In Greek dictionaries of English language I have found that the phrases 'at best' and 'at the best' have the same meaning.
In Longman dictionary and other dictionaries published in the UK or America I have found only the phrase 'at best'.
Do the phrases 'at best' and 'at the best' have the same meaning or is the phrase 'at the best' wrong?
The common phrase is 'at best', and not 'at the best'.
Here is an example from macmillan dictionary:
His chances of victory are, at best, uncertain.
The government’s response seems to have been at best confused and at worst dishonest.
Language is flexible, and so unusual phrases might fit, from time to time. But, the basic answer for an ELL student is just use 'at best'.
Neither of these things are phrases at all. In order to have any idea what you are talking about, I had to see the other answer, who's author apparebtly managed to figure out what you were talking about.
If they are correct about what you are talking about, these two terms are not "phrases", and are instead only used in "extremely academic" papers (by sound), such as logic arguments laid out in obstrusive books, actual academic papers, and newspaper articles where the author wishes to sound at least somewhat pretentious.
If the other answer is wrong, and that is not the type of sentence you were talking about, then I will state my original answer, which is that neither of these two thinhs are actually phrases at all, and so we don't really know what your question is referring to.
If you want to say that someone is the "best" soccer player etc., then you would just say "the best". Also, that isn't used too often because it is uncommon that people will be talking about who is the best at something unless it is to moderately bully each other in which case it won't be meant literally or truthfully.
