I recently interviewed two of the three makers of the computer-animated Chaos movie, Jos Leys and Étienne Ghys. (The third movie maker, Aurélien Alvarez, couldn't join the interview.) My intent was to turn the interview into an "Inspired by Math!" podcast but we were not able to get good audio quality so I had the interviewed transcribed.
This is a two-hour math movie, divided into nine 13-minute sections. It is really well animated and will hold the interest of viewers of all ages. It is a film about dynamical systems, the butterfly effect and chaos theory.
Here are some of the questions we discussed:
- What inspired the two of you (and Aurélien) to create Chaos? What is exciting to you about chaos? Also, tell us about your Dimensions film.
- Please explain to our listeners what the film is about and who would enjoy it.
- Where does your excitement for math and physics originate from? Please share your stories of how you got inspired about physics.
- What inspired you to do animation?
- Tell us about the process and the technology you used to make the film. And, how long did it take to make it?
- What advice would you give to people who want to get into computer animation of mathematical ideas?
- First there was Dimensions. Now there's Chaos. What is your next big project?
Click here to enjoy the text of the interview.
You may remember these film makers from their 2008 movie, Dimensions.
Professor Dave Richeson is one of the most exuberant math people I've gotten to know but I didn't know how exuberant he was until I interviewed him. He's also involved in a bunch of neat projects. It was one of these projects, documented in Dave Richeson's blog article, How I teach topology: an inquiry-based learning approach, that caught my attention since I have a real passion for collaborative learning.
About Dave Richeson
Dave Richeson is an Associate Professor of Mathematics at Dickinson College. He graduated from Hamilton College in 1993 with a degree in mathematics and received a Ph.D. in mathematics from Northwestern University in 1998. He came to Dickinson College after a postdoctoral position at Michigan State University. He is passionate about many areas of mathematics, but his research focuses on dynamical systems, topology, the history of mathematics, and mathematics pedagogy. He is the author of Euler's Gem: The Polyhedron Formula and the Birth of Topology, which was published by Princeton University Press. Euler's Gem received the 2010 Euler Book Prize from the Mathematical Association of America and it was selected by Choice Magazine as an "Outstanding Academic Title" for 2009. He is currently writing a book on the four problems of antiquity. He is editor-elect for Math Horizons, a publication of the Mathematical Association of America. He enjoys sharing his enthusiasm of mathematics with others on his blog (Division by Zero, http://divisbyzero.com) and on Twitter (@divbyzero).
About "Euler's Gem"
From the Princeton University Press web-site:
Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.
From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.
Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
I got to spend a delightful hour today chatting with Shecky Riemann, apparently not his real name, discussing a bunch of math blogging stuff. It was great to interview a peer as this conversation had a lot of back and forth chatting that doesn't happen when I'm interviewing someone in a higher plane! Shecky's Math-Frolic blog is among my very favorites so it was super fun to get to know who the man is behind the monkey picture!
About Shecky Riemann
"Shecky Riemann" is the fanciful pseudonym of a former psychology/communications major (Pomona College/U of Kentucky) and lab-tech (primarily clinical genetics), who's been enamored of mathematics since childhood, and now hails from N. Carolina. Following Martin Gardner's death (2010), he was inspired to create Math-Frolic blog (and now also MathTango) to pay tribute to Gardner and be a cheerleader-of-sorts for those doing, or interested in, mathematics. He's especially intrigued with number theory, geometry, and the philosophical underpinnings of math. He sometimes enjoys hiking, birdwatching, tennis, flea markets, and hand-drumming. Cats, parrots, and shelties adore him.
From the welcome post:
WELCOME Math-Frolickers!… MathTango is intended (and it'll be a bit of an experiment) to be the new residence for longer, more original entries that were occasionally posted at Math-Frolic (including book reviews, interviews, and just lengthier posts in general). Math-Frolic will continue to be a linkblog for quick links to mathematical content that I find interesting and wish to pass along, as well as a portal to many other sites/pages, and will continue posting several entries per WEEK. MathTango, on-the-other-hand, is intended to have only a few postings per MONTH.
