Say I had an array of masses and their velocities and I wanted to calculate the kinetic energy of each mass using the equation:

    E = 1/2 mv^2

With operator overloading:

    E = 0.5 * (m * v)**2

Without:

    E = (m.mult(v)).pow(2).times(0.5)

The operator overloaded example is Python (numpy) - the non-overloaded one is something I made up, but it's basically what it would need to look like.

I think the first example is much closer to the maths.

This is not some contrived example, if you have raw data and you're using mathematical equations to work out relationships you do this kind of thing all the time.

Look at this http://stackoverflow.com/questions/11270547/go-big-int-facto... and compare how the function looks with int and with big.Int. Interestingly, big.Int has a method MulRange, which does exactly what the function would otherwise do, but this won't be the case the majority of the time. Given the extra tedium involved, someone working heavily with vectors, matrices, big numbers, etc., would certainly care about operator overloading.

I am not a scientific programmer, but I'm going to attempt to provide an example anyway until someone else does one better.

I think there are certain mathematical operations that operate over what would be implemented as complex objects, so it is convenient to continue using these agreed upon symbols to implement your work.

  // addition and multiplication of native integers
  1 + 3 * 4

  // add and mult of math objects
  matrixA + matrixB * matrixC

  // here the math is slightly occluded
  add(matrixA, multiply(matrixB, matrixC))