James Tanton wears multiple mathematical hats. He is an ambassador for the Mathematical Association of America (currently serving as their Mathematician-at-Large, a fabulous title!), Chair of the Advisory Council for the National Museum of Mathematics (MoMath), cofounder of the Global Math Project, an author of mathematics books and two Great Courses DVD series, and is constantly hopping about the place to give demonstration classes in schools, workshops for educators, and general public outreach lectures on the joy of thinking and doing mathematics. He is also instigator of the International Mathematics Salute. (Did you know there is one?)
Before we ask James about the Global Math Project, we thought we’d ask for some background about his journey to mathematics.
I grew up in Adelaide, Australia, and did all my school and undergraduate work there. I certainly have devoted my career to mathematics, and I certainly have been a mathematical thinker all my life. But it took me a while to recognize that. The problem was that my mathematics K-12 education was, by and large, joyless. This is no fault of my teachers. The nature of an unenlightened 1970s curriculum, focused on “memorize and do” and on answering lots of what questions that no child naturally asks in the first place.
I was good at the curriculum. I got labeled as “talented” in mathematics. But I did not enjoy the subject one whit. I decided that mathematics was not for me. Though, I was doing mathematics somewhere else, which only now, in hindsight, I recognize as such.
My childhood home in Adelaide was an old Victorian house and each room had a floral patterned pressed-tin ceiling. The design for my bedroom ceiling was particularly striking: the vines and flowers outlined a very clear pattern of twenty-five squares arranged in a five-by-five array. Every night of my childhood fell asleep staring at that pattern. And, of course, I made up puzzles for myself to do with that grid: How many squares can I count? (55) How many rectangles can I count? (225) And so on. But there was one puzzle I made up for myself that had me stumped for years! It was this one.
Can you see what the puzzle is? Starting at different positions, is it possible to trace a path of vertical and horizontal steps that visits each and every cell exactly once? Try the puzzle for yourself. You’ll find that some starting positions swiftly lead to paths and other starting positions seem somewhat troublesome for this task.
I played with this puzzle for years, trying to find paths that would start at the troublesome spots, suspecting after a while that no paths from them were possible. But I must have been an unusual child: just because I tried to find a solution and failed to do so a large number of times does not prove that no solution exists. I wanted an iron-clad logical reason as to why finding proper paths from those identified troubled spots could not done.
But a piece of such logical reasoning eluded for years. It bugged me.
Then one day, while walking to school in grade 10, and not even thinking about this problem, I was struck by an incredible flash of insight: I suddenly saw in my mind’s eye what to do to the grid to make it visually obvious as to why no paths could possibly exist from all spots. An iron-clad proof, a stunning visual proof, hit me hard. I became so thrilled and excited, but I couldn’t share my discovery with anyone. The puzzle I made up for myself had nothing to do with what I was studying in school, certainly not in mathematics class. It looked nothing like math. I didn’t even think it could be classified as related to math!
I carried on with my schooling, went to Adelaide University, and got a degree in Theoretical Physics. But I took a class in Abstract Algebra along the way and then it hit me: my childhood puzzle was mathematics! I was doing mathematics. I am a mathematician!
Mathematics is all about the play of ideas, exploration beyond what questions, to why questions, and what else question, and, better yet, what if questions. I was home! In fact, I realized I was home all along. It was clear that was going to pursue mathematics as far as I could. I came to the U.S. in 1988 to start graduate school at Princeton, and in 1994 obtained my PhD in Mathematics.
But something else was becoming clear to me at the time. I reached the high-powered math world for sure, but I felt the calling to teach. Basically, to share with the world the joy and love I have for the subject. So I decided to follow an academic career with a strong focus on, and value of, teaching. I worked in the Liberal Arts College environment for many years and just loved it. I was at St. Mary’s College of Maryland for the bulk of my tertiary education career. There I met my fabulous wife, Lindy Elkins-Tanton.
For Lindy to pursue her academic career in geophysics, we moved to Boston. And there I fell into the wonderful world of Math Circles. I helped conduct the Boston Math Circle program with Bob and Ellen Kaplan, and also, somehow, also fell into consulting work got K-12 educators. Both led me to look deeply into the state of mathematics school education, and when I did, I was shocked: I saw, by-and-large, the same, unenlightened mathematics curriculum that I had gone through some 30 years earlier half-way across the globe. Had nothing changed? Why not? What are the barriers to joyous and confident mathematical thinking in the K-12 world? It is not the children – they are fabulous! The teachers are not to blame – all the folk I met and worked with obtain the name of fabulous too! Is it the system?
I felt morally compelled to try understand what is going on and I decided then to fully immerse myself in the K-12 world and become a high-school teacher. One snag: With only a PhD in Mathematics from Princeton, I wasn’t qualified to teach. My solution: Enter the private school world. I understand it is not akin to the full public school experience. Although, I worked at a boarding school, was required to live on campus, and provide classes six-days a week, and so it had its own series of cultural adjustments for me.
