Newton could thus confirm Kepler's laws from a single hypothesis of the inverse square law, with Newton as mathematician thereby convincingly playing the role God! This gave mathematics a tremendous boost into the queen of sciences with immense (seemingly magical) power, which is the basic argument behind extensive compulsory school mathematics: Learn math and play God!
But if Newton was playing with one planet, God is playing with many planets and thus solves the N-body problem of N bodies moving under mutual gravitational attraction with N any number. But already the 3-body problem has resisted analytical solution since Newton, which can be seen to signify the unreasonable ineffectiveness of analytical mathematics in Hamming's formulation.
But the N-body problem can be solved by computational mathematics for N very large, which expresses a reasonable effectiveness of mathematics + computer.
You can explore the N-body problem in the following apps for young minds:
- Dark Energy: NewMath by Claes Johnson
- Mechanics1: NewMath by Claes Johnson