The Institute was established on 14 Ferbuary 1947 as the Institute for Mathematics of the Czech Academy of Sciences and Arts (Česká akademie věd a umění). In 1950 it was reorganized to form the Central Mathematical Institute, which was incorporated into the Czechoslovak Academy of Sciences on 1 January 1953 as the Mathematical Institute. In 1993 the Institute became part of the newly founded Academy of Sciences of the Czech Republic. Since January 1, 2007, the Institute of Mathematics (IM in the following) received the v. v. i. status (initials of the Czech legal term veřejná výzkumná instituce = public research institution), whose founder is the Academy of Sciences of the Czech Republic, pursuant to the Act No. 341/2005 Coll. on public research institutions. This change leads to broader rights and responsibility of the institute as those of a legal person and allows for certain relaxation of the rather strict budget rules in the past.

The principal activity of the IM is to support fundamental research in the fields of mathematics and its applications, and to provide necessary infrastructure for research. The IM contributes to raising the level of knowledge and education and to utilising the results of scientific research in practice. It acquires, processes and disseminates scientific information, issues scientific and professional publications (monographs, journals, proceedings, etc.). In cooperation with universities, the IM carries out doctoral study programmes and provides training for young scientists. The IM promotes international cooperation, including the organisation of joint research projects with foreign partners and participation in exchange programmes. The IM organises scientific meetings, conferences and seminars on the national and international levels.

Research in the Institute focuses on mathematical analysis (differential equations, numerical analysis, functional analysis, theory of function spaces), mathematical physics, mathematical logic, complexity theory, combinatorics, set theory, numerical algebra, topology (general and algebraic), optimization and control, differential geometry, and didactics of mathematics.

Departments

Branch in Brno (BB)
The core research in this section carried out by a group of prospective young members concerns theory of ordinary differential equations, boundary value problems, equations on time scales, singular problems, functional-differential equations, qualitative properties of solutions.

Constructive Methods of Mathematical Analysis (CMMA)
The main topics studied in this section concern finite elements analysis, discretization and space decomposition, higher order approximations to solutions of elliptic and parabolic partial differential equations, superconvergence phenomena, mathematical modeling of melting and solidification processes. Another range of problems concerns mathematical and numerical analysis of systems of nonlinear differential equations describing the n-body problem, gravitational potentials, and other related physical quantities.

Didactics of Mathematics (DM)
This very small group represents a particular long-lasting research direction in the Institute, which has been gradually transferred to the Charles University. The members cooperate with specialized groups at universities in the Czech Republic and abroad in theoretical and practical aspects of didactics of mathematics, providing a useful linkage to secondary schools.

Evolution Differential Equations (EDE)
The scope of this section covers various aspects of theory of partial differential equations: qualitative behaviour of solutions to evolution equations, mathematical models in fluid dynamics and thermomechanics, qualitative properties of solutions to elliptic equations, unilateral problems and variational inequalities and their applications in non-smooth mechanics, biology, plasticity, electromagnetism etc. These topics traditionally belong to the core research activities in the Institute and the section represents one of the strongest groups. Members of this department are involved in the Nečas Center for Mathematical Modeling. E. Feireisl is the principal investigator of the highly prestigious ERC Advanced Grant MATHEF.
Two other research directions traditionally pursued in the Institute, namely integration theory and theory of stochastic evolution equations, are unfortunately fading away with retirement, deaths or leaving of several leading researchers.

Mathematical Logic, Algebra and Theoretical Computer Science (MLATCS)
The research programme of this section comprises mathematical logic, theoretical computer science and set theory. The main research area is proof complexity, which is an interdisciplinary field between logic and theoretical computer science. Other main areas include proof theory, forcing, computational complexity, finite and infinite combinatorics, matrix theory, scheduling and automatic control. Although not belonging to the eldest research directions in the institute, the group has built a successful tradition since 1970s when it was created by M. Fiedler, J. Bečvář and P. Hájek.
P. Pudlák is the principal investigator in the prestigious ERC Advanced Grant FEALORA.

Topology and Functional Analysis (TFA)
The section, one of the largest in the Institute, covers several loosely connected domains: operator theory in Banach and Hilbert spaces, Banach algebras and theory of functions; fine topological properties of Banach spaces, functional analysis, infinite-dimensional geometry; algebraic geometry; continuum thermodynamics; function spaces, integral operators and harmonic analysis. The strength of its members is a guarantee for the stability of the section and its further development in the Institute’s structure.