In life Neuhaus's effect on those around him was profound. His death on October 10, 1964, was mourned as the end of a cultural epoch not only by his closest friends and students, but beyond: “Despite not formally being his student, with news of Neuhaus's death, in our minds we were saying farewell to a person who had become the symbol of artistry and high spirituality in music. For me this loss severed my ties with the conservatory that had meant so much to me.” The idea that the rich inner world supporting his interpretations, his unique autopsychography, was so specific to Neuhaus that it precluded its being passed on as an inheritable legacy, can likewise seem to advocate a bitter sense of finality.

Neuhaus thought it inconceivable for a pianist's inner world of knowledge, emotions, and daily life not to be reflected in some way in his interpretations. As a pedagogue, however, Neuhaus did not try to ingrain his own experiences in the student, but rather tried to awaken the student's curiosity and capacity for expression. Although Neuhaus gladly left tantalizing elements of his inner world as revealed in his articles, open lessons, performances, and lecture-recitals, it was a spiritual labyrinth that he was reluctant to make accessible. Despite being a vibrant and sometimes scandalous figure on the Soviet music scene, known for his fiery temperament, dreamy gaze, and liberal tongue, few outside his closest circle knew much about his life.

Places and events that held emotional significance for him and acted as artistic images that shaped his interpretations, were far too irrelevant to be useful to those who did not share in these experiences. Even when he made direct references to his beloved literary titles, not many could claim that their knowledge of these texts was anywhere as thorough or profound as his, even after spending years in his company. His manner of associated thought was fast-paced and interdisciplinary and it delighted him to weave into his written work unidentified citations of poetry and philosophy. It is, however, unlikely that most of Neuhaus's audiences would be able to instantly identify and appreciate these fully. Neuhaus's terrifying reproaches—such as his famous “You have not read Kant!”—were always left open-ended and were never followed by an explanation.