## Democratizing Mathematics

An Interview with Dr. James Tanton

An Interview with Dr. James Tanton

**How did you get interested in mathematics as a career?**

Growing up as a young lad back in Australia, I actually went through my education in a rigid style of education that was just “memorize and do.” Early on, I was taught that my role was not to ask questions, especially in the mathematics class: just repeat, regurgitate, and do 50,000 pushups (i.e., exercises). It was joyless, but I was good at it. I was even labeled gifted, which I thought was absurd.

But, there was one particular puzzle I made for myself that I could not answer for years: a simple idea that stuck in my craw for years…[until] I was suddenly hit with an epiphany!

**What is the most fulfilling part of your work as a practicing mathematician?**

I love cracking the nut of mathematics for other people, showing them that the joy and beauty of mathematics is actually within their reach.

We say mathematics has much practical utility, that it’s all about applications to real world problems (which is quite motivating). But, the other side of the coin is that mathematics is philosophical and joyous, and artistic, and all the rest, which is what I value, but people don’t tend to see that side. I want to share that side of the coin and how both sides work together. Practical application often motivates such beautiful abstract mathematics; while, at the same time, abstract thinking often motivates practical mathematics.

For example, [Marin] Mersenne, back in the 17th century, was playing with the powers of two, when he decided to subtract one from each of the powers of two and found that they were prime very often. And then he wondered, How often are they prime? It turns out those Mersenne prime numbers are the key to all of today’s cryptology networks–banking encryption, internet encryption, etc. are all based on Mersenne primes. Who knew that this curious, quirky, abstract, just-for-the-fun- of-it question back in the 17th century would have a profound, practical application in the 21st century? That’s fantastic!

**What are the most important features of mathematics that should be conveyed to children (and their parents)?**

The number one message is that mathematics is a human enterprise and students are to be their fabulous human selves in relation to it… So, be bold and ask a question about what it is right in front of you.

The next thing is to acknowledge the human reaction to solving problems in mathematics… We often teach kids that they have to be right the first time they try something. I say don’t do anything relevant to the mathematics problem but do something. Could be as simple as turning the page upside down. Read the question backwards. Underline some words, draw a picture, draw a fish, close the book and go outside to let the problem sit on your mind for the day and then come back to it—or do something relevant to the problem. I think that’s the nature of mathematics, where the joy and beauty come from. We have to let that happen. It’s really a mulling process, giving students the permission to be human: to not know what to do, to flail and flummox. But let that mulling and the subconscious work on things. And then you’ll experience those epiphanies as little flashes of insight to take you forward on a journey you weren’t expecting. And that’s where the surprises happen.

**What mathematical problem are you currently investigating?**

I am actually obsessed with something that arose from just the very simple story of place-value, the exploding dots thing [see www.explodingdots.org]. Fractional bases are deeply mysterious. So, with the exploding dots machine, two dots in the box explode to become one, which leads you to base two. Or, ten dots explode to become one leads you to base 10. But you can do quirky things like three dots in the box explode to become two dots—that’s actually base 11⁄2. There’s good meaning to having fractional bases, and it’s driving me bonkers. In fact, there are unsolved problems to this day. For example, there’s only 10 numbers known to be palindromes in base 11⁄2, and 17 is the largest one [21012 in base 11⁄2]. Why does this obsess me? I don’t know. It’s just quirky and weird and fun—and why not?!

Doing mathematics properly requires one to think in a certain way about a certain sort of thing (mathematics), and eventually one becomes familiar with it and how it tends to go.

This Socratic approach equips students to take more responsibility for their learning, increasing their confidence and motivating them to undertake the further exploration of mathematical reality, just as Socrates did with the young boy in Plato’s *Meno*.

Practical application often motivates such beautiful abstract mathematics; while, at the same time, abstract thinking often motivates practical mathematics. It’s time to share that side of the coin and how both sides work together.

*Virtue *is the flagship publication of the Institute for Classical Education. It disseminates stories, ideas, research and experiences in classical education to readers across the nation, helping them pursue the classical ideals of truth, goodness, and beauty.