Thomas Streicher (11 February 1958 – 2 January 2025) was an Austrian mathematician who was a Professor of

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

Technische Universität Darmstadt The Technische Universität Darmstadt (official English name Technical University of Darmstadt, sometimes also referred to as Darmstadt University of Technology), commonly known as TU Darmstadt, is a research university in the city of Darmsta ...

. He received his PhD in 1988 from the

University of Passau The University of Passau (''Universität Passau'' in German) is a public research university located in Passau, Lower Bavaria, Germany. Founded in 1973, it is the youngest university in Bavaria and consequently has the most modern campus in the ...

with advisor

Manfred Broy Manfred Broy (born 10 August 1949) is a German computer scientist, and an emeritus professor in the Department of Informatics at the Technical University of Munich, Garching, Germany. Biography Broy gained his Doctor of Philosophy (Ph.D.) in 19 ...

Life and work

Streicher's research interests included

categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, cate ...

domain theory Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer ...

and

Martin-Löf type theory Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematicia ...

. In joint work with he constructed a model for intensional

where

identity type In type theory, a branch of mathematics, the identity type represents the concept of equality. It is also known as propositional equality to differentiate it from "judgemental equality". Equality in type theory is a complex topic and has been t ...

s are interpreted as

groupoids In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: * '' Group'' with a partial fun ...

. This was the first model with non-trivial identity types, i.e. other than

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

s. Based on this work other models with non-trivial identity types were studied, including

homotopy type theory In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory ap ...

which has been proposed as a foundation for mathematics in

Vladimir Voevodsky Vladimir Alexandrovich Voevodsky (, ; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal ...

's research program ''Univalent Foundations of Mathematics''. Together with Martin Hofmann he received the 2014 LICS Test-of-Time Award for the paper: ''The groupoid model refutes uniqueness of identity proofs''. Streicher died on 2 January 2025, at the age of 66.

Bibliography

* T. Streicher (1991), ''Semantics of Type Theory: Correctness, Completeness, and Independence Results'', Birkhäuser Boston. * M. Hofmann and T. Streicher (1996)
The groupoid interpretation of type theory
in Sambin, Giovanni (ed.) et al., Twenty-five years of constructive type theory. Proceedings of a congress, Venice, Italy, October 19–21, 1995. * T. Streicher (2006), ''Domain-theoretic Foundations of Functional Programming'', World Scientific Pub Co Inc.

References

External links

Official website
at

* 1958 births 2025 deaths 20th-century German mathematicians 21st-century German mathematicians Academic staff of Technische Universität Darmstadt University of Passau alumni {{Germany-mathematician-stub