Gaisi Takeuti was one of the most brilliant, genius, and influential
logicians of the 20th century. He was a long-time professor and
professor emeritus of mathematics at the University of Illinois at
Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age
of 91.
Takeuti was one of the founders of Proof Theory, a branch of
mathematical logic that originated from Hilbert's program about the
consistency of mathematics. Based on Gentzen's pioneering works of proof
theory in the 1930s, he proposed a conjecture in 1953 concerning the
essential nature of formal proofs of higher-order logic now known as
Takeuti's fundamental conjecture and of which he gave a partial positive
solution. His arguments on the conjecture and proof theory in general
have had great influence on the later developments of mathematical
logic, philosophy of mathematics, and applications of mathematical logic
to theoretical computer science.
Takeuti's work ranged over the whole spectrum of mathematical logic,
including set theory, computability theory, Boolean valued analysis,
fuzzy logic, bounded arithmetic, and theoretical computer science. He
wrote many monographs and textbooks both in English and in Japanese, and
his monumental monograph Proof Theory, published in 1975, has long been
a standard reference of proof theory. He had a wide range of interests
covering virtually all areas of mathematics and extending to physics.
His publications include many Japanese books for students and general
readers about mathematical logic, mathematics in general, and
connections between mathematics and physics, as well as many essays for
Japanese science magazines.
This volume is a collection of papers based on the Symposium on Advances
in Mathematical Logic 2018. The symposium was held September 18-20,
2018, at Kobe University, Japan, and was dedicated to the memory of
Professor Gaisi Takeuti.
