He provided a solution to Waring's problem and demonstrated the basis theorem in invariant theory. His work dealing with Euclidian geometry culminated in a set of 21 axioms for that field. A thought experiment about countable infinity is known as this man's Grand hotel and both infinite dimensional spaces and vector spaces 
He provided a solution to Waring's problem and demonstrated the basis theorem in invariant theory. His work dealing with Euclidian geometry culminated in a set of 21 axioms for that field. A thought experiment about countable infinity is known as this man's Grand hotel and both infinite dimensional spaces and vector spaces in which an inner product can be defined bear his name. Gödel's incompleteness theorem frustrated his attempts at a proof that all mathematics derives from a finite set of consistent axioms, his namesake program. For 10 points, identify this German mathematician, the leader of the formalist school, who at a conference in Paris in 1900 proposed a series of 23 namesake problems.
He provided a solution to Waring's problem and demonstrated the basis theorem in invariant theory.
David {Hilbert}