# ¶ Rational points

Mathematicians sometimes make a game of counting rational points on elliptic curves with rational coefficients over <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">\mathbb R</annotation></semantics>[/itex], in other words, considering the mathematical structure of the curve over <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">Q</mi></mrow><annotation encoding="application/x-tex">\mathbb Q</annotation></semantics>[/itex] (the rationals) rather than <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">\mathbb R</annotation></semantics>[/itex] (the reals).