The purpose of the paper is to give the state of the art on Michael's problem, the long-standing open question odf continuity of characters on commutative Fréchet algebras. We first quote two well-known consequences of the "abstract Mittag-Leffler theorem", the theorem of Arens, which shows that characters on finitely rationally generated Fréchet algebras are continuous, and the fact that the existence of a nonincreasing sequence (Ωn) n≥1 of Fatou-Bieberbach domains in C p such that ∩ n≥1 Ωn = ∅ would imply that all characters on commutative Fréchet algebras are continuous. In the opposite direction the existence of a discontinuous character on some commutative unital Fréchet algebra is equivalent to the existence of a character on a quotient algebra of the form U/I where U is a 'test algebra' for Michael's problem and where I is a dense ideal of U which is a Picard-Borel ideal, which means that every family of pairwise linearly independent invertible elements of U/I is linearly independent. It was recently shown that all Picard-Borel ideals in commutative unital Fréchet algebras are prime, and Picard-Borel ideals of H(C) can be easily described. We raise a question concerning Picard-Borel ideals of H(C p), p ≥ 2 which could lead to important general information about the quotient of commutative unital Fréchet algebras by Picard-Borel ideals. The fact that entire functions of several variables oerate on quotients of Fréchet algebras by ideals which are not necessarily closed plays an essential role in the paper.Read less <