Erika Klarreich, Quanta Magazine, Mathematicians Shed Light on Minimalist Conjecture, here. This is a Simons Foundation publication.
Millennia ago, mathematicians explicated the rational solutions to polynomials whose highest exponent is less than 3. And 30 years ago, Gerd Faltings, now of the Max Planck Institute for Mathematics in Bonn, showed that most polynomial equations whose highest exponent is greater than 3 can have at most a finite sprinkling of solutions.
But cubic equations have defied mathematicians’ attempts to classify their solutions, though not for lack of trying. Attempting to classify the rational solutions to cubics — more specifically, to a family of cubics called elliptic curves which are, with a few exceptions, the only cubics that can have any rational solutions — has occupied all the great number theorists of the modern age, starting with the 17th-century French mathematician Pierre de Fermat, said Benedict Gross of Harvard University.
Andre M. Konig, The NYC startup scene, here.