size ''height'' important example gauss circle problem asks integers points ''x'' nbsp ''y'' satisfy math x leq r math geometrical terms given circle centered origin plane radius ''r'' problem asks many integer lattice points lie inside circle hard prove answer math pi r e r math math e r r math math r infty math difficult part great achievement analytic number theory obtaining specific upper bounds error term nbsp ''e'' ''r'' shown gauss
Formal science Mathematics Pure mathematics Number theory Analytic number theory