Mathematics encompasses quantitative and geometrical reasoning in a wide range of manifestations, both in the abstract and as an essential tool across the natural, social, and applied sciences.
The University College Utrecht Mathematics track spans both pure and applied mathematics. In applied mathematics, you master a variety of mathematical techniques, use them to model physical and social phenomena, and interpret and communicate the real-world significance of mathematical findings. In pure mathematics, you study abstract structures in their own right as well as the foundations of concepts like infinity and the continuum, and you see the power of reasoning at a formal level using exact formulations and rigorous proofs.
Mathematics is singularly abstract, yet it describes the world. It is widely applicable with unreasonable effectiveness in an ever-growing number of areas. At the same time, many mathematicians are as likely to characterise the purpose of their enterprise in terms of “the desire for aesthetic perfection” or “the honor of the human spirit”.
A background in Mathematics opens the door for many potential career paths. For overviews of such possibilities, see for example: AMS, MAA, SIAM, weusemath.org, prospects.ac.uk, UU.