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Nowadays there are plenty of different proofs of the celebrated Szemerédi's Theorem but for historical reasons I would like to read and understand the original proof. The proof is very tricky and, for instance, he uses a primitive version of the Regularity Lemma (weaker and more complicated), so I would like to find some source with a 'modern' language.

My question is then the following: is there any survey/book/... where the original proof is presented (with more details possibly), apart of course of the original paper?

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  • $\begingroup$ I doubt that anybody decides to rewrite such complicated original proof modernizing only language. $\endgroup$
    – Fedor Petrov
    Dec 21, 2015 at 8:38
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    $\begingroup$ www.math.ucla.edu/~tao/preprints/Expository/szemeredi_theorem.dvi : though Tao later states that in this exposition he "was unable to find much of a simplification, and my exposition is probably not that much clearer than the original text". See also terrytao.wordpress.com/2012/03/23/… $\endgroup$
    – Ben Green
    Dec 21, 2015 at 9:16
  • $\begingroup$ Thank you, that's what exactly the type of thing I was looking for $\endgroup$
    – Johnny Cage
    Dec 21, 2015 at 9:59

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