Tomorrow, the first post appears (a book review).
I look forward to following Shecky's new baby blog.
I just discovered the Math Munch blog. It promotes itself as "A Weekly Digest of the Mathematical Internet." Their blog further explains:
Here you will find links to lots of cool mathy things on the internet. We'll post some new items each week for you to enjoy. We hope you are as inspired and excited by these creations as we are!
This is a really terrific blog that's been publishing for just a bit over a year. It's chock full of images, graphics, and videos. Justin, Paul, and Anna, the "Math Munch Team" are doing a terrific job so I want to give them a plug.
Today I got to interview another great author of a Princeton University Press title. "Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry" is a delightful exploration of the techniques that ancient and medieval people from different cultures used to navigate and map the stars and the seas along with modern methods. There's a strong focus on the historical setting for these explorations. This setting brings the mathematics to life. I was very impressed to learn how very smart ancient astronomers and mathematicians were. Our twentyfirst century perception that we are smarter than our predecessors is simply not true. I was also delighted to learn an elegant variation of the familiar Pythagorean Theorem when applied to a sphere.
I thoroughly enjoyed getting exposed to this very elegant branch of mathematics and hope you too will catch some of Professor Van Brummelen's enthusiasm.
Chapter 1 of the book is available as a free PDF download.
About Glen Van Brummelen
From the Quest University Website:
Glen Van Brummelen, mathematics tutor, is a historian of mathematics, especially trigonometry and astronomy in ancient Greece and medieval Islam. He is past president of the Canadian Society for History and Philosophy of Mathematics, and senior fellow at the Dibner Institute for History of Science at MIT. In addition to authoring 30 scholarly and 10 encyclopedia articles, he is co-editor of "Mathematics and the Historian's Craft" (Springer) and recently published the first history of trigonometry in over a century with Princeton University Press called "The Mathematics of the Heavens and the Earth: The Early History of Trigonometry".
Glen has taught mathematics at small liberal arts colleges his entire career. He has taught over 30 different courses, including most traditional topics in math but also mathematics and music, mathematics and democracy, mathematics and computer graphics, spherical trigonometry (using a 19th-century textbook), and how to be an ancient astronomer. Several of his students have published their undergraduate research with him in recent years. In the summer he teaches the history of math regularly at MathPath, a math camp for bright 7th- and 8th-graders.
As if this wasn't enough, he keeps busy with his three very active kids of his own: Ariel (13), Matthew (9) and Andrew (5), all of whom will be mathematicians some day, and wife Heide (age unspecified). He is an avid soccer player, and played goal on the college team at his two previous colleges. He is undefeated at chess in the past 20 years, with a record of 2-0. Glen notes that "the key is to choose one's opponents carefully".
About "Heavenly Mathematics"
From the Princeton University Press Website:
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Dr. Keith Devlin joins me for a second podcast interview. Keith Devlin and I first spoke last February. Last night Keith Devlin shared in great detail his experience teaching "Introduction to Mathematical Thinking" MOOC (Massive Open Online Course). If you're considering enrolling in the MOOC when it's next offered in March, or if you might someday want to teach a MOOC, assist in a MOOC, or if you just want to understand the important role of MOOCs in the future of education, you won't want to miss this podcast.
Oh, and there's a teaser at the end about Dr. Devlin's next big "thing," being announced in just a few weeks.
More about Keith Devlin:
Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 31 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.
Shecky over at the Math Frolic Blog has been a great supporter of this podcast series and recently made this observation:
I've been pleasantly surprised by the degree to which 'math people,' including such prominent and busy ones as [Ian] Stewart, Keith Devlin, Steven Strogatz and others, are willing to share themselves with the learning community, through such online outlets. It is really wonderful, and I think a reflection of the desire on the part of mathematicians to transform their subject from one that is too-often feared to one for eager engagement.
Having had the opportunity to have a very pleasant and very informal conversation with Dr. Steven Strogatz this afternoon really brought home Shecky's point. Dr. Strogatz and others are making a difference by giving generously of their time to bloggers who aren't likely to reach as many people as their books will reach.
