Math isn't ready to solve this problem

Mathematicians study rational points on algebraic curves, seeking coordinate pairs where both x and y are rational numbers satisfying a given equation.

Ancient Greek and Babylonian mathematicians discovered the one-to-one correspondence between rational points on the unit circle and primitive Pythagorean triples.

Mathematicians study elliptic curves as fundamental objects in algebraic geometry and number theory, with equations of the form y² = x³ + ax + b where a and b are integers.

Poincaré developed the cord and tangent process in the late 1800s as a method for generating new rational points on elliptic curves from known ones.

Mathematicians characterize the dimension of rational point structure on elliptic curves using the concept of rank, describing how many independent generator points are needed.

The rank conjecture poses one of mathematics’ most difficult open problems, stating that among all elliptic curves, 50% have rank zero and 50% have rank one.

Mathematicians Armand Brumer, David Heath-Brown, and Matthew Young progressively improved average rank bounds using analytic number theory from 1992 through 2006.

Manjul Bhargava and Arul Shankar proved in 2015 that the average rank of elliptic curves is at most 1.15, work that contributed to Bhargava’s 2014 Fields Medal.