Memory is not an art, nor could it ever be. The arts are Memory's gift to us, but memory itself cannot be taught or attained by any art. It is an advantage that some receive from nature, or the luck of their immortal soul. Without it, humanity would have no connection to eternality, and nothing we learn could ever be taught, if Memory did not dwell within us.
Whether Memory should be called the Mother of Time or its Child, I leave to the poets, who can say what they want. But no one among the truly wise would be dumb enough to throw away their good standing by [claiming to train the memory through mystic arts, and] posing like a juggler in front of little kids—the kind of thing that gives actual pedagogy a bad name.
So how did the students of Dionysius of Miletus all have such prodigious memories? The answer is that his lectures were so enjoyable that his listeners craved to hear them again, and Dionysius, in awareness of his own charisma, was obliged to repeat them many times. They became stamped in the minds of his brightest students, who declaimed them to each other until all had memorized through practice what memory alone could not supply. This is how they came to be called the "Mnemonic School," and were credited with turning memory into an art. It's also why people say the declamations of Dionysius are a piecemeal corpus, augmented in different places by different individuals where Dionysius himself had been succint.
From Lives of the Sophists by Flavius Philostratus