In vertebrates, ovulation is triggered by a surge of LH from the pituitary. The precise mechanism by which rising oestradiol concentrations initiate the LH surge in the human menstrual cycle remains a fundamental open question of reproductive biology. It is well known that sampling of serum LH on a time scale of minutes reveals pulsatile release from the pituitary in response to pulses of gonadotrophin releasing hormone from the hypothalamus. The LH pulse frequency and amplitude vary considerably over the cycle, with the highest frequency and amplitude at the midcycle surge. Here a new mathematical model is presented of the pituitary as a damped oscillator (pulse generator) driven by the hypothalamus. The model LH surge is consistent with LH data on the time scales of both minutes and days. The model is used to explain the surprising pulse frequency characteristics required to treat human infertility disorders such as Kallmann's syndrome, and new experimental predictions are made.