First post here. Would dearly like to have some answers for book I am writing on aesthetics and psychology. Can't find FAQ section, or anywhere else these questions are answered succinctly, so here they are. Feel free to give yes/no answers, links or even to contemptuously brush aside (although I'd love to know, if so, why these questions are stupid). Needless to say I am not a mathematician and would appreciate as much simplification as possible without distortion. 1. Is it true that the number that pi represents, being infinitely "long", cannot be imagined / accurately represented / exactly known; only the symbol or approximation can be? 2. Does it follow that it is impossible to imagine / accurately represent / exactly know the area of a circle? 3. Is this also true for numbers like e and i? - that all we can know for sure about the calculations based on them are very good approximations? 4. What calculations are based on these numbers? What branches of modern mathematics are based on pi, e and i? Could you give me a simple list (logarithms, calculus, set theory, etc) or does it pretty much amount to "all"? 5. Is there some way that pi, e, i are connected to either prime numbers or chaos theory? 6. Why are prime numbers useful or beautiful? I read an Oliver Sachs book where two autistic twins were thinking up and then "enjoying" (as if drinking fine wine) massive prime numbers. Any idea why would this be so? 7. When a proof of theorum is said to be "beautiful" what criteria does it satisfy? Efficiency is obviously one of them - succinctness. Use of startling analogy another (i.e. reasoning from quite a remote perspective to the one at hand)? What about harmonic arrangement (the formula in some way "feels" nice, like a Fibonacci series looks nice)? 8. Quantum mechanics is, in some ways, the science of the impossible to imagine - what elements of maths are used to deal with wavicles and time travelling particles and whatnot? Does pi, e, i, primes or chaos figure in any way? 9. Would you say that interesting maths tends to come from interesting mathematicians? Knee jerk response I suppose is "of course not". But do the lives of the most "creative" mathematicians look different to the lives of the less brilliant? I know Fermat, for example, led a dull life, but is there any indication that there was "something about him" that set him aside from others in some other way than mathematical skill? That's all. Thanks for reading. Dron.