Is the three-body problem actually unsolvable, or just unsolved?
It is genuinely unsolvable in the sense that matters: there is no general closed-form analytical solution. This is not a gap waiting for a smarter mathematician. A two-body system like Earth orbiting the Sun has an exact solution — Kepler ellipses, clean formulas you can run forward ten thousand years. Add a third comparable mass and the equations stop yielding any closed expression. The problem was effectively settled in the 1890s, not last week.
Who proved the three-body problem has no solution?
Henri Poincaré, in the late 1880s, while competing for a prize set by King Oscar II of Sweden on the stability of the solar system. Studying the three-body problem, he found the system is extremely sensitive to initial conditions: change the starting position or velocity by a hair, and the trajectories diverge wildly within a few steps. That discovery is the actual birth of chaos theory, decades before Edward Lorenz popularized the "butterfly effect."
If it is deterministic, why can't a computer just calculate it?
Because chaos is deterministic but not predictable. Every step obeys Newton's laws exactly — nothing is random. The trap is sensitivity to initial conditions: you can never measure the starting state precisely enough, and any measurement error grows exponentially. A tiny rounding difference today becomes a completely different orbit later. Simulation gives you short-term forecasts, but long-term prediction is mathematically out of reach. The same chaotic logic underlies how the chaotic motion of three suns governs the novel's world.
What about Sundman's series solution?
In 1912 Karl Sundman did publish a convergent series solution. It is real, and it is useless in practice — the series converges so slowly that reaching meaningful accuracy would need an astronomically large number of terms (estimates run to roughly 10 to the 8-millionth power). So it "exists" mathematically while being computationally hopeless. Mathematicians can solve only special cases: Lagrange points, Euler's collinear configurations, the figure-eight orbit found in 2000 — all carefully tuned setups that collapse back into chaos the moment you nudge them.
How does Liu Cixin use this in The Three-Body Problem?
He turns a math fact into a survival condition. The Trisolaran world orbits three suns (modeled on Alpha Centauri), and their chaotic motion means the planet can be scorched, frozen, or flung away with no warning. Civilization advances only during rare Stable Eras and dehydrates through Chaotic Eras. Wang Miao's repeated failures to predict the suns inside the Three Body game dramatize the unsolvability directly, and the Trisolarans' eventual choice to emigrate rather than predict is the story admitting the problem has no answer. For the full audit of what the trilogy gets right and wrong about real physics, the chaos of the three-body problem is the one piece of hard science the novel builds its entire premise on.