Every performing instrumentalist faces the issue of playing from memory. Most of us have over the years managed to store an enormous amount of repertoire in our brains' memory circuits. Yet the thought of performing something in public can be a scary thought. Obviously, if someone is to play a work only once, doing so by heart seems a pointless waste of time, energy and nerves. There is a difference in knowing a piece from memory and being able to execute it faultlessly in front of an audience. Most of us, at least the sensitive ones, have a fear of playing wrong notes or just making a fool of ourselves in front of a crowd.
I maintain that in order to understand a musical work, one cannot be tied to the written text and has to have every note imprinted in his/her memory. Even if one decides to keep the sheet music available, it should be for reference only and counter possible mistakes by a musical partner, such as an accompanist. Those can become quite unnerving: if you expect to hear something and it is not there or shows up in a wrong place, your first reaction is that you have made a mistake. Then there are those unwritten rules of playing sonatas with music. In good old days it was considered a sacrilege for a violinist to perform a Beethoven or Brahms sonata without the music in front of him/her. One didn't necessarily open the book but it was there out of respect, the same way a man of cloth would not quote the Bible without having the book at hand.
As a teenager in1967 I was in Vienna, Austria, and bought a ticket to hear David Oistrakh play the Beethoven Violin Concerto during the Festwoche. I had already heard him play numerous times and was looking forward to this concert as Oistrakh was considered a Beethoven expert and had performed this piece probably more than a thousand times. During a first movement the soloist got lost and panicked. One memory lapse was followed by another and yet another. I remember counting eight major ones. To a young unknown soloist this would have meant an abrupt end to his/her career but since Oistrakh was a hero, the audience responded with an instant standing ovation and the applause took easily a quarter of an hour to die down.