by Josh Rappaport
O.K., I admit I feel self-conscious writing the title for this article. A voice within me says: “Don’t be crazy … No one believes there’s a fun side to math.”
Well, whether or not you think I’m nuts, I’ll still assert that this fun side of math exists.
In case you were wondering I’m not talking about arithmetic or algebra; nor am I referring to standard geometry trig, pre-calculus or even calculus (though calculus is pretty amazing, I have to say) What I am talking about are the far-out aspects of math that students usually never even hear about unless they stumble upon them — or get beyond Calculus 2 in college.
To give some examples, I’m talking about questions and topics like these:
➢ In the world of numbers, we hear a lot about ‘infinity.’ But how many levels of infinity are there? (It turns out that there is not just one order of infinity but at least two such orders, at last count, anyhow.)
➢ What branch of math states that there’s no difference between a donut and a coffee cup? (Topology, as it so happens).
➢ What subject area of math helps people determine what decisions they should make when choosing friends, applying for a summer job, playing chess? (Game theory, the explored mined by John Nash, the mathematician depicted in the hit movie, “A Beautiful Mind”)
➢ What aspect of math inspires modern artists? (Fractal geometry, of course!)
➢ What kind of numbers are used to safeguard the security of our personal info each time we buy something online with a credit card? (Prime numbers.)
➢ How many degrees are there inside triangles created in a non-Euclidean world? (Either more than 180 degrees or less than 180, depending on the shape of that world!)
➢ Which branch of math is used to make sense of the cooked-spaghetti-like, twisty shape of proteins and the way the human DNA molecule has evolved over the millennia? (Knot Theory, naturally!)
What’s really crazy is that these topics are not conceptually impossible to grasp, so there’s no reason I can see why they’re not at least introduced during the teenage years.
In any case, the good news is that there are ways for laypeople (like most of us) to get a taste for these topics. So now I’d like to point you to resources that do just that.
First, there’s a set of videos on a YouTube channel called “Numberphile” that explores many intriguing aspects of math and does so with a good sense of fun (and wonderful British accents). These videos explore everything from the math required for safecracking to the incidental math jokes that appear on “The Simpsons.” Most of the videos are 10 minutes long, or less.
For families that enjoy occasional TV shows, I recommend a CBS series called “Numbers,” which ran for six seasons. The show features a pair of crime-fighting brothers in L.A. The older brother works as a lead agent for the FBI, while his younger brother teaches math at a university modeled after CalTech. As you’ve probably guessed, the younger brother gets called in to help solve the federal crimes and uses advanced (but accessible) math to catch the bad guys. With lots of great graphics showing how the math works, along with exciting storylines, this series shows how math can be used in real-world scenarios.
Then there are books, written for non-math experts. Here’s a brief list of recommended books from this genre.
The Numbers Behind Numbers, by Keith Devlin and Gary Lorden. This book provides background info on the areas of math used in the TV show, Numbers. This provides an intellectual follow-up read after watching the show.
Fermat’s Enigma by Simon Singh. Singh’s classic book brings to life the 350-year quest to solve one of math’s most famous problems, “Fermat’s Last Theorem.” An engrossing read, peopled with fascinating characters and spiced with drama. Highly recommended.
The Man Who Loved Only Numbers, by Paul Hoffman. Delightful biography of the 20th century numbers theorist Paul Erdos. Lots of insights into the life of this highly eccentric, creative, peripatetic mathematician.
The Boy Who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heiligman. This is a children’s book about the same Paul Erdos, tracing his childhood in Budapest and exploring his love of math from a very early age. Great bedtime book for younger children.
Imagining Numbers, by Barry Mazur. The author details the invention/discovery of those intriguing imaginary numbers, shedding light on what they are for and how they are used today.
The Math Book, by Clifford Pickover. This is a mathematical “coffee-table” book, sparkling with captivating illustrations and great writing. Each spread relates a vignette from the “far-out” side of math.
Zero: The Biography of a Dangerous Idea, by Charles Seife. This book tells about the revolutionary invention/discovery of the number 0 and its impact on the world.
Of course, this list represents just a beginning of what is “out there.” Like other homeschooling pursuits, your journey into these exciting areas of math will lead you to resources and topics that work particularly well for you and your family.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
O.K., I admit I feel self-conscious writing the title for this article. A voice within me says: “Don’t be crazy … No one believes there’s a fun side to math.”
Well, whether or not you think I’m nuts, I’ll still assert that this fun side of math exists.
