Hip to be Square

Zach Wissner-Gross (Five Thirty Eight) shares a Dean Ballard puzzle about partially covering a square with non-overlapping squares. https://fivethirtyeight.com/features/are-you-hip-enough-to-be-square/ What is the greatest number of white squares you can place so that each covers part of the blue square without overlapping one another? (The entire blue square does not have to be covered, while the blue area that each white square covers must be nonzero.)