Ask HN: Mathematically demandig areas in IT

[j-l-]

What are the most mathematically demanding areas in IT? Answers can contain field description (SW devel - gis/graphics/radiocommunication), problem description (interpolation), key math abilities (convolution, impulse response), basic literature (wolberg - digital image warping; pharr & humphreys - physically based rendering), reference/notable (but preferably lightweight) implementations (anti-grain geometry), and so on.