There is some ambiguity in this case; are the studies co-authored by the four, or are you referencing some studies from each?
If the former, you would append an apostrophe and s to the last name (some style guides would recommend only an apostrophe, placed before the last s); this is the treatment for joint possession. In the second case, when each study belongs to only one of the authors, I believe it is correct to add an apostrophe to each name. I had trouble finding a source for this, however; this site concurs, but they do not themselves cite sources, and I could not find any other statements about it one way or the other. This could get really painful if different studies are co-authored by different members of the list, but assuming this is not the case, your final phrase should be one of these two, as described above:
In Fermat's, Lagrange's, Newton's and Gauss's studies,
In Fermat, Lagrange, Newton and Gauss's studies,
As I mentioned, the possessive of Gauss is a matter of debate, but I would strongly recommend the extra s.
The sentence as a whole also has significant unrelated errors; I am not sure what the intended meaning is, though, so I do not want to recommend specific corrections. As tkp suggested, it might be more clear if you had it translated by software and than asked for advice, corrections, or explanation of that version.