I read that GCC supports the long long int type which is required to be at least 64 bits wide. But how can it make math operations with it on a CPU that is only 32 bits wide?
The compiler will synthesize math operations (or use function calls) that use more than one CPU instruction to perform the operation. For example, an add operation will add the low order components (the low words) of the long long values and will then take the carry out of that operation and feed it into an add operation on the high order words of the long long.
So the following C code:
long long a;
long long b;
long long c;
// ...
c = a + b;
might be represented by an instruction sequence that looks something like:
mov eax, [a.low] ; add the low order words
add eax, [b.low]
mov edx, [a.high] ; add the high order words,
adc edx, [b.high] ; including the carry
mov [c.low], eax
mov [c.high], edx
And if you consider for a moment, compilers for 8 and 16 bits systems had to do this type of thing for 16 and/or 32-bit values long before long long came into being.