Twenty Pieces of Advice for a Young (and also not so young) Mathematician --
Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) Learn to use and write programs in Maple (or Mathematica, or any computer algebra system) (Doron Zeilberg)
Why models should be wrong --
Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity. (George Box)
Why you should not read math while watching TV --
Although we hope that this book is entertaining in places, most of it, in fact, is rather dull except perhaps to the odd technical fanatics. Thus we do not recommend it for class notes or for reading during TV commercials. (Luc Devroye, Nonparametric Density Estimation: The L1 View)
Why you should not be too formal --
An axiomatic presentation of a mathematical fact differs from the fact that is being presented as medicine differs from food ... Understanding mathematics means being able to forget the medicine and enjoy the food. (Gian Carlo Rota, Indiscrete Thoughts)
Why you should not use "it's easy to see" in a paper --
... we all know that behind things that are easily seen there may be years of thinking and/or huge piles of scrap notes that lead nowhere, and one sheet where everything finally worked out nicely. (Allan Gut, Probability: A Graduate Course)