"[4] In 2018, he was awarded the Levi L. Conant Prize for his article “A Conceptual Breakthrough in Sphere Packing,” published in 2017[5] in the Notices of the AMS.

[6] In 2003, with Chris Umans, Cohn initiated a group-theoretic approach to matrix multiplication,[7] and is a core contributor to its continued development with various coauthors.

[8][9][10][11][12] In 2004, Cohn and Noam Elkies used linear programming methods to prove[13] upper bounds on sphere packings in all dimensions.

In March 2016 Maryna Viazovska published[14] an arXiv preprint with such a magic function - a weakly holomorphic quasimodular form - proving the optimality of the E8 lattice packing.

Cohn contacted Viazovska, and within a week, Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Viazovska had similarly solved the sphere packing problem in 24 dimensions via the Leech lattice Λ24.