Mathematics is a complex, fascinating and essential field that underpins many disciplines, including cryptography, cybersecurity and engineering. From ancient Babylonian times to the present day, mathematicians have studied and explored the myriad of topics in the field, developing new theories and discovering new applications. Names such as Pythagoras, Cartesian and Penrose are all linked to mathematics, with the latter being most famous for his work on Penrose tilings.
Tiling of surfaces is a common occurrence in many places, with examples such as bathrooms, kitchens and walkways. Carpeted areas often have square tiles, while roof tiles are designed to overlap to keep rain out without needing to be sealed. Penrose tilings, however, are a special class of tile patterns known as aperiodic tilings, as they never repeat, no matter how carefully the next piece is chosen and placed. This was discovered by Sir Roger Penrose in the 1970s.
Recently, a mathematical foursome led by British shape-searcher David Smith have claimed to have found an einstein, a single tile that can be repeatedly laid down to cover an infinite surface without ever repeating. This Holy Grail of tiles is a triskaidecagon, more creatively known as the Hat. The team have proved that the Hat generates an aperiodic pattern, and the proof has even been turned into a cookie cutter for those who want to explore this concept through baking.
To conclude, mathematics is a broad and ever-evolving field of study that has been explored for centuries. Today, it has many applications, from cryptography to engineering and cybersecurity. Penrose tilings are a particularly interesting part of mathematics, offering a finite set of shapes to create never-repeating patterns. The recent discovery of the Hat as an einstein is a major breakthrough that could have many practical applications in the future.