Whether a task is meaningful or meaningless depends on how we think about meaning. I tend to think about it in terms of correspondences between structures. Such

Whether a task is meaningful or meaningless depends on how we think about meaning. I tend to think about it in terms of correspondences between structures. Such structures are usually what we think of as information, so this comment has meaning when interpreted using the corresponding knowledge of English in your brain. A computer simulation of the weather has meaning to the extent that it corresponds to actual weather, and its behaviour. The environmental mapping data structures in a Roomba’s memory has meaning to the extent it corresponds to the environment it is navigating. So meaning is about correspondences, but also about achieving goals. We communicate for many reasons, maybe in this case to help us understand problems better. The weather simulation helps us plan activities. The Roomba’s map helps it clean the room. So there’s also an element of intentionality. What is the intention behind these mathematical proofs? What are their correspondences to other information and goals?