Assertion vs Statement I am not a English native speaker. I apologize if I ask something obvious. According to my knowledge, a statement is a sentence about specific numbers, sets or other objects, the sentence being either true or false. So
$3\times 7=11$
is a (false) statement, that continuity does not imply differentiability is a (true) statement, that the polynomial $n^2+n-41$ produces prime numbers for all integer values of $n$ from 1 to 40 is a (true) statement and so on.
Nevertheless,  (http://strangebeautiful.com/other-texts/geroch-math-assertions.pdf)

According to the author that all prime numbers are odd is an assertion.
I am puzzled a bit. Are the words statement and assertion (and the verbs state and assert) interchangeable? Is assertion preferable?
 A: There are three distinct concepts to consider. Take the sentence “some elephants can fly.” The grammatical form of this sentence indicates that it is a proposition since it has a truth value, but to assert it is to claim that there really are elephants that can fly. This sentence can be understood as a judgement, i.e. as saying that “some elephants can fly” is true.
To summarize, an assertion claims the reference of sentence, a statement is a sentence with a truth value, and a statement can be judged as true/false.
These concepts have been discussed by the likes of Frege, Russell/Whitehead, Wittgenstein, Kripke, Tarski, and so on. Russell and Frege are probably the most pertinent source to look into for specific references, and the SEP article “Assertion” can give an overview of the full context.
A: Requested in comments:
Mathematical English has many sets of words used with similar meanings, sometimes with slightly different emphasis such as theorem/lemma/corollary.
Here you have statement and assertion, but there are also words like proposition and claim and hypothesis and conjecture and more.
A: According to https://abstractmath.org/MM/MMMathEnglish.htm:

Math English, just like everyday English, is used for making
statements. Every statement is either true or false. (...)


Mathematical English also has sentences that are like statements, but may contain variables and may be true or false depending on the values chosen for the variables.  In abstractmath.org these are called assertions. In particular, any statement is regarded as an assertion with no variables.


In mathematical logic, statements may be called propositions or sentences and assertions may be called predicates or formulas.   I don’t use those words because they can cause semantic contamination.


The words "statement" and "assertion" also have connotations in English that are not relevant here.


In the abstractmath usage, a statement is simply a sentence that is true or false; it doesn’t have to be a witness’s report, for example.
An assertion is a sentence that becomes true or false when you substitute values for the variables.  It doesn’t have to be emphatic.

