An elementary proof of the Komlós conjecture

We give an elementary proof of the Komlós conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors $v_1,\dots ,v_n\in {\mathbb{R}}^d$ with $\mathrm{\parallel }{v}_i{\mathrm{\parallel }}_2\le 1$ admit signs ${\epsilon }_i\in \{-1,1\}$ such that $\mathrm{\parallel }{\sum }_{i=1}^n{\epsilon }_i{v}_i{\mathrm{\parallel }}_{\mathrm{\infty }}\le 36$. The proof uses only elementary combinatorial and probabilistic arguments and basic calculus.