what do we call statements that we assume to be true without proofs
Mathematical proof In mathematics, a proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms,[2][3][4] along with accepted rules of inference. Axioms may be treated as conditions that must be met before the statement applies. Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning (or "reasonable expectation"). A proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed to be true is known as a conjecture.
Question Questions that ask whether or not some statement is true are called yes–no questions (or polar questions, or general questions[8]), since they can in principle be answered by a "yes" or "no" (or similar words or expressions in other languages). Examples include "Do you take sugar?", "Should they be believed?" and "Am I the loneliest person in the world?"