A new dawn of Intuitionism: mathematical and philosophical advances

Starting date
December 1, 2017
Duration (months)
33
Departments
Computer Science
Managers or local contacts
Schuster Peter Michael

Intuitionism and more generally constructive mathematics is enjoying a renaissance. Surprising connections between the traditionally distant areas of mathematical logic and geometry have emerged through the constructive Univalent Foundations of Mathematics research program,
formulated by the Fields medallist Voevodsky. Areas of mathematics such as abstract algebra that appeared to be dominated by highly incomputable objects have shown surprising amenability to constructive approaches. Our central claim is that much of mathematics and related areas (e.g. philosophy and computer science) can benefit from the subtler distinctions and structures revealed by constructivization, i.e., by replacing classical with intuitionistic reasoning. This study reveals some of the fundamental structures of mathematics and potentially of physical reality.
Building a strong team at the interface of logic and computing, we target several areas where constructivization will produce important insights. Our specific research topics exhibit considerable breadth across mathematics, philosophy, and computing that encompasses univalence, intuitionistic type theory, algebra, philosophy of mathematics, proof theory, and complexity.

Sponsors:

John Templeton Foundation
Funds: assigned and managed by the department

Project participants

Ingo Blechschmidt
Research Scholarship Holders
Giulio Fellin
PhD student
Peter Michael Schuster
Associate Professor
Research areas involved in the project
Matematica discreta e computazionale
Mathematical logic and foundations - -

Activities

Research facilities