“Mathematics as a whole“ is a leading principle of the BMS. Its focus encompasses fields that are traditionally termed “pure“ or “applied“ mathematics, though we prefer not to make that distinction. Instead, research topics are grouped into eight areas, each covering a broad, but coherent, part of mathematics:

Area 1: Geometry and topology   
          Differential geometry, algebraic topology and mathematical physics

Area 2: Algebraic geometry and number theory
             Algebraic geometry, arithmetic geometry and number theory

Area 3: Stochastics and mathematical finance
             Probability, statistics and stochastic analysis

Area 4: Discrete mathematics and optimization
             Combinatorics, graph theory, discrete optimization and algorithms, complexity

Area 5: Discrete geometry
             Discrete geometry, discrete differential geometry and visualization

Area 6: Numerical mathematics
             Numerical analysis, continuous optimization and scientific computing

Area 7: Applied analysis
             Modelling, Analysis and Optimization with Differential Equations

Area 8: Mathematics for AI
             Mathematics of data science and AI





The areas were revised in 2024. You can find the old area titles here:

RTA 1: Differential geometry, global analysis, and mathematical physics

RTA 2: Algebraic and arithmetic geometry, number theory

RTA 3: Stochastics and mathematical finance

RTA 4: Discrete mathematics and optimization

RTA 5: Geometry, topology, and visualization

RTA 6: Numerical analysis and scientific computing

RTA 7: Applied analysis and differential equations

RTA 8: Mathematics of data science