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What is the most specific word that describes both? As in "all theorems and conjectures are ..." ?

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Mathematical statements? – Ragib Zaman Oct 4 '11 at 23:25
@Ragib - possibly. I'm not a native English speaker, I wasn't sure that was the term. You can post it as an answer. – ripper234 Oct 4 '11 at 23:34

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up vote 4 down vote accepted

A Proposition.

Or perhaps a '(mathematical) assertion'

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I'll just point out that the words "proposition" and "claim" are used in papers (loosely speaking) as an alternative to "theorem" and "lemma". When used in that context, a proposition or a claim has to be of the 'verified' sort :) – Srivatsan Oct 5 '11 at 0:45
I think Assertion is the word I'm looking for. – ripper234 Oct 5 '11 at 8:00
up vote 5 down vote

The term "Mathematical statements" is perhaps slightly too general for many intended purposes. Though theorems and conjectures form a subset of all mathematical statements, theorems must be true and we hope for conjectures to be true, while there are many mathematical statements which are false. This distinction is very far from minor (for a mathematician), however due to the inherent difference between a theorem and a conjecture, for a more precise description you would definitely have to sacrifice conciseness.

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+1 Besides, a theorem-conjecture is -to some degree- general, significant, fundamental (it's not only true but -potentially- a source of mathematical truth). "15 is greater than 13" is a true mathematical statement, but it's hardly a theorem (in common speak) – leonbloy Oct 5 '11 at 1:29

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