David Hilbert Natur und mathematisches Erkennen

At the time of David Hilbert's death in 1943, his leading disciple, Her­ mann Weyl, wrote that " . . . the era of mathematics upon which he impressed the seal of his spirit and which is now sinking below the horizon achieved a more perfect balance than prevailed before and after, between the mastering of concrete problems and the formation of general abstract concepts. "l Weyl attributed this "happy equilibrium" in no small part to Hilbert 's work and its influence, adding that "no mathematician of equal stature has risen from our generation. ,,2 Surely, it would be difficult to exaggerate the importance of Hilbert's contributions to twentieth-century mathematics or even to conceive of what mathematics today would be like without them. He overturned the concep­ tual framework of older fields ranging from invariant theory and algebraic number theory to the foundations of geometry. He rehabilitated the Dirich­ let Principle, propelled integral equation theory to the forefront of active research, derived the field equations governing Einstein's general theory of relativity, created modern proof theory and metamathematics, and through­ out his career he championed the power and efficacy of the axiomatic method not only for mathematics but for all of the exact sciences. Every educated mathematician knows something about Hilbert space, the Hilbert problems, and Hilbert 's formalist program.