I will start with a motivation of what algebraic (and model-theoretic) properties an algebraically closed field of characteristic 1 is expected to have. Then I will explain how these properties can be obtained by the well-known (in model theory) Hrushovski construction and then formulate very precise axioms that such a field must satisfy. The axioms have a form of statements about unlikely intersections in terms of a 'multi-dimensional' valuation theory and the validity of these statements is an open problem to be discussed.