I love and am absolutely fascinated by both mathematics and physics but have no training of any worth in either. As such I should be grateful if anyone answering any of the three questions below avoids (if at all possible) terminology or language that requires such training. Thank you very much for your consideration. My three questions are: 1. Which area (or areas) of mathematics is (are) basic in the sense that all other areas can be derived from it (them)? Or, alternatively, if this question is itself the ‘wrong’ one to ask, what is the ‘correct’ question along these same lines? 2. My understanding is that the two pillars on which physics is based are experiment and mathematics. I can see the value of experiments but why is mathematics (at the most fundamental level) so important in physics? 3. Given 2, why is it that, time after time, developments in mathematics that start out as ‘pure’ turn out to be key to providing insights into developments in physics? Euan Note to moderators. I don’t want to double post but should I also post this on one of the physics forums?