Pikachu
The mysteries surrounding Pikachu are primarily biological and thermodynamic. How does a 6-kilogram rodent generate 100,000 volts? What metabolic pathway converts berries into lightning? These questions, whilst entertaining, admit straightforward answers: the creature operates according to cartoon physics, not natural law.
The fictional nature of Pikachu places firm boundaries on its mystery. All questions can be answered by consulting canonical sources or, in their absence, simply inventing consistent explanations. The mystery is manufactured, not inherent.
Time
Time has confounded the greatest minds in human history. Newton believed it absolute; Einstein demonstrated its relativity. Quantum mechanics suggests it may not exist at fundamental scales. Philosophers continue debating whether Time flows, whether the present is real, and whether the past persists.
The harder science examines Time, the stranger it becomes. It dilates near massive objects, freezes at light speed, and may run differently in parallel universes. Despite millennia of investigation, we cannot definitively explain what Time is, only what it does.