I can only attest that it is common folklore that Hilbert is the last mathematician to have understood all of mathematics (I can't recall where I've read this; but I know I've seen or heard this in more than one place).
But this is folklore; I of course can't judge whether this is true (or if more recent mathematicians, you mention Picard, and Joel David Hamkins says von Neumann) truly fit this criteria. I feel this is very subjective and the only people who may be allowed to make such claims should be experts very knowledgeable in the history of mathematics.