The video celebrates the year 2025, a special year because the creator will turn 45, which is the exact square root of 2025. This unique coincidence inspires a birthday celebration themed around squares, highlighting the mathematical beauty of square numbers. The creator reflects on the significance of 2025 not only as a square number but also its connection to triangle numbers, specifically that 45 is the ninth triangle number. This leads to an exploration of interesting mathematical relationships, such as the sum of cubes equaling a perfect square, which is a rare and fascinating property.
To illustrate these concepts, the video showcases a physical installation created in collaboration with Jane Street, a financial company that sponsors the creator’s videos. The installation consists of acrylic layers representing cubes of different sizes, stacked to demonstrate the sum of cubes equaling 2025. This puzzle, known as the Partridge Puzzle, challenges participants to arrange these layers into a perfect 45x45 square. The puzzle is notoriously difficult to solve by hand, requiring careful planning and often resulting in dead ends, as early placement decisions heavily influence the possibility of completing the arrangement.
Despite the puzzle’s complexity, there are over 1.7 million possible solutions, discovered through computer algorithms developed by the creator and collaborators. These solutions vary in structure, including L-shaped arrangements and single stacks of nine-by-nine squares, with some solutions being more aesthetically pleasing and balanced than others. The video highlights the collaborative effort between the creator, Jane Street employees, and programmers who wrote code to find and categorize all possible solutions, demonstrating the intersection of mathematics, programming, and problem-solving.
The video also features interviews with Jane Street employees who discuss their experiences attempting the puzzle physically and then turning to computational methods to find solutions. They explain the backtracking algorithms used to systematically explore possible configurations, emphasizing the puzzle’s difficulty and the satisfaction of finally solving it. One employee, Andy, is noted as the only person known to have solved the puzzle by hand, underscoring the puzzle’s challenge and the dedication required to tackle it.
Finally, the video connects the mathematical theme to Jane Street’s broader work in quantitative trading and machine learning. It introduces a neural network puzzle created by Jane Street’s machine learning team, inviting viewers to engage with it as a test of their analytical skills. The video concludes by highlighting the company’s culture of valuing puzzle-solving abilities as a proxy for problem-solving skills in their work, encouraging viewers interested in such challenges to explore career opportunities with Jane Street. The creator also mentions performing at the Edinburgh Festival Fringe, tying together the themes of creativity, mathematics, and community engagement.
