...We find ourselves in agreement with the philosophers, especially with Kant. Kant already taught - and indeed it is part and parcel of his doctrine - that mathematics has at its disposal a content secured independently of all logic and hence can never be provided by a foundation by means of logic alone; that is why the efforts of Frege and Dedekind were bound to fail
Rather as a condition for the use of logical inferences and the performance of logical operations, something must be given to our faculty of representation, certain extra logical concrete objects that are intuitively present as immediate experience prior to all thought.
(In Kantian terms, his immediate experience is pure intuition; and thought is that thought after the apperception of unity; and after the synthesis of the intuition - and this carried out in the Imagination)
He's claiming contra the Fregean programme which insisted that mathematical propositions were always reduced to logic, that is in Kants language, are analytic and in character are a priori; that they are in fact synthetic.
This Kantian influence on Hilbert I find surprising as I have associated the name of Hilbert with the formalist programme; and Kant with Brouwer's Intuitionism - which in some ways were in opposition.
Is there a more pronounced influence of Kant on the Formalist programme? Apart from the one here where he uses Kantian thought to demonstrate why the Fregean programme - in strict terms, and in this sense - was bound to fail; and it seems post-hoc.
(This is not to say that the Fregean programme wasn't important in other ways).