Although it's a meaningful break-thru in the field of mathematics, this will not affect how ballistic calculations are done at all.
Here's my take.
Newton formulated his laws of motion which are basically formulas which describe how things move, collide, etc. Then he and others set about to solve the formulas so we can predict things. We've been very successful at solving the formulas in many ways. Especially with modern computational power, we can apply iterative (time stepping) solutions which solve the equations of motion in tiny (0.001 seconds or smaller) time steps which result in answers that are approximate
by math standards, but that just means they're not guaranteed to be accurate to the 100th decimal place; NOTHING of practical concern. What this young German (or Indian?) boy has done is to solve the equations of motion for projectile flight in an analytical
form, which is what mathematicians consider 'exact'. The solution is far more efficient since you don't have to take many small time steps, but considering modern computational resources found even in small phones, the efficiency is a non-issue in most applications.
Some more detail about the 'break-thru' solution:
* The exact analytic solution assumes constant drag coefficient, which is only close to reality in pure subsonic flight. So the equation cannot be applied accurately to supersonic flight at all.
* The 'stroke of genius' that made the analytic formula possible was a transformation of variables from positional space to 'velocity space'. Transformation of variables is a known means of solving problems in math but it takes great insight to find a transformation that will actually work.
My hat's off to the young man for his genius. Unfortunately I don't see this break-thru affecting our ability to calculate trajectories any more accurately than we do now.
In my experience, the biggest limitation with our ability to predict accurate trajectories is accurate inputs: MV, BC, atmospherics, range, actual value of scope adjustments, etc.
Sorry to be a buzz kill, but the news is well known for pumping things up.
Here's a link to a site where you can read more discussion about the actual math, by actual mathematicians:
klackity comments on Teen Solves Newton