Perhaps only useful within compilers, and otherwise a party trick.
A mathematician, a computer scientist, and a first year undergraduate walk into a bar. The first two tell the latter to get out, but instead we'll pretend we're in Britain.
The bartender asks them to write a function that swaps two integers. Here's what each writes:
First year undergraduate:
void swap(int& a, int& b) {
int c = a;
a = b;
b = c;
}
Mathematician:
void swap(int& a, int& b) {
a = a + b;
b = b - a;
a = a - b;
}
Computer Scientist:
void swap(int& a, int& b) {
a = a ^ b;
b = a ^ b;
a = a ^ b;
}
The computer scientist proceeds to implement argument register swapping with no temporaries in their compiler using the theorem that any permutation is a series of swaps.