| >One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me. You are very wrong on the other point: none of what I said is borne out of a view that mathematics should be difficult and "hard" an impenetrable (rather than soft and approachable). Indeed I view this sort of overlong prose as impenetrable and confusing, and the succinct style of e.g. Landau textbooks much clearer (see my other comment). >The commenter is again taking a minority viewpoint and baselessly extending it. This is not a minority viewpoint. I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head. It is also plainly true: mathematics is about rigour. It is not an obstacle, nor is it an end in itself, but it is a fundamental part of mathematical study and reasoning. If you aren't being rigorous, you're not doing mathematics, it's just a waste of time. I'll let Michael Spivak speak for me: "In addition to developing the students’ intuition [...], it is important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions." >be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart), and again, not in the least bit what I mean with my criticism. |
There are reasons partly historical and partly due to the subject matter of CS that mathematicians closer to it tend to place relatively higher value on formality.
> It is also plainly true: mathematics is about rigour.
This is taking taking it too far and you're placing yourself in the formalist camp, which is a minority viewpoint. You gave a nice quote from Spivak where he characterizes rigor, "...the natural medium in which to formulate and think about mathematical questions."
Labelling it a 'medium' is very informative. Computer programs likewise depend totally on the formality of the medium; it's in intrinsic part of how they are able to operate. Same with the magic of formality + inference in mathematics.
That said, the psychological questions of pedagogy involve much more than the intrinsic features of some subject. In learning to write completely formal computer programs, one benefits immensely from instruction which departs from total formality. I'm assuming this would be obvious to the readership here so I won't go into more detail.
> Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart)
I was referring to the social standing of the languages (which is all that matters for the points I was making), not their intrinsic features.