Comment by dahart

I don't know your background, but speaking as someone who has done a PhD in Pure Math, and working with a lot of people who have done PhDs in Pure Math, I disagree with you. It's very much a case of feeling stupid, and being able to embrace that and live with it.

The "being curious" thing is independent of the "feeling stupid" thing. It definitely exists, but it's absolutely not the same thing.

Looking at the rest of your comment, maybe we have a lot in common, but I definitely disagree with a lot of what you've written here, so no doubt our experiences are wildly different. Perhaps over a coffee[0] we could talk constructively about education, math, struggles to understand, and work ethics, but suffice to say here that even if we do have substantial common ground, I think we might have very different points of view.

[0] Other beverages are available.

Well, mathematics at a graduate level really is a subject that can only be self-taught, as are most subjects at the graduate level. Yes, some guidance can be available, but the pedagogical hand-holding that is undergrad is simply not possible. The analogy to language only really applies to mathematics that is well-understood and can be taught this way. In grad school, almost no mathematics you encounter is that well understood, so the teaching methods are absent.

There are two authors here, since the post contains an inset about dealing with your own ignorance by another professor. They aren't saying quite the same thing. The inset is saying that every grad student will confront their "absolute ignorance" and it will be difficult, scary and possibly painful. The author of the post is saying it can be a source of joy. I suppose they can be reconciled. It could also be that so little of our behavior is based on knowledge that the only sane reaction is at least somewhat negative, whether characterized by being overwhelmed, or sad, or detached.

Reframing it as curiosity is a good point, although the essay as written resonated with me because it emphasizes the "productive ignorance" of research.

One of the central problems of our time in research and academics, I think, is an incentive to focus on areas that are well-established because we know they are likely to produce results that we have confidence in (according to whatever inferential criteria we use). The idea of it being ok to not know something a priori, to have lack of confidence in it, seems sort of discouraged in the current climate, because it's too risky.

> But one of the big problems with math education is that we force students to struggle to a far greater degree than other subjects, under a belief that personal struggle, the “trying”, is the only way to truly get it.

I disagree. In fact, I found that often the better and more didactically streamlined the exposition is in a book, the less deeply I end up learning the material. It is precisely the personal struggle, having to make my own sketches and derivations, starting out with a misconception because of bad phrasing in the book and having to explore that misconception until I find what I misunderstood etc. makes the knowledge stick much better because it now feels my own, like an intimate friend.

Spoonfeeding may get people quicker to the point of solving the standardized quiz at the end of the chapter but that's not the same as learning and understanding. Another instance of metric-chasing in action.

It's a bit like how I learned MS Office or Photoshop by trial and error as a kid, or programming by mucking around trying to make a website do what I want. And you bet it was a struggle. Struggle but with reward at the end. Compare that with a handholding tutorial where you do learn how to do whatever the tutorial makers had in mind, but it won't generalize as much. Sounds totally dry. I loved computers, but hated school lessons that tried to teach us MS Office in the handholding spoonfeeding way. It's the death of the subject.

It's a safari in a safe car, looking at the animals through binoculars vs running around in the jungle in your own adventure amongst the beasts.

Curiosity is when you're reaching out to find out about a thing (let's call it X) which you want to learn more about.

Feeling stupid is when you're confronted with an external you cannot understand why it works.

Curiosity can help push through feeling stupid, but you can be curious about something you won't struggle understanding it at all.

kids struggle with grammar, pronunciation, pragmatics, vocabulary, etc. they do so naturally, and maybe you've forgotten your own struggles, but they're very real

i think we can do better than we are doing at math education, much better, but there is no way to learn math, or anything else, without diligent effort. it won't happen by passive absorption. you can listen to people speaking spanish all day every day for years without learning more than a few words of spanish if you don't make any effort

curiosity is one possible motivation for making that effort, but the immediate result of the effort is, at first, failure. that's true of language, it's true of playing the guitar, it's true of programming, it's true of throwing clay on a potter's wheel. that failure feels like being clumsy, weak, or stupid, depending on the form it takes

and that's what the article is talking about. trying to do things that are beyond your mental ability makes you aware of, and frustrated with, that mental ability. that's not curiosity, it's feeling stupid. it's also how you increase your mental ability!

But he is not talking about education, about doing a course, where "getting the right answer makes you file smart". He is talking about research where nobody knows the right answer.

> He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing.

I disagree.

How can you be curious without something you don't understand?

The point, as I see it, is that if you find yourself in a position of complete understanding, then you must also have a complete lack of curiosity. If you think you are in that position, then the way to revive your curiosity is to deconstruct your position of expertise, i.e., recognize your position of stupidity.

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Curiosity is step 2. Stupidity is step 1. Learning moves us from step 2 to step 3. The important thing to recognize is that step 3 is actually a new instance of step 1. Expertise is the base case of this recursive tree traversal: it's how you stop the learning process.

The struggle isn't necessarily bad for learning. It really is a good way to learn. I like it.

But alas, I never thought as a kid that I didn't have time for other things. I was always into something.

As someone who is currently studing maths I strongly disagree with this

> He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing.

One of the most important characteristics to succeed in maths is the ability to acknowledge things you don't understand, to fail, and to persist in spite of failure. Trying really is the only way to understand some hard things, because there are some things that are conceptually extremely difficult.

He's not talking about relative stupidity where there are other people you feel are smarter, he's talking about stupidity on an absolute basis. You don't know. You don't understand. But somehow you have to find a way to carry on, and then later on, looking back once you do understand, you're baffled by why you didn't know/understand or couldn't see some crucial things. You have climbed up a ladder and pulled it up behind you and it's hard now to imagine what it is like to be on the ground.

It's not about curiousity. Of course you have that - if you didn't you wouldn't be there in the first place.

I think the framing as "stupidity" is to highlight that you don't always chase creative questions. Quite often, you should chase the obvious or understood points.

The problem, I think, comes from the weaponization of "stupid" against people. The XKCD of the lucky 1000 plays a good role here. If you are constantly deriding others for stupid takes, then anyone that derides one of your stupid takes will hit hard. And that seems to be getting worse.