“breakthrough” is nothing more than an artifact of mathematicians not being able to properly specify the rules of their games in natural language… the theory of computer science has a culture that actively discourages running algorithms on a computer.

This is not an entirely faithful characterization. TCS and does make the distinction between galactic algorithms and what are called “feasible” algorithms (e.g., Karatsuba’s or Strassens’s algorithm), which yield a measurable speedup on practical inputs.