I taught at St. Mark’s School in Southborough, MA, for eight-and-a-half years. (I had one year at another school prior to that, but we shan’t talk about that. Not a good fit.) Not only did I teach full time and worked as a dorm parent, I also created an Institute of Mathematics for public outreach. In conjunction with Northeastern University I developed, and conducted each year, five graduate mathematics content courses for in-service teachers. I also ran ten-week long extracurricular math research classes for children all across the Boston area, gave workshops and lectures, wrote articles and books, and did all I could humanly do to promote joyful mathematics for one and all. And it was a joy for me too.
The Joy of Math
During one of my outreach lectures, I met a lass by the name of Cindy Lawrence. While introducing herself she said that she was in the process of establishing a math museum, the nation’s first math museum in fact. And I knew she meant it and that it was going to happen! The sparkle and joy in her eye made it clear she was a person of action, with a kindred passion for sharing mathematical wonder and love with the world. I was a friend of MoMath even before it had doors to open. Cindy is also a cofounder of the Global Math Project.
My greatest challenge as a high school teacher was the one that drew me to it: how can I teach the standard curriculum, of which I have no control, and still teach the joy and love and poetry of mathematics to uplift the soul, help my students become confident “flailers” – to try things, to get things wrong, to persevere, that is, to flail with confidence and success – and to still pass all those timed, high-pressure tests? I loved that challenge. I am not sure I always succeeded, but I got some major parts of it right. Tthe joy of math and the societal expectations of math, both met. This is what led me to write books, develop www.gdaymath.com and the videos on www.jamestanton.com, and more.
Then my fabulous wife got offered a Directorship at the Carnegie Institute of Science in Washington DC, and off we went. It turned out, unbeknownst to me, that I had a bit of a reputation and the MAA offered me a position as their Mathematician-in-Residence upon my arrival. I felt flattered. They simply asked me to continue the outreach work I was planning to do and help promote the MAA in all the fabulous work it does, both in undergraduate collegiate education, and in its support of K-12 education too. I felt honored, and thrilled, and I said YES. (Check out the MAA’s Curriculum Inspirations Project too, www.maa.org/ci, to see some of the work we did to bring problem-solving into the classroom.)
Next, my fabulous wife, who I will follow anywhere, became lured to Arizona State University. She’s Director of the School of Earth and Space Exploration. (She is, literally, a NASA rocket science, leading the 2022 space mission to the asteroid Psyche.) And it turned out – flattery again – that the MAA decided I wasn’t really leaving and made me their “Mathematician-at-Large.”
My work now is to think about and write about mathematics, answers loads of emails about mathematics teaching and thinking, and to hop on planes and go talk to wonderful students and teachers all across the globe about joyous mathematics.
I am a mighty lucky fellow: to be married to Lindy, and to have a career that allows me follow and share the pure, uplifting joy of mathematics.
Recently, I wrote to the occupants of my childhood home back in Adelaide and told them the story of the bedroom ceiling. I hoped that they might be able to send a photo of it. Sadly, the house has since been remodeled and the pressed-tin ceilings have been taken down. Never mind. The love for mathematics that that ceiling induced endures.
James Tanton (PhD, Mathematics, Princeton 1994) is committed to sharing the delight and beauty of the subject. In 2004 James founded the St. Mark’s Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He worked as a fulltime high-school teacher at St. Mark’s School in Southborough, MA (2004-2012), and he conducted, and continues to conduct, mathematics courses and workshops for mathematics teachers across the nation and overseas.
James is the author of Solve This: Math Activities for Students and Clubs (MAA, 2001), The Encyclopedia of Mathematics (Facts on File, 2005), Mathematics Galore! (MAA, 2012) and twelve self-published texts. He is the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark’s School, and a 2010 recipient of a Raytheon Math Hero Award for excellence in school teaching.
He also publishes research and expository articles, and through his extracurricular research classes for students has helped high school students pursue research project and publish their results. James is currently an ambassador for the Mathematical Association of America and Advisory Council Chair of the National Museum of Mathematics in New York.
James is married to Lindy Elkins-Tanton, a planetary scientist with expertise in planet formation and evolution and Director of the School of Earth and Space Exploration at Arizona State University. He is absolutely adoring his life with her and they are very much fascinated by the flora and fauna of Arizona. Their backyard is full of all sorts of birds and critters, with the occasional visits of coyotes, road runners, and bob cats too. They still have a little vacation home in the hills of Massachusetts, and enjoy visiting there too whenever they can. They very much enjoy exploring nature.
When not working on a space mission or on mathematics (or both), James and Lindy love to cook, play silly games, watch both good and bad TV, and host dessert and wine evenings with friends.
You can see the influence of James’ childhood five-by-five in much of his work. For example, see his video contribution to MoMath’s BEAUTIFUL MATH project here: http://momath.org/home/beautifulmath/. In part II of this piece we’ll learn about the Global Math Project.