It wasn’t until Tadashi Tokieda, now a professor of mathematics at Stanford University, was in his twenties that he began to study math. Growing up in Japan, Tokieda was a painter, and later in France he was a classical philologist – an expert in ancient languages. While in a mathematics program at Princeton University, he broadened his studies to include physics and other phenomena of the natural world.

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Eventually, Tokieda combined all of this with his long-standing interest in magic, and videos of his resulting tricks have attracted millions of views online.

At the root of Tokieda’s unusual career path and varied interests is a deep appreciation for the value of surprise.

“To me, surprise means that I used to assume something – to think something was absolutely true – and then it turns out to be wrong,” said Tokieda. “I’m really hungry for surprises because each one makes us ever-so-slightly but substantially smarter.”

Rather than building on science that has a long legacy and is often at the edge of breakthrough – what he calls “science in flower” – Tokieda prefers pursuing answers amidst the unknown – “science in bud.” He likes to share his discoveries with others, often while he’s still exploring what he’s found. For this purpose, Tokieda has collected and fashioned over 200 toys and tricks to model the surprises he studies.

Compared to typical playthings, Tokieda’s toys are common objects that, when manipulated or thought about in creative ways, do something unexpected. These are not to be mistaken for oversimplified teaching implements but rather instruments of surprise that are designed to encourage a collaborative discovering experience.

From magic to math

A memorable exchange between a professor and student during the first math lecture Tokieda ever attended in part inspired his career path.

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“I got the surprise of my life when a student suggested that something didn’t seem right and the professor looked at it for a few seconds and said, ‘Ah, yes. I’m wrong. You are right,’” recalled Tokieda. “To hear a dignified adult say that and just move on? It was astonishing!”

Tokieda maintains that deep appreciation for the privilege of being wrong, considering every mistake or overturned assumption an opportunity for learning and discovery. For this reason, he gravitated toward studying familiar phenomena and objects, which are particularly ripe for revelation because we accumulate a lifetime of assumptions about how they work and why. Dealing in these also helps non-scientists, colleagues in other fields, and friends and family share in Tokieda’s experiences of discovery.

“I decided that each time I figured out something or wrote a paper, I would design a little tabletop experiment which would show – if only partially – the fun and the surprise that I experienced when I was doing the research,” said Tokieda.

His collection made the recent journey overseas from the University of Cambridge to its new home on the shelves of his Stanford office. Some of the toys and tricks can be seen in action in the videos produced by Numberphile. This August in Rio de Janeiro, Tokieda will give one of the public lectures at the International Congress of Mathematicians on a particularly intriguing selection of these toys and the theme of “singularity” that emerges from them.

Inspiring science

Many of Tokieda’s magic tricks require only everyday items, such as paper, rubber bands and coffee mugs. Other parts of his repertoire are extensions or examinations of toys that already exist, including a penguin that rocks down a wooden ramp, spinning tops and a kendama, the traditional Japanese wooden skill toy where the player attempts to swing a ball onto a spike.

Tokieda prefers tricks that can build on each other and moments of wonder that take time to perfect. The magic teaches him as well, with new curiosities occasionally leading to publications.

No matter who is in Tokieda’s audience as he performs a trick – whether a family member, a student or a renowned mathematician – he hopes to elicit the same reactions of astonishment and curiosity. And even if he’s done this trick a hundred times before, he is always looking for new surprises and seeking opportunities to make himself and others ever-so-slightly but substantially smarter.