Rock around the old oak tree

Question

I'm the reason why Ireland doesn't sink,
And what sometimes keeps people from the drink,
I'm not Fahrenheit, my choice tells you that,
Rotten rotten me, almost proved Fermat.

Answer 1

I gotta be...

   ... C O  R  K

The title, “Rock around the old oak tree,” refers to this riddle’s answer and first line in at least three ways:

“Rock Around the Clock” and “Tie a Yellow Ribbon Round the Ole Oak Tree” are well-known rock songs and Cork Rock is a book about rock music in County Cork, Ireland.
Better— thanks to Ankoganit:   “rock” turned “around” spells “cork.”
Corks are traditionally made from the bark of cork oak trees.

I’m the reason why Ireland doesn’t sink,

Cork (a city, and its county) is in Ireland and cork (the bark of cork oak) floats.

And what sometimes keeps people from the drink,

Can’t guzzle without uncorking the bottle.

I’m not Fahrenheit, my choice tells you that,

I’m C  o r  K (Celsius or Kelvin), Jim, not an F (Fahrenheit).

Rotten rotten me, almost proved Fermat.

More thanks to Ankoganit, for solving the pyramidion of this riddle:

Two applications to “C O R K” of alphabetic rotation by ten steps produces “W I L E,” which almost spells “Wiles,” the last name of the mathematician who proved Fermat’s Last Theorem.

         Original             After                 After another
        letter and           rot-ten                   rot-ten
       alphabetical       (rotation by              (rotation by
         position           10 steps)                 10 steps)

          C    3  - - - -  13   M   13  - - - - - -  23   W   23
          O   15  - - - -  25   Y   25  - - - - - -  35   I    9 (=35-26)
          R   18  - - - -  28   B    2 (=28-26) - -  12   L   12
          K   11  - - - -  21   U   21  - - - - - -  31   E    5 (=31-26)
          +                                               +
          Y   25  - - - -  35   I    9 (=35-26) - -  19   S   19
 

      Frosting on the cake, from a comment by this puzzle’s author:
         “Corky Rotscore proved Fermat’s Last Theorem”

Answer 2

I'm gonna guess:

Degree.

I'm the reason why Ireland doesn't sink,

I'm guessing the temperature (weather) not causing the sea to rise high enough to sink Ireland.

And what sometimes keeps people from the drink,

I checked the statistics and people with higher education drink more. So maybe it's a reference to how people without a degree (and lower pay) are financially kept from being able to purchase as much alchohol.

I'm not Fahrenheit, my choice tells you that,

I can only guess that's a reference to Europe using Celsius.

Rotten rotten me, almost proved Fermat.

Perhaps a reference to Fermat's Last Theorem and the mathematical degrees, when if greater than 2 with all positive integers becomes an unsolvable equasion. ()