The term 'donut, mathematically' is a reference to two geometric shapes. The first is a TOROID, which is a doughnut-shaped object with a circular cross-section. It is formed by rotating a circle around an axis that does not intersect the circle. The second shape is a torus, which is similar to a TOROID but has a circular cross-section that passes through the center of the circle. Both shapes are three-dimensional and have a hole in the middle.