A hyperoval is a set of q+2 points in a finite projective plane of even order, with no three collinear. Its classification, which is still in progress, has motivated more than seventy years of work in finite geometry, with connections to number theory through finite-field arithmetic, to algebraic geometry through curves over finite fields, and to combinatorics and coding theory. I will survey the development of the subject from the classical conic and its nucleus to nonclassical examples and the o-polynomial representation of hyperovals. I will conclude with recent progress on rigidity and local recognition, showing how incidence information from the lines through only a few points, when translated into finite-field arithmetic, can impose strong constraints on the entire geometric configuration.

丁治国，现为湖南师范大学教授，曾就职于国防科技大学，中南大学。丁治国教授于中国科学院获得博士学位，研究方向为数论。他长期与国际知名数学家 Michael Zieve合作，在有限域的算术领域做出了一系列杰出工作，研究成果发表于Proc. Lond. Math. Soc., Int. Math. Res. Not., Science China Math., J. Comb. Theory A., J. Number Theory, J. Algebra等著名期刊，获得了国内外同行的广泛认可，并曾受邀在第十届世界华人数学家大会(ICCM2025)作报告。