New Frontiers of Infinity: Mathematical, Philosophical and Computational Prospects


Human beings have been always fascinated by infinity. From ancient Greece, philosophers and mathematicians have studied its nature and been bewildered by the paradoxes that defy its rational comprehension. In medieval times, infinity was thought of as the ultimate attribute of God, and as such totally unassailable to humans. But a new mathematical theory of the infinite, the calculus of Leibniz and Newton, was precisely what made possible the birth of modern science. Mathematical Analysis, a symphony of the infinite according to Hilbert, was at the heart of critical developments in Physics during the nineteenth century, and up to the present day. At the turn of the twentieth century, following the dramatic discoveries of Cantor on transfinite numbers -- the first true investigation of the infinite realm -- it became possible, and necessary, to establish a purely mathematical theory of infinity. This was achieved by Zermelo, Fraenkel, Gödel, von Neumann, and others, culminating in the current ZFC system of modern set theory. As an extremely general theory, whose objects of study are the abstract infinite sets, ZFC serves as the standard foundation of mathematics, and therefore has great significance for all of science. Set-theoretical research has been a continuous source of original ideas and results, as well as of deep and highly technical tools that are now finding applications in many areas of mathematics, computation, and even natural and social sciences. This is the golden age of set theory. Major breakthroughs have been made recently and new ones are expected.

The main objective of the Programme is to stimulate the exchange of ideas among researchers pursuing different approaches to infinity: mathematical, philosophical, and computational. Its aim is to promote cooperation at European and international levels, scientific mobility and integration of national activities and groups with complementary backgrounds and expertise, and training of young researchers.


Five years from 16 March 2009 until 15 March 2014

For more information go to website

To see related ESF activities click here