In case you were wondering I’m not talking about arithmetic or algebra; nor am I referring to standard geometry trig, pre-calculus or even calculus (though calculus is pretty amazing, I have to say) What I am talking about are the far-out aspects of math that students usually never even hear about unless they stumble upon them — or get beyond Calculus 2 in college.
To give some examples, I’m talking about questions and topics like these:
➢ In the world of numbers, we hear a lot about ‘infinity.’ But how many levels of infinity are there? (It turns out that there is not just one order of infinity but at least two such orders, at last count, anyhow.)
➢ What branch of math states that there’s no difference between a donut and a coffee cup? (Topology, as it so happens).
➢ What subject area of math helps people determine what decisions they should make when choosing friends, applying for a summer job, playing chess? (Game theory, the explored mined by John Nash, the mathematician depicted in the hit movie, “A Beautiful Mind”)
➢ What aspect of math inspires modern artists? (Fractal geometry, of course!)
➢ What kind of numbers are used to safeguard the security of our personal info each time we buy something online with a credit card? (Prime numbers.)
➢ How many degrees are there inside triangles created in a non-Euclidean world? (Either more than 180 degrees or less than 180, depending on the shape of that world!)
➢ Which branch of math is used to make sense of the cooked-spaghetti-like, twisty shape of proteins and the way the human DNA molecule has evolved over the millennia? (Knot Theory, naturally!)
What’s really crazy is that these topics are not conceptually impossible to grasp, so there’s no reason I can see why they’re not at least introduced during the teenage years.
In any case, the good news is that there are ways for laypeople (like most of us) to get a taste for these topics. So now I’d like to point you to resources that do just that.
First, there’s a set of videos on a YouTube channel called “Numberphile” that explores many intriguing aspects of math and does so with a good sense of fun (and wonderful British accents). These videos explore everything from the math required for safecracking to the incidental math jokes that appear on “The Simpsons.” Most of the videos are 10 minutes long, or less.
For families that enjoy occasional TV shows, I recommend a CBS series called “Numbers,” which ran for six seasons. The show features a pair of crime-fighting brothers in L.A. The older brother works as a lead agent for the FBI, while his younger brother teaches math at a university modeled after CalTech. As you’ve probably guessed, the younger brother gets called in to help solve the federal crimes and uses advanced (but accessible) math to catch the bad guys. With lots of great graphics showing how the math works, along with exciting storylines, this series shows how math can be used in real-world scenarios.
Then there are books, written for non-math experts. Here’s a brief list of recommended books from this genre.
The Numbers Behind Numbers, by Keith Devlin and Gary Lorden. This book provides background info on the areas of math used in the TV show, Numbers. This provides an intellectual follow-up read after watching the show.
Fermat’s Enigma by Simon Singh. Singh’s classic book brings to life the 350-year quest to solve one of math’s most famous problems, “Fermat’s Last Theorem.” An engrossing read, peopled with fascinating characters and spiced with drama. Highly recommended.
The Man Who Loved Only Numbers, by Paul Hoffman. Delightful biography of the 20th century numbers theorist Paul Erdos. Lots of insights into the life of this highly eccentric, creative, peripatetic mathematician.
The Boy Who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heiligman. This is a children’s book about the same Paul Erdos, tracing his childhood in Budapest and exploring his love of math from a very early age. Great bedtime book for younger children.
Imagining Numbers, by Barry Mazur. The author details the invention/discovery of those intriguing imaginary numbers, shedding light on what they are for and how they are used today.
The Math Book, by Clifford Pickover. This is a mathematical “coffee-table” book, sparkling with captivating illustrations and great writing. Each spread relates a vignette from the “far-out” side of math.
Zero: The Biography of a Dangerous Idea, by Charles Seife. This book tells about the revolutionary invention/discovery of the number 0 and its impact on the world.
Of course, this list represents just a beginning of what is “out there.” Like other homeschooling pursuits, your journey into these exciting areas of math will lead you to resources and topics that work particularly well for you and your family.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
At his blog, Josh writes about math education, offering tips and tricks. Josh also authors Turtle Talk, a free monthly newsletter with an engaging "Problem of the Month." You can see a sample issue here or subscribe at this site. Josh also is co-author of the "learn-by-playing" Card Game Roundup books, and author of PreAlgebra Blastoff!, a "Sci-Fi" cartoon math book featuring a playful, hands-on approach to positive and negative numbers.
