> They tell the self-learner that solutions aren't provided because everyone has the ability to know if their solutions are correct without having their work ch

> They tell the self-learner that solutions aren't provided because everyone has the ability to know if their solutions are correct without having their work checked. Would you write a complicated program and write no test cases, or could you instantly know your program is bug free the first time you write it? Why is math suddenly any different? Math is an art of making a specific type of rigorous, formal arguments that are meant to convince, beyond all doubt, another human being that one statement follows from another. If an argument like that fails to convince even the proof author themselves, then you know the argument isn't good even without comparing it to another solution. In practice, after you've written down your proof, you examine it for weak spots. If any particular step raises doubts or objections then you recursively spell it out in greater detail (or replace with an alternative approach) until eventually all doubt dissipates. At that point you don't need to compare it to another solution. In fact, as you recognized yourself, your solution is likely to be different from the book author's, so comparison isn't helpful. Similarly, a problem like "write a small application to..." in a coding book or an assignment like "write an essay on..." in a writing book don't include solutions. Code, proofs and essays are all too free-form to subject them to correctness verification by comparison with a standard. Perhaps what you have in mind are examples. All good math textbooks include worked-out proofs that illustrate the techniques. In fact these are generally the bulk of the book! Perhaps you're asking for more examples. That's fair. Proof problems OTOH should be given without solutions to encourage independent creative thought of the reader and to avoid incorrect implication that there is the single correct solution. (Disclaimer: Not a mathematician.)