Tadashi Tokieda lives in a world in which ordinary objects do extraordinary things. Jars of rice refuse to roll down ramps. Strips of paper slip past solid obstacles. Balls swirling inside a bowl switch direction when more balls join them.

Yet Tokieda’s world is none other than our own. His public mathematics lectures could easily be mistaken for magic shows, but there’s no sleight of hand, no hidden compartments, no trick deck of cards. “All I’m doing is to introduce nature to the spectators and the spectators to nature,” Tokieda said. “That’s an interesting, grand magic show if you like.”

Tokieda, a mathematician at Stanford University, has collected more than 100 of what he calls “toys” — objects from daily life that are easy to make yet exhibit behavior so startling that they often puzzle even physicists. In public lectures and YouTube videos, Tokieda showcases his toys with witty, sparkling commentary, even though English is his seventh language. But his goal is only partly to entertain — it’s also to show people that scientific discoveries are not the exclusive preserve of professional scientists.

“The part of the universe that we can experience with our own biological senses is limited,” he said. “Nonetheless, in that range we can experience things ourselves. We can be surprised, not because we have been told to be surprised but because we actually see [something] and are surprised.”

Tokieda followed an indirect route into mathematics. Growing up in Japan, he started out as an artist and then became a classical philologist (someone who studies and reconstructs ancient languages). Quanta Magazine talked with Tokieda about his journey into mathematics and toy collecting. The interview has been condensed and edited for clarity.

You like to emphasize that the kind of toys for sale in a shop are not toys in your sense of the word.

If you can buy something from a toy store, then it’s not a toy for me, because that means that somebody has already designed a certain use for it, and you’re supposed to use it that way. If you buy some sort of very sophisticated electronic toy, the child is kind of a slave to this product. But it’s often the case that the child is completely uninterested in that toy itself but plays endlessly and happily with the wrapping paper and box, because the child by his own initiative and imagination makes those objects interesting.

People often confuse my toys with games — puzzles, Rubik’s Cubes and so forth. But these are absolutely outside my interest and competence. I’m not interested in games whose rules were set down by humans. I’m only interested in games set down by nature.

You see, puzzles are made by humans to make a situation tricky for other humans to crack. And that’s against my grain. I want all humans to cooperate and find something really good and surprising in nature and just understand it. Nobody should make it any harder. Nobody should put in any extra rules. A child and a scientist can share the same surprise.

How did you become a toy collector?

I used to do very pure mathematics — symplectic topology. And in those days, I could not possibly share what I was doing with friends and family who are not scientific.

But then when I was a postdoc, I was teaching myself physics and becoming a physicist, and some of it was tangible, especially since I’m often interested in macroscopic phenomena. So I decided that every time I wrote a paper or figured out something, however modest, I would design some tabletop experiment, or toy if you like, that I can produce in front of people in the kitchen, in the garden, and so on — some simple but robust thing that will share some of the fun I had in doing this. And of course, as you can imagine, this was a great success with friends and family.

And then it gradually took over, and now it’s the other way around. I look around my daily life and try to find those interesting phenomena. And then I start doing science out of that.

But you came upon one of your very first toylike phenomena much earlier in life, right? One that involves gluing together two Möbius strips and then cutting along their center lines, to produce, well, a surprise.

I stumbled on it when I was about seven. Anyone who is interested in mathematics plays with Möbius strips in childhood, obviously, and there’s a lot of places in popular literature that tell you that it’s interesting to cut a Möbius strip along the center line. And I was a Japanese boy interested in origami, so it’s very natural for such a boy to do this.

But then, between cutting the Möbius strip along the center line, and gluing Möbius strips together and then cutting — well, I wouldn’t call it an inevitable step, but there is a heuristic step there. It’s not that it’s miles off. And once you take that step, you discover a wonderful phenomenon, which is so beautiful and romantic. It’s waiting for you there.