Mathematics deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative and qualitative aspects of the life sciences. Mathematics provides basic reasoning for natural science including physics, chemistry, and biology. It creates new tools for applied science and engineering such as mechanical, electronic, chemical, structural engineering, computer science, medical science, and economics. Therefore, Mathematics is an indispensable subject not only for Mathematics majors, but other majors as well.

The undergraduate program in Mathematics at Yonsei University is designed for students from the various fields. The subjects offered by the department vary from such fields as scientific computing, combinatorics, probability, and statistics, to such basic areas of mathematics as analysis, algebra, geometry, logic, and topology. The major research areas of our faculty members are as follows:
1) Algebra; commutative algebra, representation theory, algebraic geometry, ring theory, homological algebra.
2) Combinatorics; algebraic combinatorics, symmetric function theory, graph theory, cryptology, DNA computation, Cauchy theorem, conformal mappings.
3) Differential equation; Fourier transform on hyper-function spaces and its applications, separation of variable, regularity, dynamical system.
4) Differential geometry; unified field theory, Riemanian geometry, level theory, dynamical system. symplectic geometry, complex geometry.
5) Functional analysis; Wiener integral, Feymman integral, function space integral.
6) Harmonic analysis; potential theory.
7) Logic; set theory, proof theory, artificial intelligence, computability theory, model theory and its applications to algebra, analysis, number theory and geometry.
8) Mathematical physics; statistical physics, dynamical system, diffusion, C*-algebra. mathematical foundation of quantum field and string theories.
9) Number theory; algebraic number theory and analytic number theory.
10) Numerical Analysis; computational mathematics, numerical methods for PDE.
11) Partial differential equation; linear and non-linear equation of elliptic type and hyperbolic type, existence and regularity, index theory, inverse problem.
12) Probability; geometric probability, large deviation.
13) Statistics; mathematical statistics, non- parametric analysis, regression, time serious, data analysis, experimental design, sampling theory.
14) Topology; category theory, homotophy, function space, fuzzy logic, topology in low dimensions.

Graduates of the mathematics program follow various career paths. Many go on to jobs in industrial sectors, including finance business, or even government, for which their mathematical backgrounds have prepared them. Many others go on to graduate work in other fields (often ones that are mathematics-related), including business school, economics, computer science, engineering, statistics, and physics. Others go on to graduate work in mathematics, eventually intending to become professors or high-level researchers.