Komlós' discrepancy conjecture

Let $n$ be a positive integer, and let $\bm{v}_1,\dots,\bm{v}_n\in\mathbb{R}^n$ satisfy $\|\bm{v}_i\|_2\leq 1$ for $i\in[n]$. Komlós' conjecture. There exists a constant $C$ such that one can choose signs $x_1,\dots,x_n\in\{-1,1\}$ with

$$\left\|\sum_{i=1}^n x_i\bm{v}_i\right\|_\infty\leq C.$$

This is a central open problem in discrepancy theory, asking whether vectors with uniformly bounded Euclidean norm always admit a signing whose coordinate discrepancies are bounded independently of the dimension.