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.
Ietsism Ietsism (Dutch: ietsisme (pronounced [itsˈɪsmə]) – "somethingism") is an unspecified belief in an undetermined transcendent reality. It is a Dutch term for a range of beliefs held by people who, on the one hand, inwardly suspect – or indeed believe – that "there must be something undefined beyond the mundane and that which can be known or can be proven", but on the other hand do not necessarily accept or subscribe to the established belief system, dogma or view of the nature of a deity offered by any particular religion. Some of the English language related terms are agnostic theism (though very many ietsists do not believe in one or more gods and are thus atheists), eclecticism, deism and spiritual but not religious. Ietsists might call themselves Christian or followers of an other religion based on cultural identification with that religion, without believing in the dogmas of that particular religion.