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The winters mattered because of what they ruled out.
Two decades of trying to build intelligence from logic and rules had produced real systems, and real evidence that logic and rules alone weren't enough.
That negative result cleared the ground. Researchers who came after could stop treating the old approach as the obvious path forward, because the winters had shown its limits.
What came next, the learning-based AI that eventually became the systems people learned to interact with directly, grew from that cleared ground.