The problem of modeling the creativity is shown to be entirely connected with another mysterious challenge — the “Explanatory Gap” between the concepts of “Brain” and “Mind”. We use the Natural Constructive Cognitive Architecture, with its important feature being the combination of two subsystems, for generation of new information and for its conservation. “Brain” is considered as records of the raw images of real objects (individual objective information), while “Mind” refers to individual subjective information created inside the cognitive system (symbols). We argued that creativity can be treated as “an effort to bring a piece of personal “Brain” into the “Mind” and World”. Specific thinking mode (intellectual panic or throes of creativity) is shown to enhance the creative work resulting in over-mobilization and even enriching personal deep inside (“Brain”) experience. It is simulated by chaotic jumps of the noise amplitude around abnormally high value. The nature of Aesthetic Emotions and the concept of Chef-D’oeuvre are analyzed. It is shown that they are caused by the “recognition paradox”: an object seems both, familiar but unusual. This occurs if the “Brain” does see its subtle features, while the “Mind” does not realize. Bright aesthetic emotions (goosebumps) are caused by irregular excitation of implicit associations provided by weak (“gray”) connections of the halo neurons (simulating the subconsciousness). General formula for Chef-D’oeuvre in science and art could be expressed as “condensed capacity to see the invisible, to combine the incompatible”.