Question: Why would human physicists care a fig about solving 3-body math/algo?

Still only half-way through 1st book, so this may be answered as I read on.
By Chapters 16 & 17, it becomes obviously that at least 3 people - Wei Cheng, Shen Yufei, and Wang Miao - have been actively involved in trying to solve the physics & mathematically-challenging 3-body problem - plus a few others in other countries.

Why?

Since Earth has no multi-sun 3-body problem, why would earthly physicists even be looking into this? Even if astronomers noticed other star systems, 100s of light years away, that demonstrated possible multi-sun, multi-orbit problems, why would brilliant earth-bound mathematicians and physicists spend even one minute of time trying to isolate a pattern that could predict stable-period livability on distant planets in those suns' orbits?

Even for 'theoretical curiosity' - since no application would be needed on Earth - I cannot imagine brilliant physicists wasting a lifetime of hours and computer resources on such an abstract non-sequitur.