Exercises in textbooks usually focus on proofs, but mathematics isn't just about proving theorems. Mathematics is also about: 1. Understanding mathematical con

Exercises in textbooks usually focus on proofs, but mathematics isn't just about proving theorems. Mathematics is also about: 1. Understanding mathematical concepts (e.g. what is an "acyclic" relation? What is KL divergence?) and theories (several interrelated concepts, e.g. decision theory). This also includes knowing why those concepts are important in the first place, which is often neglected. 2. Knowing the meaning of mathematical notation and technical terms, e.g. to be able to read papers in some field. Papers are often full of mathematical and other jargon while otherwise not necessarily being difficult to follow. 3. Learning mathematical formulas (e.g. Bayes' rule) and algorithms (e.g. differentiation), in order to solve specific problems by calculation or computation (mostly in applied mathematics, more rarely in pure mathematics) 4. Proving conjectures (mostly in pure mathematics, less often in applied mathematics) 5. Learning how to formalize informal problems using mathematical concepts and theories (by applying conceptual understanding gained by 1) in order to understand the problem better, or to make it easier to solve, e.g. by employing calculation (2). (This is often done in engineering and science) Problem sets in textbooks often focus on proofs (4) or some more difficult algorithms (3) but less on the other applications of mathematics. They could also check conceptual understanding (1) by asking the reader to explain some concept in their own terms, or how two different concepts relate to each other, or which concepts various example cases have in common, or how the cases differ on a conceptual level. Though verifying the answers might require a human teacher. 5) could be taught by coming up with word problems from a scientific or engineering (or economics etc) example, where the solution is easy once the correct formalization is known. Unfortunately it is hard to come up with such artificial word problems in which the correct formalization is unique, non-trivial, and doesn't require technical background knowledge from engineering/science etc. Moreover, in the real world, the difficulty with formalization is often to recognize in the first place that there is some problem that could be formalized, which can't be replicated in an artificial word problem. Overall, coming up with good exercises, especially for 5, but also partly for 1, might require the writer of the textbook to know a lot of possible practical applications. Writers of math textbooks are often mathematicians, so they probably don't know a lot about engineering, computer science, empirical science etc in order to come up with good word problems.