Classical physics is fun

Should anyone think that only the quantum boundaries of physics are interesting, here is an example: The Existence of Noncollision Singularities in Newtonian Systems by Zhihong Xia
The Annals of Mathematics, 2nd Ser., Vol. 135, No. 3 (May, 1992), pp. 411-468.

Unfortunately, I know this article only by reflected light, I have not been able to find a freely accessible version. But the ripples and comments it has made are quite numerous, for example Noncollision Singularities: Do Four Bodies Suffice? by Joseph L. Gerver, or EJECTIONS AND CAPTURES BY SOLAR SYSTEMS

What is the point: simple that there is a possibility to cleverly construct a classical (Newtonian) system of five bodies that would result in expulsing one of them to infinity in finite time.

Just pure fun? Not really - it turns out that such result has implicationsas to physical computability, Church-Turing hypothesis, the whole issue of determinism in classical physics. If a body can be expulsed to infinity that by simple time reversal and initial conditions reversal a body can appear in the system and become a part of it, in finite time from infinity! And this means that there might be an essentially unknown and unknowable influence (unknowable because it is infinitely removed) that would act on the system - again, not infinitely far in the future but in finite time.

The paper is quite old (15 years) but compared to the age of Newtonian theory it simply shows that an old dog still has a lot of tricks to learn.