We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence.

我们讨论了球的稳定同伦群的当前知识状态。我们描述了一种使用动机同伦理论的计算方法，这种方法被视为经典同伦理论的一种变形。这样就可以对前61个稳定的同伦基团进行简化的计算，并提供有关尺寸62至90中的稳定的同伦基团的信息。作为一个应用，我们确定了同维球体的组，这些同构球体通过尺寸90对球体上的光滑结构进行分类，除了维数4.该方法比以前的方法更依赖于机器计算，因此不易出错。主要的数学工具是亚当斯光谱序列。