I've been tasked with proofreading an Engineering/Mathematics thesis paper. I was always told that numbers under 10 should be spelled out (one, two, three, ...) but I was wondering if this rule holds in math and science fields as well. This paper understandably uses a lot of numbers in it and switching back and forth between numbers written out in words and numerals seems inconsistent at best and somewhat confusing at worst.
Generally speaking you should try to distinguish between an English number and a mathematical number. As in "Over the next five chapters we will prove that 5 is a prime number." Never spell out a number which is a subject of study, like the "5" in that sentence.
However ordinals like in "Section 4" and "Lemma 2" are always written with digits. "There are three results in Theorem 3."

1$\begingroup$ Note also that some authoritative style guides, such as the Chicago Manual of Style, prescribe lower case in "section 4" and "lemma 2" and "theorem 3". See mathoverflow.net/questions/27693/…. $\endgroup$ – Joel David Hamkins Mar 6 '13 at 13:25

18$\begingroup$ Joel, you've just (slightly) lowered my opinion of the Chicago Manual of Style. $\endgroup$ – Andreas Blass Mar 6 '13 at 13:53

3$\begingroup$ The Chicago Manual of Style is outstanding! It is clear, precise, thorough and thoughtfully reasoned. Although my previous practice like yours was to capitalize theorem and lemma references, since discovering this CMS recommendation, I've adopted it in all my own writing, and I've found that I like it much better. The CMS recommendation is part of a larger call for a "lowering of the volume" in excessive unnecessary capitalization. $\endgroup$ – Joel David Hamkins Mar 6 '13 at 14:07

13$\begingroup$ Shouldn't it then be the chicago manual of style? ;) [While this is formulate playfully I actually have a serious question in that to me Theorem 5 is a name (of a result) and thus(?) it should be capitalized as any(?) other name. So the rational is unclear to me, which does of course not exclude there being one, even one I might appreciate.] $\endgroup$ – user9072 Mar 6 '13 at 14:39

5$\begingroup$ Although I used to agree with you, quid, I no longer agree that Theorem 5 is a name or proper noun. I doubt you would refer to "Page 16" with capitals this way or write that you parked your car in "Space 23". But this discussion is offtopic on this answer, so I suggest further comments if any be posted on the other page: mathoverflow.net/questions/27693/…. $\endgroup$ – Joel David Hamkins Mar 6 '13 at 16:35
Also in engineering watch for units... "The two rods had diameter 5 mm." "A 6volt battery was used."

1$\begingroup$ Especially watch for lack of units. "... had diameter 5." and "...volltage reading was 6." are to be avoided. (In engineering and physical sciences more than in pure mathematics,) Numbers not associated with units should be clearly marked so, as in "observations suggest the frictionratio coefficient has a (dimensionless) value close to 6.28 ." . Gerhard "Format Is Read As Year.Month.Day" Paseman, 2013.03.05 $\endgroup$ – Gerhard Paseman Mar 6 '13 at 16:47
I believe that the rule here is to spell out numbers used for counting (unless they require three or more words to be spelled out), and use digits otherwise. Just check the examples in the answers above to see that they all fit this rule. As one more example: "There are five theorems in the manuscript labeled Theorem 5".