Abstract: How densely can one pack identical balls that do not overlap in $R^n$? Although it looks like an innocent question, this turns out to be one of the most difficult problems in geometry. Before 2016, the answer for the problem was known only in dimensions 1, 2 and 3. In 2003, Cohn and Elkies found a connection between this problem and a Fourier optimization one. Using Cohn and Elkies result, Viazovska constructed magic functions that solve the sphere packing problem in dimension 8 and, later on, she and her collaborators also solved the problem in dimension 24 using similar techniques. In this talk, we introduce the sphere packing problem and discuss Viazovska's construction and the role played by modular forms in it.