What is the -fPIC flag in GCC and why is it needed when building libraries?

Hello everyone! I started learning C++ and trying to build a dynamic library (.so) on Linux using GCC. I see everywhere that when compiling objects for a library, they add the -fPIC flag, but I don't understand why it's needed. Here's my simple example. There's a file `math_utils.cpp`: ```cpp int add(int a, int b) { return a + b; } int multiply(int a, int b) { return a * b; } ``` I compile like this: ```bash g++ -c math_utils.cpp -o math_utils.o g++ -shared math_utils.o -o libmath.so ``` And it works! The library is created, the program links it and uses the functions. But if I add -fPIC: ```bash g++ -c -fPIC math_utils.cpp -o math_utils.o ``` The result is the same. What's the difference? When I googled it, they write that without -fPIC on x86_64 there might be an error, but everything compiles for me. Explain