Journal cover: Notices of the American Mathematical Society

Notices of the American Mathematical Society

Welcome to the current issue of the Notices of the American Mathematical Society.
With support from AMS membership, we are pleased to share the journal with the global mathematical community.

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On the Geometry of Deep Learning

Randall Balestriero, Ahmed Imtiaz Humayun and Richard G. Baraniuk

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in multiple dimensions). In particular, we overview work over the past decade on understanding certain geometrical properties of a deep network’s affine spline mapping, in particular how it tessellates its input space.

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Selected Results from the Mathematical Conventions Survey

Thomas Lam

Mathematics is fraught with an amusing number of clashing conventions. The author amassed 100 such questions and sent them out in a survey to a few friend circles and social media sites. The survey and its results proceeded to go viral, particularly on TikTok, and he received a wide range of emotional responses towards his work. In this article, he discusses a few questions from the survey that are likely to be of general interest to the mathematical community.

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Short Stories: Triangulations of the Sphere

John C. Baez

If you cut out this star, you can fold it into a polyhedron where all 11 of its tips meet at one point. This polyhedron will be tiled by the small gray equilateral triangles, though some may get bent. There will be 12 points where five such triangles meet: the 11 indentations in the star, and the point where all its tips meet. There are also points where six triangles meet. This may seem like a curiosity, but Bill Thurston discovered some profound facts about stars of this sort.