The rivalry between two of the 20th century art world’s most towering figures, Henri Matisse and Pablo Picasso, was complex, and by some accounts, fiery, attracting its own mythology. In a story related by the American writer and art collector Gertrude Stein, the two artists swapped paintings in the autumn of 1907, Matisse choosing Picasso’s still life Pitcher, Bowl and Lemon and Picasso picking Matisse’s portrait of his daughter Marguerite. Picasso’s followers proceeded to use the painting of Marguerite as a dart board.

“But of course there are no dart holes in the painting,” says Jane Kinsman, Head of International Art at the National Gallery of Australia, where the relationship between Matisse and Picasso is charted in a new exhibition. While the story may be dubious, it speaks to the intensity of the competition between the artists – and Kinsman posits that the “Picassoites” were “far meaner about Matisse than probably Picasso was.”

The two artists knew about each other before...