PZ has criticized Powerpoint lectures in the past for being obfuscating and substituting annoying special effects for content. Now he clarifies that Powerpoint can be used well, by linking to a lengthy primer on Archaeoastronomy about how to properly use PPT slides in lectures.
My take on it is that what can be appropriate in archeoastronomy need not be appropriate in math. Math lectures tend to proceed along a theorem-proof sequence. I’ve tried suppressing that traditional sequence as much as possible in my math posts, and still it’s glaring. Mark Chu-Carroll‘s math posts do a better job at suppressing it, but they’re more of an overall survey, which I think is too general even for seminars, which in my experience prove fewer things than lectures.
In non-mathematical subjects, blackboards are used mostly for writing down the main points, so that PPT can be a good substitute, at least when used intelligently. In math, professors fill the entire blackboard with the details of a proof or examples, then go back to the beginning of the blackboard and erase it to write more, lather, rinse, repeat.
I haven’t seen any math professor at Columbia use any technological power tool; but in Singapore, my professors often used an overhead projector with text-saturated slides, or even projected a PDF file and scrolled down to reveal entire proofs. The theorem-proof sequence apparently works better with ordinary math text. I presume that just like a good PPT presentation in biology is just a typed up version of blackboard bullet points, so is a good PDF presentation in math a typed up version of the proofs the lecturer would write on the blackboard.
At least, that’s what my experience with math is. Your mileage may vary.