I like geometry, and probabilities. Geometry was always a favourite
Though ancient Greek mathematicians pretty much used algebra along with geometry, eg there is a very elegant work by Archimedes, where he uses his idea of the balance/scale in geometry, so as to come up with calculating the relation between the volumes or related (same diameter) spheres, cylinders and cones.
Also the pythagorean proof for the existence of irrational numbers is very beautiful - using just geometry (it was about the square root of 2).
Though ancient Greek mathematicians pretty much used algebra along with geometry, eg there is a very elegant work by Archimedes, where he uses his idea of the balance/scale in geometry, so as to come up with calculating the relation between the volumes or related (same diameter) spheres, cylinders and cones.
Also the pythagorean proof for the existence of irrational numbers is very beautiful - using just geometry (it was about the square root of 2).