Published books

How can we prove that a determinant is not merely large—but as large as mathematically possible?

Unlocking Maximal Determinants over Third Roots of Unity transforms Daoyu Dong’s order-15 proof into a clear, step-by-step journey through one of computational mathematics’ most intricate determinant problems.

At its center is a remarkable exact result: among all order-15 matrices whose entries are third roots of unity, the maximal determinant is $120,932,352\sqrt{19}$. But discovering this value is only part of the story. Proving that no matrix can do better requires a powerful combination of Eisenstein arithmetic, Gram matrices, spectral inequalities, support graphs, Schur complements, and carefully organized computational elimination.…