Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of Mathematicians 2022. It covers recent advances in the study of critical point equations in optimization and statistics, and it explores the role of nonlinear algebra in the study of linear PDE with constant coefficients.

翻译：作者在2022年国际数学家大会上发表演讲的同时,这篇文章介绍了最近在研究优化和统计的关键点方程式方面取得的进展,并探讨了非线性代数在以恒定系数研究线性PDE中所起的作用。