Mathematically, with truly infinite monkeys, typewriters, and time, they would eventually produce Shakespeare's complete works with probability 1, but recent studies show that in our finite universe, even with countless monkeys typing for eons, the chance is astronomically small, essentially impossible, far exceeding the universe's lifespan. The classic theorem highlights probability, but real-world constraints (finite time, atoms, energy) make it practically impossible, meaning we're more likely to see "infinite broken typewriters" first.