Prove or disprove the existence of God.
Answering this question requires a definition of God, which we don't have of course. We could propose a temporarily definition like 'God is the entity that created life on planet Earth, a modest definition because it leaves the question of who created the universe unanswered.
Although still debated, Gödel's incompleteness theorems imply that we won't be able to build computers with a conscious mind capable of creating new mathematics or writing a program that solves all open problems in mathematics. Besides cloning and modifying what we have ( DNA ) we won't be able to create a 'machine' smarter than ourselves.
Our own existence is a paradox we don't understand. History proves that in cases like that humans are creative in inventing a God capable of fixing any problem. Despite centuries of scientific advances we still need a God to explain our existence.