Been a long time since we had a very deep connect, so here goes.

The mathematician/astronomer (1) solved an age old problem in classical mechanics (X) in an interesting way. He predicted a quirky side-effect of this (Y) that was only confirmed many years later in the interactions between (2) and the groups represented by (3) and (4).

Identify 1, 2, X, Y and the groups represented by 3 and 4.

Cracked by vijayaraghavan , udupendra , Chandrakant Nair , joe , akhi , Prasad , Atul Mathew , Dibyo , varuns88 , Rohan and ludwig. Glad many of you liked the question, too :-)

vijayaraghavan, udupendra, Chandrakant Nair, joe, akhi, Prasad, Atul Mathew, Dibyo, varuns88, Rohan and ludwig