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In general, in a thesis we recall the theorems of other mathematicians before stating our results published in a scientific journal. My question, is it essential to give the proofs of these theorems (for example these theorems are mentioned in the first chapter of the thesis) or I will give the outline of the demonstration or only the statements ?

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This is something you should discuss with your adviser. It really should depend on the theorems; how important is including their proofs to the understanding of what one has done? Also, how long are their proofs? And how much is your own work using proofs which build off of those theorems? There's no simply response here. You'll see both dissertations and papers where relevant theorems have their proofs included, and others where they are referenced.

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  • Even if it is not my demonstration I can put it in my thesis or I have to use another version of the demonstration? Thank you
    – Theory Nombre
    Commented Dec 17, 2018 at 17:38
  • @TheoryNombre This is the sort of thing you should discuss with your adviser also. But yes, reproducing a proof in your own words as long as you are noting that the proof is from a given other source is generally fine.
    – JoshuaZ
    Commented Dec 17, 2018 at 17:43
  • It would be very unusual to include someone else's proof, particularly if it is available in print. For unpublished work, you should make sure their author is fine with you including their result and/or proof. Even if the proof is unpublished, you may want to check with your advisor.
    – Andrés E. Caicedo
    Commented Dec 17, 2018 at 17:44
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    @AndrésE.Caicedo is it that unusual? I've seen a fair number of theses which includes proofs from sources that were in print when they are pretty obscure, or when I'm going to modify their proof and it is useful to first include the proof, or when it is a very short lemma. And I've seen a fair number of even published papers which include something like "for completeness, we include the proof here" which is from some other source.
    – JoshuaZ
    Commented Dec 17, 2018 at 17:51
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    There is also the case where a proof is given with relatively few details in the literature, and the dissertation includes a more detailed proof that is more accessible for non-experts. This occurs with some frequency.
    – Alexander Woo
    Commented Dec 17, 2018 at 22:38

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