Franz Liszt was not the first one who started to perform without music. Clara Schumann was. The former gets the credit due to his name recognition, I guess.
Vladimir Horowitz was not good at memorizing music either. His public performance repertoire was rather limited, while his recording repertoire was much larger. He used music while he made recordings. During one of his performances on his famous Russian concert tour, he forgot the music and had to “embarrassingly improvising" to keep the music going.
Arthur Rubinstein had impeccable photographical memory. Late in his life, he said he could still “see” the coffee stains on the music which he used when he was a young boy.
