Hilbert's Programs and Beyond

Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. Thisintellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.

Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them., Certainly mathematical logicians with a historical bent will eat [Hilbert's Programs and Beyond] all up like candy. But others will, too. It is, or at least should be, the case that all of us have some awareness of the controversies of the early 20th century and the role they played in bringing about the shape of contemporary mathematics. ... To revisit these themes and explore certain of their facets in great detail is a beneficial and pleasant experience.

Wilfried Sieg is the Patrick Suppes Professor of Philosophy at Carnegie Mellon University. He received his Ph.D. from Stanford University in 1977. From 1977 to 1985, he was Assistant and Associate Professor at Columbia University. In 1985, he joined the Carnegie Mellon faculty as a founding member of the University's Philosophy Department and served as its Head from 1994 to 2005. He is internationally known for mathematical work in proof theory,historical work on modern logic and mathematics, and philosophical essays on the nature of mathematics. Sieg is a Fellow of the American Academy of Arts and Sciences.