[beng-nl]

My opinion on this is that in mathematics the material can be presented in a very dry and formal way, often in service of rigor, which is not welcoming at all, and is in fact unnecessarily unwelcoming.

But I don’t believe it to be used as gatekeeping at all. At worst, hazing (“it was difficult for me as newcomer so it should be difficult to newcomers after me”) or intellectual status (“look at this textbook I wrote that takes great intellectual effort to penetrate”). Neither of which should be lauded in modern times.

I’m not much of a mathematician, but I’ve read some new and old textbooks, and I get the impression there is a trend towards presenting the material in a more welcoming way, not necessarily to the detriment of rigor.

[zozbot234]

The upside of a "dry and formal" presentation is that it removes any ambiguity about what exactly you're discussing, and how a given argument is supposed to flow. Some steps may be skipped, but at least the overall structure will be clear enough. None of that is guaranteed when dealing with an "intuitive" presentation, especially when people tend to differ about what the "right" intuition of something ought to be. That can be even more frustrating, precisely when there's insufficient "dry and formal" rigor to pin everything down.

[TimPC]

If it's actually in the service of rigor then it's not unnecessaryily unwelcoming. If it's only nominally in the service of rigor than maybe, but Mathematics absolutely needs extreme rigor.