#PhysicsJournalClub
F. Diacu "The Solution of the n-body Problem"
Math. Intell. 18, 66 (1996)
https://doi.org/10.1007/BF03024313
In Physics we are often guilty of cutting corners when it comes to Mathematics (to be honest, we are in very good company). One example is in Chaos theory, where statements like "the 3-body problem is unsolvable" are common but misleading.
The author of this paper actually complains about his fellow Mathematicians colleagues (not about Physicists), and then explain in a very understandable way how the sentence "the 3-body problem is unsolvable" must be understood (spoiler: it just means we have fewer conserved quantities than degrees of freedom), how a full solution to the n-body problem in terms of an infinite but convergent series had been found already in 1991 by a Chinese student, and how this solution (albeit correct) is completely useless for any practical purpose, as it converges horribly slow.
An easy and very interesting reading if you know just a little bit about classical mechanics.