There are many discoveries in Shakespeare's The Tempest.
Prospero, the usurped King, is marooned on an a desolate island with his daughter Miranda. He has the opportunity to finally take revenge on the wrong doers who plotted against him, taking his throne and setting him and his daughter adrift many years ago. Most importantly, the storm that sends his enemies towards him is a storm that Prospero has magically conjured.
The play itself works from the discovery of the island. The shipwreck carrying Alonso, Antonio and his party are taken away from their usual world to a sometimes dangerous and lonely place. Here the interplay of the imagined world and the real world takes place as Prospero decides what to do with his enemies.
We see many examples of wicked human behaviour, the wrecked team plotting against each other with dangerous subterfuge; we also see Caliban, who represents the bestial in man, drunk and always behaving badly. As such we see much evidence to suggest that harsh punishment is the only way to deliver justice and to create order in an unruly world. For the plotters they finally discover remorse for their actions; for Caliban he has nothing but regret for having discovered knowledge through language. He rather had stayed ignorant than to know of 'better' ways.
Prospero's daughter Miranda, seeing her first potential man partner ever, Ferdinand, discovers love, and also learns about her noble past. We also see the lovers playing chess at the play's conclusion, a reminder that love is a game that has rules; there is more to love than just passion and powerful emotions. As such, Miranda makes may discoveries which are unexpected.
Prospero however decides to pardon rather than punish Alonso and Antonio, the plotters, motivated by his consideration of the future world to be inherited by his soon to be married daughter Miranda. Prospero discovers virtue over vengeance.
A storm is an unpredictable thing, unleashing unpleasant chaos upon humanity. The Tempest is a storm, both metaphorical and real - it is the moment of fury, Prospero storm and his fury, a decisive moment of revenge for Prospero. The question is, how will he act towards those who have harmed him and who are now in his reach? How will he met out justice, if at all, in a world where plotting, murder and base desire are forever present, but a world into which those he loves will inherit and live in and hopefully….prosper? ( yes - it's a pun on the character's name !)
The play reminds us that life is not always smooth sailing, and that discovery can be both pleasant and unpleasant, with the consequences of responsible action.