delusion
A strong false belief that ignores clear facts and reality.
A delusion is a false belief that someone holds onto firmly even when presented with clear evidence that it's wrong. Unlike simply being mistaken (like thinking your test is on Tuesday when it's actually Wednesday), a delusion persists despite facts that prove otherwise.
In medicine, delusions can be symptoms of serious mental illnesses. Someone might believe they have superhuman powers, that people are plotting against them, or that they're a famous historical figure, even when friends, family, and doctors gently explain that this isn't true. These kinds of delusions require professional help.
More commonly, people use the word delusion in everyday conversation to describe unrealistic beliefs that aren't quite as severe. If your friend insists he's going to become a professional basketball player despite never practicing and being the shortest kid in class, someone might say he's deluding himself. When we're under a delusion, we're fooling ourselves about reality.
The phrase delusions of grandeur describes believing you're more important, powerful, or talented than you actually are. A student with delusions of grandeur might assume they'll ace the final exam without studying, simply because they think they're naturally brilliant.
Being delusional means holding beliefs disconnected from reality. It's different from being optimistic or hopeful: optimism means believing good things are possible while working toward them, while delusion means ignoring facts entirely.