Page "David Hilbert" Paragraph 41

In an account that had become standard by the mid-century, Hilbert's problem set was also a kind of manifesto, that opened the way for the development of the formalist school, one of three major schools of mathematics of the 20th century.

According to the formalist, mathematics is manipulation of symbols according to agreed upon formal rules.

It is therefore an autonomous activity of thought.

There is, however, room to doubt whether Hilbert's own views were simplistically formalist in this sense.