Halting Problem
There’s no algorithm that can decide, in general, whether any given program will halt.
Equivalently, there’s no algorithm that decides the truth of all arithmetic statements. If you tried to “implement all of classical math” as a total, always-terminating program that answers every question, you’d run into a contradiction or non-termination.
The halting problem is why we need branch prediciton in CPUs. Since they are turing complete.
About 1% of the time, we can’t predict which branch will be chosen.