Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations . Hilbert's mathematical abilities were nicely summed up by Otto Blumenthal, his first student:
Hilbert ambag sa maraming mga sangay ng matematika, kabilang ang mga invariants, algebraic number mga fields, functional analysis, integral equation, matematiko physics, at ang calculus ng mga pagkakaiba-iba. Hilbert's matematiko kakayahan ay maganda ang summed up sa pamamagitan ng Otto Blumenthal, ang kanyang unang mag-aaral: