[abdullahkhalids]

The point of attending those talks is to get a flavor of the area. To get a sense of the language the practitioners use, and how they reason about things. Perhaps what sort of results they consider important. These are incredibly important things, if you want to work within the social institution of academia.

And of course, sometimes you are presented with a wonderful theorem, that just makes you open the book/paper and start seeing why it is true.

[andirk]

Much like cliffhangers in fiction, sciences should be taught this way as well. Cause the student to anxiously seek out what happens next. Some will, some won't. Those who do are the ones the program should want to keep.

[nohuck13]

"To get a sense of the language the practitioners use, and how they reason about things."

Isn't the article assuming you already are a practitioner?

[abdullahkhalids]

By practitioner I mean, you are one in your own research areas. And not in other areas of math.

People in different areas of maths have radically different languages and ways of thinking about things. And subareas will develop their own ways of thinking and talking about things. If you are a young researcher, you almost certainly have to learn these, if you want to understand the area. A more mature researcher can be confident enough to understand the new area in their own language.