In this fashion did Turjan enter his apprenticeship to Pandelume. Day and far into the opalescent Embelyon night he worked under Pandelume's unseen tutelage. He learned the secret of renewed youth, many spells of the ancients, and a strange abstract lore that Pandelume termed "Mathematics."

"Within this instrument," said Pandelume, "resides the Universe. Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space. Your spells and runes are built upon its power and codified according to a great underlying mosaic of magic. The design of this mosaic we cannot surmise; our knowledge is didactic, empirical, arbitrary. Phandaal glimpsed the pattern and so was able to formulate many of the spells which bear his name. I have endeavored through the ages to break the clouded glass, but so far my research has failed. He who discovers the pattern will know all of sorcery and be a man powerful beyond comprehension."

So Turjan applied himself to the study and learned many of the simpler routines.

"I find herein a wonderful beauty," he told Pandelume. "This is no science, this is art, where equations fall away to elements like resolving chords, and where always prevails a symmetry either explicit or multiplex, but always of a crystalline serenity."

This is a fantastic series of stories, straddling the line between science fiction and fantasy. Apart from its mathematical content (which is minimal) this story and its fellows have always inspired me to enter the sciences.

This is one of my favorite passages in the Dying Earth books. I am by no means a math person, but had I heard this description in high school it may have changed my opinion.

I just re-read this story yesterday. I always wished Vance would have gone into a little more detail on the relationship of the spells to the mathematics. But I'm not really sure that he actually had a theory about it. He loved to suggest ideas to the reader and let them fill in the details in their own minds.