Nets Katz California Institute of Technology The sums differences approach is a set of problems in additive combinatorics for which the optimal results could completely solve the Minkowski version of the Kakeya problem. There are non algebraic combinatorial approaches, the elementary proofs, which give the best known results in the Kakeya problem in high dimensions, but these approaches cannot solve the Kakeya problem. In principle, the polynomial method might provide a non elementary approach.