There are many other versions of this ancient puzzle. The French philosopher Jean Buridan used its contradictory logic in his proof of God's existence: "God exists. None of the sentences in this pair are true." There's also the self-referential chain, "The following sentence is true. The following sentence is true. The first sentence in this list is false."
Here's why the liar paradox causes philosophers so much grief: if the sentence is true, then it must be false. But if the sentence is false, then it must be true. That's what makes it a paradox. It's an argument that leads to a self-contradictory conclusion. There are probably as many schools of thought on how to solve this paradox as there are philosophers in the world, but one thing is true (not false!): it highlights the limitations of classical logic. Puzzle over potential solutions to the paradox with the video below.