1862 – 1943
David Hilbert (1862–1943) was a German mathematician widely regarded as one of the most influential mathematicians of the 19th and 20th centuries. He made foundational contributions to algebra, functional analysis, mathematical physics, and the philosophy of mathematics, most notably through his formalist program seeking to ground all of mathematics in a complete and consistent axiomatic system. His 1900 list of 23 unsolved problems shaped the trajectory of 20th-century mathematics.
Proposed Hilbert's Program: the formalist project to axiomatize all of mathematics and prove its consistency via finitary methods
Published 23 open problems in 1900 that defined the research agenda for 20th-century mathematics
Developed Hilbert spaces, foundational to functional analysis and quantum mechanics
Contributed to the axiomatization of Euclidean geometry in Grundlagen der Geometrie (1899)
Made independent contributions to the field equations of general relativity alongside Einstein
Reichenbach was not able to recognize the Weyl method as other than an equivalent account of empirical determination of the metric
claimMetric geometry is neither true nor false.
claimFor any real number x, the terms of a conditionally convergent series can be rearranged so that x is the sum of the rearranged series.
claimThe semantics of a formal system rich enough to contain elementary mathematics cannot be fully defined in terms of mathematical functions within that same system.
claimThe universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive