You might remember the media storm a few months ago about the schoolboy who "solved problems posed by Sir Isaac Newton that have baffled mathematicians for 350 years"
, etc., etc.. (e.g. http://bit.ly/KPeBFk
At the time there was no real explanation of what he had done. Now there is, courtesy of Ralph Chill and Jürgen Voigt at Dresden University: goo.gl/jh6Pr
The answer is that he produced analytic solutions for the equations of motion of a particle in fluid and under gravity, e.g. the path of a ball (modelled as a particle) travelling through the air, taking air-resistence into account.
So, did mathematicians already know how to do this? Short answer: yes."The work is without doubt exceptional for a high school student and it merits the attention that it received in a national science competition for high school students... nevertheless all his steps are basically known to experts, and we emphasize that he did not solve an open problem posed by Newton."