Pire. I am glad you pointed that out and I was waiting for somebody to mention it. Being a maths co-major myself I should know and I did. Fourier and Laplace came much later than Newton. However, there was an article that spoke about Newton's understanding of these transformation methods much much ahead of the time they were discovered. It started with saying how Newton had developed calculus much much before Leibnitz developed it but Newton kept it to himself. It then gave some example of functional transformation that resembled Fourier or Laplace. I probably shouldn't have used this as a fact that nobody else has confirmed this, but my point was that to come up with the formulae of that magnitude, or to prove the correctness of the formula you would need to have that level of understanding. Sure there are empirical ways of proving a formula too, without mathematical derivations, but the kid didn't do that either.

10 points to pire.