Mathematicians have solved several long-standing problems that have implications for digital data storage, privacy of electronic communications, and modeling the properties of complex systems. A team at Brown University solved the interpolation problem, which asks for a curve that passes through a million points in a 1,000 dimensions. Researchers at Technion University and the University of Texas solved the bubble problem, which asks for the optimal configuration of larger bubble clusters. And mathematicians at Stanford solved the Kahn-Kalai conjecture, which allows researchers to better understand the properties of complex networks.
1. Euclid proved the shape of a line and circle over 2000 years ago
2. The interpolation problem deals with finding a curve through a million points and has applications in data storage, cryptography, and communication
3. Eric Larson and Isabel Vogt solved the interpolation problem for all possible types of curves
4. The bubble problem involves finding the optimal configuration of multiple bubbles
5. John Sullivan described the optimal cluster for bubble configurations in the late 19th century, and it took until 2002 for mathematicians to prove it for double bubbles
6. Milman and Neeman proved Sullivan's conjecture for triple bubbles and are working towards solving the problem for clusters of up to five bubbles
7. Random graphs are used to model complex systems and finding thresholds is a central subject in random graph theory
8. The Kahn-Kalai conjecture involves determining the location of thresholds for many interesting properties, and a logarithmic factor is used to estimate this location
9. Jinyoung Park and Huy Pham stumbled upon an elegant six-page solution to the Kahn-Kalai conjecture while working on related conjectures
10. Park and Pham utilized a mathematical object called a cover to prove the Kahn-Kalai conjecture and their proof is expected to lead to new breakthroughs in understanding complex properties of networks.