I firmly believe that, in the coming years, molecular biology will play a rolein shaping mathematics research analogous to that played by physics during thepast three centuries. New areas in mathematics will arise, and novel problemsin established areas will be formulated. These will provide the conceptualframework needed in order to analyze, and eventually help solve, many of thequestions of central importance to biology.After a quick introduction of some basic concepts in biochemistry andgenetics, as well as some basic notions of feedback control, the emphasis ofthe talk will be on "systems molecular biology" as a generator of new problemsin mathematics, and particularly in control theory.Rather than generalities, the talk will specifically describe several researchvignettes (picked from my own recent work), including (and subject to timelimitations): the development of monotone i/o systems, in order to analyzesignaling cascades under negative feedback (small gain theorems) and positivefeedback (multi-stability and hysteresis); the formulation of an "internalmodel principle", motivated by E-coli chemotaxis; the study of robustly stablechemical reactions, motivated by kinetic proofreading and receptor-ligandmodels, and associated new types of global nonlinear state estimators; a noveltechnique for unraveling gene and protein network structure; and mathematicalobstructions to regular feedback laws, giving rise to the need for hybridcontrollers.