Higher brain function : music, mathematics, chess. History, anecdotes, correlations, and interviews ; Spatial-temporal and language-analytic reasoning in learning math and science ; Music enhances spatial-temporal reasoning ; Implications : scientific, educational, clinical -- Structured brain and symmetry. Symmetry as a common theme ; Introduction to the brain : basic brain features and brain imaging ; Mountcastle theory of mammalian cortex : internal neural language of higher brain function ; Trion model and symmetries ; Trion music : reasoning and creativity ; Trion model of higher brain function : prediction that music enhances spatial-temporal reasoning -- Tests of predictions in human behavior. Highly accurate mental rehearsals : correlation with top performance in sports ; Listening to Mozart Sonata (K.448) enhances spatial-temporal reasoning : the "Mozart effect" ; Music training enhances spatial-temporal reasoning in preschool children ; Music training plus spatial-temporal training equals improved math -- Tests from brain imaging and animal studies. EEG and fMRI studies of Mozart effect ; Symmetry in primate higher brain function ; Musical structure of the internal neural language of the brain : using music as the Rosetta stone to help decode this internal language ; Animal behavior while listening to music and doing higher brain functions -- The future of music as a window into higher brain function. Child brain development and adult brain reorganization ; Education : music training plus spatial-temporal training improves math ; Clinical implications ; The spatial-temporal thinking machine ; Final thoughts.