Before revision:  We achieve near perfect estimates of qualitative characteristics of the systems , and good approximations of numerical quantities, demonstrating that neural networks can learn advanced theorems and complex computations without built-in mathematical knowledge.
After revision:  We achieve near perfect estimates of qualitative characteristics of the systems , and good approximations of numerical quantities, demonstrating that neural networks can learn to perform complex computations, grounded in advanced theory, from examples, without built-in mathematical knowledge.