At the bottom of this post I feature two of Dr. Strogatz' books, "The Joy of x," published by Houghton Mifflin Harcourt, and the lesser known but equally important book, "The Calculus of Friendship," published by the Princeton University Press. We discuss both in the podcast.
About Steven Strogatz
From Dr. Strogatz' web-site:
Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He holds a joint appointment in the College of Arts and Sciences (Mathematics) and the College of Engineering (Mechanical and Aerospace Engineering).
After graduating summa cum laude in mathematics from Princeton in 1980, Strogatz studied at Trinity College, Cambridge, where he was a Marshall Scholar. He did his doctoral work in applied mathematics at Harvard, followed by a National Science Foundation postdoctoral fellowship at Harvard and Boston University. From 1989 to 1994, Strogatz taught in the Department of Mathematics at MIT. He joined the Cornell faculty in 1994.
He has received numerous awards for his research, teaching, and public service, including: a Presidential Young Investigator Award from the National Science Foundation (1990); MIT's highest teaching prize, the E. M. Baker Award for Excellence in Undergraduate Teaching (1991); the J.P. and Mary Barger '50 Teaching Award (1997), the Robert '55 and Vanne '57 Cowie Teaching Award (2001), the Tau Beta Pi Teaching Award (2006), and the Swanson Teaching Award (2009), all from Cornell's College of Engineering; and the Communications Award from the Joint Policy Board for Mathematics (2007), a lifetime achievement award for the communication of mathematics to the general public. In 2009 he was elected a Fellow of the Society for Industrial and Applied Mathematics for his “investigations of small-world networks and coupled oscillators and for outstanding science communication.” In 2012 he was elected a Fellow of the American Academy of Arts and Sciences.
Strogatz is passionate about public outreach and loves sharing the beauty of math and science with a wide audience. He has spoken at TED and is a frequent guest on RadioLab. In the spring of 2010 he wrote a weekly blog about mathematics for the New York Times; the Harvard Business Review described these columns as "must reads for entrepreneurs and executives" and "a model for how mathematics needs to be popularized." His second New York Times series, Me, Myself and Math, appeared in the fall of 2012. Strogatz has also filmed a series of 24 lectures on Chaos for the Teaching Company’s Great Courses series. He is the author of Nonlinear Dynamics and Chaos (1994), Sync (2003), and The Calculus of Friendship (2009). His most recent book, The Joy of x, was published in October 2012.
About "The Joy of x"
A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined
Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.
Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.
Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.
About "The Calculus of Friendship"
From the publisher's website:
The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough.
Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters.
For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.
Joshua Zucker shared this great Numberplay puzzle at the New York Times Wordplay Blog:
Start with a first row with two number ones separated by a space:
Row 1: 1 1
For each subsequent row, insert the sum between each two adjacent numbers, so you get:
Row 2: 1 2 1
Row 3: 1 3 2 3 1
Row 4: 1 4 3 5 2 5 3 4 1
How many 2013s are in row 2013?
Mircea Pitici has taken on a huge task, to present the best articles in Mathematics for the year. For three years running he's edited a book for Princeton University Press with his picks. Since identifying great communicators is a big interest of mine I'm delighted to get to pick his brain for an hour.
[ Note: The audio is a little bit choppy in places, especially the first few seconds. The phone connection was not the best so we did the best we could do. Call quality aside, this is an important interview for anyone interested in math communication. ]
About Mircea Pitici
From Mircea's Cornell web-site:
Mircea has taught mathematics courses and writing seminars at Cornell University, Ithaca College, and Wells College. He received a teaching award from the Cornell Department of Mathematics in 2011 and the Buttrick-Crippen Scholarship awarded by the Knight Institute of Writing in the Disciplines in 2008.
Deeply interested in mathematical communication to professional audiences and to the general public, Mircea edits the annual series The Best Writing on Mathematics (Princeton University Press). He holds a bachelor’s degree in mathematics from the University of Bucharest, Romania, and a master’s degree from Cornell, and he is working toward a doctorate in mathematics education at Cornell.
About "The Best Writing on Mathematics 2012"
From the Princeton University Press web-site:
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.