Wondrous qualities can be found in even the smallest details, through the eyes of Japanese mathematician Tadashi Tokieda. ‘Small mathematics in a big world‘ felt more like a spectacle than a public lecture. “Billions of people around the world drink from a cup like this,” he proclaimed as he walked onto the stage, displaying a little white teacup.

 

With a keen eye for enigmas in daily life, Tokieda’s work has been crucial in the dissemination of mathematics. The puzzles that he discovers and solves captivated the curiosity of both children and experienced mathematicians at an ICM public lecture.  Introducing his colleague, Marco Moriconi (Federal Fluminense University) revealed a unique trajectory: “He started as a painter in Japan, became a classical philologist in France, and a mathematician in England.”

 

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His observations were about familiar objects, but his questions profound. Why does a coin falling to the ground make that iconic sound it makes? Why does the sound of a spoon hitting the side of a teacup change in pitch or stay the same depending on the point along its rim? His persistence with these mysteries opens pathways to concepts of physics and mathematics that are often ground-breaking.

 

Tadashi Tokeida with rice-filled jars and an inclined plane

 

With the air of a magician, he opened an old Russian tin of tea. A camera filmed his movements up close, projecting them onto the screen behind. “Georgian tea, extra quality, ” he translated effortlessly from Russian. Removing several scented cedar wooden balls from the tin, he placed a few in a bowl and started swirling anticlockwise. “They swirl in the same direction as the cup,” he observed, adding a few more, “but if I increase the number of balls, they will start swirling in the opposite direction. It is very, very interesting. There has been a change of state, such as the change from gas to liquid. With just a few balls, they behave like independent particles. But after five units, each spin rubs off on the next, and they start to move in unison. “The crowdedness is the only parameter,” he explained, as he continued to swirl and add more balls. “If you keep increasing the number of balls, it eventually freezes the movement.” From gas to liquid to solid, he demonstrated the transitions of movement to the bewilderment of the audience.

 

Speaking as fast as the host of an auction, he moved from object to object without pause: rolling heptagons, paper balloons, origami polygons, and rice-filled jars rolling down a slope. “Every once in a while, you run into a person who happens to be carrying an inclined plane,” he joked, without breaking his seemingly serious demeanor. “One of the jars is filled with basmati rice from India and the other with air from Rio de Janeiro. One jar is empty and the other one 100% full.” He went on to show the audience other jars – 1/3 full, almost empty, and 2/3 full – and the incredibly different ways they roll down a slope. The angle of repose must be less than the point of gravity to force a downward motion. The experiment also contains two opposing physical forces: viscous and inviscid movement.

 

The most commonplace items contain examples of astonishing laws of physics and mathematics. “In all natural phenomena there is something of the marvelous,” he concluded.