He went to the Leiden University, where he obtained an MSc degree cum laude in mathematics in 1983.

[5] Van der Vaart was elected a member of the Royal Netherlands Academy of Arts and Sciences in 2009.

[8] In 2015 he was one of four winners of the Dutch Spinoza Prize and received a 2.5 million euro grant.

[10] On being awarded the prize Van der Vaart stated that 2.5 million euro was too much, claiming he could have 35 postdoctoral and Ph.D. students work with the grant.

[11] In June 2019 Van der Vaart was made a Knight of the Order of the Netherlands Lion.