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Posts Tagged "math"

Anecdotes from the Archive

Anecdotes from the Archive: A ship-shooting formula

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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Anthropology in Practice

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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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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Beautiful Minds

Why Education Needs More Radioactive Spiders

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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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Budding Scientist

The New, New Math: A Parent’s Guide

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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Cross-Check

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

Benoit Mandelbrot

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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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

Genetic Memory: How We Know Things We Never Learned

I met my first savant 52 years ago and have been intrigued with that remarkable condition ever since. One of the most striking and consistent things in the many savants I have seen is that that they clearly know things they never learned. Leslie Lemke is a musical virtuoso even though he has never had [...]

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Guest Blog

Play, Informal Learning Cultivate Kids’ Interest in STEM

A visitor learns to solder and connect a circuit in a workshop at the New York Hall of Science's Maker Space.

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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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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Guest Blog

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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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

American Pi: Why the Day Belongs to the U.S. (and Belize)

Pi may be a universal constant, but only two countries can natively celebrate Pi Day: the U.S. and Belize. That’s because they are the only ones (if Wikipedia is correct) to shorthand their date format so that it can match the first few digits of pi (3.1415), or March 14, 2015. Most of the rest [...]

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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

Glow Sticks Prove the Math Theorem behind the Famous Flatiron Building

The Pythagorean theorem projected onto the Flatiron building

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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Observations

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

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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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

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

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

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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Roots of Unity

12 Things I Had Way Too Much Fun Writing This Year

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

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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Roots of Unity

What We Talk about When We Talk about Holes

A visualization of some points on the sphere and their fibers in the Hopf fibration. Image: Niles Johnson, via Wikimedia Commons.

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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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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Symbiartic

Yes, T-Shirt Messages Matter

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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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Symbiartic

SciArt of the Day: Hyperdimensional Suffering

Dali-Hypercubemini

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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