Question

can it be poved mathematically that EM waves are transverse in nature????

Answer 1

use the dot product to prove that the direction of motion is always perpendicular to the electric and magnetic fields.

Answer 2

Its like asking can you prove mathematically that planets attract each other with 1/ r^2 law :D
its one of fundamental facts of the universe.. that Em waves ARE transverse.. once we UNDERSTAND it.. (ofcourse experimentally.. polarization proves it), then we build the math behind it.. right?.. ;-)