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This mathematician's contributions to invariant theory include the syzygy ("SIZZ-uh-jee") theorem and a theorem that gives conditions for when a ring of invariants is finitely generated. An operation named for this man convolves the input with the function "one over pi x." A theorem named for this man holds that the ring of polynomials over a Noetherian ("nur-TARE-ee-in") ring is itself Noetherian. This man declared that "in mathematics there is no ignorabimus" to motivate his namesake program of axiomatization, a project that was proven intractable by Gödel's ("GUR-tle's") incompleteness theorem. In a thought experiment named for him, a countably infinite number of new guests can be housed even though his namesake "hotel" is fully occupied. For 10 points, name this German mathematician who chose the continuum hypothesis as the first of his list of 23 unsolved problems.
This mathematician's contributions to invariant theory include the syzygy ("SIZZ-uh-jee") theorem and a theorem that gives conditions for when a ring of invariants is finitely generated.
David Hilbert &lt;Other Science (Math)&gt;