This is genuinely uncertain, and I'd be skeptical of anyone who claims confidence either way.

**Reasons it might not:**
- AGI may arrive later than expected, or prove harder than anticipated
- Governance structures could successfully constrain AI systems
- "Rule" implies goals and agency that AGI might not have in relevant ways
- Multiple competing AI systems might balance power rather than concentrate it
- Humans may remain in meaningful control loops

**Reasons it might:**
- 2100 is a long timeline; transformative AI seems plausible well before then
- Economic and military advantages could make AI dominance a convergent outcome
- Human institutions often struggle to regulate powerful technologies
- Recursive self-improvement could create rapid capability gains

**The question itself is tricky:**
- "Rule" could mean many things—direct control, or just being indispensable to decisions
- It might be AI + certain humans rather than AI alone
- The transition could be gradual enough that "ruling" isn't the right frame

My honest take: By 2100, AI systems will likely be deeply embedded in how power operates. Whether that constitutes "ruling" depends on definitions. The question of alignment and control seems more important than the prediction itself.

What aspect interests you most—the timeline, the governance challenge, or something else?
