That’s not to say it’s easy work. It wasn’t until 1983 that the mathematician Hendrik Lenstra proved that the general problem was even solvable, providing the first algorithm that could do it. Lenstra thought about ILP geometrically. First, he turned the inequalities at the heart of ILP into a convex shape, such as any regular polygon. This shape represents the constraints of the individual problem you’re solving, whether it’s couch production or airline scheduling, so the shape’s interior corre...