Komlós's Conjecture

Komlós’s Conjecture is an unsolved problem in mathematics related to sequences of vectors in a high-dimensional space. It asks whether, given any bounded sequence of vectors, it is possible to find a way to combine their averages so that the resulting sums stay within a specific limit, regardless of how the original sequence behaves. In essence, it explores whether there's a universal method to control the combined size of averages of these vectors, which has implications in areas like probability, analysis, and combinatorics. The conjecture remains open, posing a fundamental challenge in understanding the structure of vector sequences.