. Public domain, via Wikimedia Commons.

“We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time.” —from Little Gidding by T.S. Eliot If you took calculus in high school or college, you might remember the chain rule. One of the main topics in calculus [...]

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Roots of Unity

We Only Need to Fill Out 425 Brackets Each to Win Buffett’s Billion

Will your bracket be a slam dunk? Image: Acid Pix, via flickr.

Warren Buffett’s Bracket Challenge* has put even more of a spotlight than usual on March Madness, the annual NCAA basketball tournament. Buffett has offered a billion dollars to anyone who correctly predicts the outcome of all 63 games in the tournament. There are 2 possible outcomes of every game and therefore 263— 9,223,372,036,854,775,808, or about [...]

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Roots of Unity

The Math Wars, Lewis Carroll Style

Lewis Carroll in 1863, photographed by Oscar Gustave Rejlander. Image: Public domain, via Wikimedia Commons.

In 1879, Charles Dodgson, better known as Lewis Carroll, published an odd little book called Euclid and his Modern Rivals (available for free at the Internet Archive). Though it takes the form of a play, it is a defense of Euclid’s Elements as the best textbook for geometry. Carroll’s introduction lays out his purpose and why [...]

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Roots of Unity

Chasing the Parallel Postulate

If you'd like to see these again, accept the parallel postulate. Image: Webber, via Wikimedia Commons.

Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” But as I mentioned in my recent post on hyperbolic geometry, one of the postulates, the parallel postulate, is not like the others. [...]

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Roots of Unity

Knotted Needles Make Knitted Knots

A knitted (5,15) torus link. Image: sarah-marie belcastro.

Step aside, infinity scarves, you aren’t infinite at all. The (5,3) torus knot cowl is where it’s at. For me, one of the highlights of January’s Joint Mathematics Meetings was the mathematical fiber arts session. You can view a slide show I put together from the session here. During the session, co-organizer sarah-marie belcastro gave a [...]

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Roots of Unity

Has Anyone Ever Flipped Heads 76 Times in a Row?

What are the odds? Image: Evelyn Lamb

Tom Stoppard’s absurdist play Rosencrantz and Guildenstern Are Dead begins with one of them, Guildenstern (or is it Rosencrantz?), flipping coins. “Heads,” Rosencrantz says, and takes the coin. Guildenstern flips again. “Heads,” Rosencrantz says, and takes the coin. Another flip. “Heads.” Again, “Heads.” Soon we find out that Guildenstern has flipped 76 coins, and all [...]

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Roots of Unity

Does 1+2+3… Really Equal -1/12?

Divergent series Lucille says, "1+2+3...=-1/12." Video from Fox, gif from fanpop.com.

A Numberphile video posted earlier this month claims that the sum of all the positive integers is -1/12. I’m usually a fan of the Numberphile crew, who do a great job making mathematics exciting and accessible, but this video disappointed me. There is a meaningful way to associate the number -1/12 to the series 1+2+3+4…, [...]

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Streams of Consciousness

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

worksheet for times 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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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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The Curious Wavefunction

Do you need to know math for doing great science?

Writing in the Wall Street Journal, biologist E. O. Wilson asks if math is necessary for doing great science. At first glance the question seems rather pointless and the answer trivial; we can easily name dozens of Nobel Prize winners whose work was not mathematical at all. Most top chemists and biomedical researchers have little [...]

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