I am still unsure if Fourier Transform has any fundamental significance in Physics. Is it anything more than a calculation tool? For example sometimes people Fourier transform an equation to solve it relatively easily and then transform back. So from this point of view this is not a fundamental topic. Can anybody please clear my doubt: Would our knowledge in physics be reduced if Fourier transform were never discovered?
Finally, is it correct to say that Fourier series is more fundamental than Fourier transform? or are these equivalent?