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In Portuguese, the following is considered the accepted terminology for the implication of theorems: $$\text{Theorem:}\\ \text{Hypothesis } \Rightarrow \text{ Thesis}$$ Hypothesis is the antecedent and I found that to be the normal English terminology in that case, but I never saw Thesis as the consequent or conclusion, so, is this terminology valid in English?

Just to make it clear of what I'm talking about, this is valid terminology in portuguese:

$\text{Theorem: Proposition 8 from Elements}\\ \text{Hypothesis: } AB=DE;~BC=EF;~CA=FD.\\ \text{Thesis: } \triangle ABC\equiv\triangle DEF.$

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I've never seen "thesis" used in that sense; it is often used to refer to the main argument in an essay or presentation ("His main thesis is that X occured because of y and z"). I don't recall seeing it used that way in Spanish either (at least in Mexico). It's possible that it may be used that way in, say, philosophy... – Arturo Magidin Apr 23 '12 at 1:37
I think it is valid but extremely uncommon mathematical English. I have seen it used before, but only in very old texts on Euclidean geometry. (It used to be fashionable to make English textbooks on geometry sound as much like ancient Greek as possible, and this use of "thesis" reminds me of that.) To me, it sounds very "old", and outside of classical geometry, very foreign. I would avoid it. (Like Arturo, I would not be surprised if this use of "thesis" were common in English-language philosophy or rhetoric. These fields use a great deal of Greek-derived terminology.) – leslie townes Apr 23 '12 at 1:45
I can confirm that expressions like "the thesis of the theorem" are common in Argentina. Not that I like them... It sounds old fashioned and used mostly by formality loving types that teach math but don't know how to use it (sorry, personal rant here ;) ) – Martin Argerami Apr 23 '12 at 3:21
@MartinArgerami, I tottally agree with you. The first time I saw this terminology was in my undergraduate Geometry book in Brazil and I even questioned my teacher about the strange (and possible incorrect use). Later I found it used again in other books by other authors... I find that extremely unsettling. BTW: I'm in a second graduation to get licensed in Math (being able to teach it) lol. – Luiz Borges Apr 23 '12 at 10:00

The term "thesis" in English has connotations of centrality in a presentation or string of arguments, so unless a particular conclusion is the central goal of a paper or note or whatever, it isn't the best term to use and might confuse the reader, or at least signal a different command of language than usual. Some better terms would be "result," "conclusion" or "consequence."

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@Gerry: Yeah, I just looked back at the OP and saw "Theorem" over top of an implication with a hypothesis and realized this.. – anon Apr 23 '12 at 1:46

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