> I personally find these obscure technical (and highly abstract) explanations often far more easy to understand. I do, too, but I also know that nontechnical,

> I personally find these obscure technical (and highly abstract) explanations often far more easy to understand. I do, too, but I also know that nontechnical, nonmathematical people are turned off by a quick immersion in mathematical reasoning. I have a theory (not just mine by any means) that if the beauty of mathematics could be presented before the required discipline and attention to detail, we might lose fewer possible future mathematicians. As things stand, the public level of innumeracy is depressing. > On the other hand: when using "simple" definitions, you always have to worry whether, if something sounds strange, it is because you haven't understood it or if the "simple" explanation was simply bad. Yes, very true, one must be very careful to get it right while making it simple. I personally think a persuasive layman's explanation of something mathematical can go wrong in so many ways, and the more persuasive, the more room for error. Consider all the crazy "explanations" of quantum theory out there -- the more popular ones have no connection to reality.