In discussions like this, we should be careful about our terminology, so that we're all using words in the same way. One can "believe" in the existence of the tooth fairy, but one does not -- in the same sense of the word -- "believe" in the existence of his own mother. Belief in the first proposition (tooth fairy) requires faith, which is the belief in something for which there is no evidence or logical proof. The second proposition (mother) is the kind of knowledge which follows from sensory evidence. There is also that kind of knowledge (like the Pythagorean theorem) which follows from logical proof. In either case -- that is, belief in things evidenced by sensory evidence or demonstrated by logical proof -- there is no need for faith.
In between mother and the Pythagorean theorem are those propositions we provisionally accept (or in common usage "believe"), like relativity and evolution, because they are scientific theories -- logical, testable, and therefore falsifiable explanations of the available, verifiable data (which data is knowledge obtained via sensory evidence).
Too many creationists come into these threads and appear to be clueless about the vital distinctions between reason and faith. There are vitally significant differences between an axiom and an article of dogma, fact and fantasy, hypothesis (or a more general theory) and conjecture. These fundamental differences allow us to distinguish reason-based science from faith-based teaching. They are commonly confused, but they are very different intellectual enterprises.
The theory of evolution is far more than a wild imaginary belief (such as belief in Zeus or the tooth fairy). Darwin proposed his theory as an explanation for the proliferation of species that we observe. It was scientific, in that it was a rational, comprehensible, cause-and-effect explanation that fit the data. This was about 150 years ago. Since then, hundreds of thousands of fossils have been uncovered, and NONE has been found that contradicted the theory. This alone is powerful evidence, as the theory predicts that all fossils will conform to the theory, so each new fossil find is therefore a test of the theory; and the theory successfully passes each such test. Purely theological matters are not capable of such testing, and thus theology is not scientific. The same can be said of quasi-theological propositions like Intelligent Design.
Then there's the matter of "proof." Except for math and geometry, there is little that is actually proven. Even well-established scientific theories can't be conclusively proven, because at least in principle, a counter-example might be discovered. Theories are always accepted provisionally, and are regarded as reliable only because they are supported by the facts they purport to rationally explain and by the predictions which they make. All scientific theories (including the theory of evolution) are subject to revision if new data is discovered which necessitates this. When a scientific theory (such as evolution) has a long history of being supported by the evidence, the most appropriate word for acceptance of the theory is usually "confidence," not "faith."
Useful website in this context: Do You Believe in Evolution?
"faith, which is the belief in something for which there is no evidence or logical proof. The second proposition (mother) is the kind of knowledge which follows from sensory evidence."
The problem with that, of course, is the assumption (Or should I say, 'adamantine prejudice?') that there is no equivalent or superior sensory evidence for the existence of God.
As so often turns out to be the case, that assumption is false.
In between mother and the Pythagorean theorem are those propositions we provisionally accept (or in common usage "believe"), like relativity and evolution, because they are scientific theories -- logical, testable, and therefore falsifiable explanations of the available, verifiable data (which data is knowledge obtained via sensory evidence).
There are also other usages of the word "belief". For example, that of general reputation--"You're never going to believe what those cretins at Air America said now !"
Or, belief of an individual person: "He said he was studying in his dorm room all night and didn't go near the party." "I don't believe it for an instant!"
Then again, you have "scientific" belief, in which you strongly suspect something based upon preliminary physical evidence, but you haven't double-checked: "I believe this man was POISONED!" (After the autopsy, the belief is ratified, and you say the man WAS poisoned; or you shamefacedly explained why you jumped to the wrong conclusion.) This differs from your Pythagorean theorem above in that it is a specific concrete instance and not a general proposition.
And of course there is religious belief.
Cheers!