I must sincerely and strongly disagree with you. Technology can help elucidate mathematics beyond plug and chug. Teaching is one of the best ways of learning. a

I must sincerely and strongly disagree with you. Technology can help elucidate mathematics beyond plug and chug. Teaching is one of the best ways of learning. a rough paraphrase of something I read someone say is they write a new book every time they wish to learn something new. Writing a computer program which embodies a mathematical concept is teaching the most retarded entity that is capable of more than just arithmetic. Certainly anything which is non-constructive falls outside of this, but in laying a motivation and providing a foundation that reduces the amount of problems you need to do by say an order of magnitude? Technology is unmatched. Although the requirement on constructive* maths seems restricted you would be surprised that both your [1] and [2] level of abstraction can be tackled with such tools. http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf, http://haskellformaths.blogspot.com/ http://haskellformaths.blogspot.com/, http://blog.sigfpe.com/2006/08/algebraic-topology-in-haskell.html http://blog.sigfpe.com/2006/08/algebraic-topology-in-haskell... You do it this way, vary enough examples and try to anticipate results, you will develop a number sense that is required to be comfortable with maths. It worked for me. * I am skeptical in the reality of arbitrarily real numbers because I am skeptical in the reality of hypercomputation.