Aim for brevity while avoiding jargon.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
There should be no such thing as boring mathematics.
Many mathematicians derive part of their self-esteem by feeling themselves the proud heirs of a long tradition of rational thinking; I am afraid they idealize their cultural ancestors.
The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.
I mentioned the non-competitive spirit explicitly, because these days, excellence is a fashionable concept. But excellence is a competitive notion, and that is not what we are heading for: we are heading for perfection.
