Sphere packings in 8 and 24 dimensions: a new construction

Viazovska was awarded a Fields medal for the solution of the sphere packing problem in dimensions 8 and 24: what is the densest packing of spheres in 8 and 24 dimensions?  The key to the solution is a function whose Fourier transform has very special properties. These functions are popularly called “magic functions”. Inspired by a paper on circle packings in the massive OpenAI dump of papers on October 6, this talk will give a new construction of the magic functions. The magic functions are obtained by solving an infinite linear system of equations.  This new construction was discovered by ChatGPT, with prompting provided by the speaker.  Reference: hexagon:2610.00330v1.