When I was a kid, I used to wonder about numbers and shapes. Math always seemed like something ancient that was already figured out. But today, modern mathematicians are exploring new and uncharted territories.
In this episode of Science Quickly, we dive into the world of modern math with mathematicians like Eugenia Cheng and Craig Kaplan. They are pushing the boundaries of what we know about numbers, shapes, and patterns.
One fascinating area of math is tiling. Think of the tiles on your kitchen backsplash or bathroom floor. Mathematicians study how shapes can cover a flat surface without gaps or overlaps. Periodic tilings repeat in a gridlike pattern, while aperiodic tilings do not repeat themselves.
In the 1960s, mathematician Robert Berger shocked the math world by showing that you could tile an infinite plane with a finite set of shapes. He started with 20,426 shapes, then reduced it to just 2 shapes. Later, mathematicians like Roger Penrose proved that you could aperiodically tile an infinite plane with just one shape.
Recently, a mathematician named David Smith discovered a new shape called the “hat.” This hat shape turned out to be the first-ever aperiodic monotile, meaning it could be duplicated infinitely without repeating the same pattern. This discovery opens up a world of possibilities for creating new and unique designs.
But the implications of tiling research go beyond just creating beautiful patterns. In the past, Penrose tilings found in nature led to the development of new materials like nonstick pans and ultrastrong steel. Aperiodic monotiles like the hat shape could have similar practical applications in the future.
Mathematics is not just about solving problems with clear answers. It’s about exploring the unknown, pushing the boundaries of what we know, and finding joy in the process. Mathematicians are like artists, using their creativity and imagination to unlock the mysteries of numbers and shapes.
So the next time you look at a tile on your kitchen floor, remember that behind that simple shape lies a world of mathematical discovery and innovation. Math is not just a subject to be learned in school; it’s a playground where we can explore, create, and have fun.