In, The Tempest, William Shakespeare introduces the character Prospero as a magus, an adept at occult, but white, magic. In creating this character, Shakespeare drew on several real people living in the late 16th century.
The first of these is the Welsh mathematician and astronomer, John Dee. Dee had served as astrologer to Queen Elizabeth, though James I’s religious objections to anything that smacked of the supernatural left him out of a job.
During the Renaissance, the word occult didn’t necessarily have the malevolent connotations it does not, it merely meant “hidden.” Astrologers, alchemists, and even mathematicians were search for the hidden nature of the world around them.
Dee, however, moved increasingly towards the mystical as he got older and believed he could invoke spirits he believed were angels, one of which he named Uriel. The latter bit sounds very much like what Prospero does, and he is served by a sprite called Ariel. Dee was noted for having an enormous library on both science and the occult, again very much like Prospero.
Because of John Dee’s fame in the Elizabethan court, it’s very clear that Shakespeare would have known about him.
Danish astronomer Tycho Brahe is the next candidate for influencing Shakespeare. While Tycho was primarily an astronomer, he was also an alchemist and he was interested in medicine as well.
There’s a direct connection from Shakespeare to Tycho via the king. When James was still James VI of Scotland, he was engaged to (and married) Anne of Denmark. When he traveled north for the wedding, his ship was battered by storms and nearly sunk. On that same voyage, he visited Tycho, who lived on an island that he had complete control over, much as Prospero ruled his island. Tycho also had a dwarf for a jester who was said to be quite ugly and a marriageable daughter, elements which show up in The Tempest as well.
Again, Shakespeare would have been familiar with the adventures of the king, and also he’d written about Denmark earlier in Hamlet, and there are those who suggest Tycho shows up there as well.
Both John Dee and Tycho Brahe were commoners, however, and Prospero is presented as royalty – the deposed Duke of Milan. This brings us to the third influence, Rudoph II of Bohemia.
Rudolph, who was also the Holy Roman Emperor, was fascinated by art, science, and the occult, and spent huge sums of money acquiring scientific instruments, supporting alchemists, and commissioning or purchasing art. John Dee visited Rudolph in 1584, hoping to held discover the philosopher’s stone, and Tycho Brahe moved to Prague in 1601 to work for Rudolph after he fell from favor with the King of Denmark.
In 1606, Rudolph’s brother Matthias stripped him of his crown and he lost the rule of Hungary, Austria, and Moravia, and in 1609, Matthias made him a prisoner in his own castle in Prague. Prospero, as you may recall, was usurped by his brother Antonio and imprisoned as well.
Of course, there’s one more factor in play here, as well. Many scholars consider Prospero to be a metaphor for Shakespeare himself, with Prospero’s magic arts an analog for Shakespeare’s stage magic. At the end of The Tempest, Prospero puts aside his magic cloak and staff and retires from the practice of the occult arts. The Tempest was Shakespeare’s final play. (Shakespeare did collaborate on three other works following The Tempest, but didn’t write anything further on his own.)