I mean, kind of? But not really: high schoolers are never going to be able to answer tossups on Alexander-Lefchetz duality, whatever that is, ever ever ever. Because they'll never know jack about it, because that sort of information is simply inaccessible to the immense majority of high school students. But everyone can read a book, so nothing prevents them from learning quiz bowl lit to the point where they can one-line tossups on it. But even if you made math something that you absolutely had to dedicate one student to, in a game with 25% theoretical math, you'd just get a lot of math guys who wouldn't be able to answer a lot of the really hard tossups.

So the Alexander-Lefchetz duality thing was my example of a bad math question using a common-link sort of deal and has nothing to do with HS difficulty. It was the first line of a tossup in my room at EFT and I got buzzer-raced out of it (by Harvard A) because both me and the guy who answered had taken a class that vaguely mentioned this existed. But there's no need for any real knowledge when the tossup mentions Alexander-Lefchetz, which is really the case for most such tossups.

Also, there are such things as math books (note that everything I'm proposing are things usually studied before or during the first year of college).

The fact that you must not only know how to solve the problem but also solve it makes this not quiz bowl. I suppose the language many people have been using is a little imprecise: we don't just mean computational speed as in "speed at which one can evaluate arithmetic:" it's the speed at which one can do some kind of manipulation on something. One must solve the problem faster. And I'd argue that there are people with more knowledge about a subject in math who are not capable of solving the problem faster.

So in the case of, say, the fundamental theorem of calculus, is your argument more or less: "there exist people, Alice and Bob, so that Alice 'knows more' about the FTC, but Bob can solve calculus problems involving the FTC faster. in this case, Alice needs to get the tossups, rather than Bob." It seems like this makes it an issue of semantics, since one could say that we're testing the knowledge of how to solve the problem.

Here's what the "do something" argument is saying: quizbowl is about taking a clue, figuring out what the answer is in terms of that clue, and buzzing in, while computational math is about taking a problem, establishing the formula needed to solve the problem, computing the answer, and then buzzing in. I don't care how long or short that computing step takes. It doesn't matter how far you boil the "doing it" step down, whether you're working with big numbers or small numbers or variables or anything. That extra step is still there, and that's not fair from a continuity standpoint.

Okay, so do you accept that "establishing the formula needed to solve the problem" is legit? Because if so, at least on some level, easy computation can be memorized. (the multiplication tables, the basic rules for multiplying variables, etc). Strangely, this would be similar to a math competition in quite few ways.

Whether or not you've never heard of Pope Gregory the Great (hint: he is known for a namesake chant) or Orpheus in the Underworld, the source of the Can Can, doesn't make them any less relevant and askable. I would contend that both of these have their place in the canon well earned.

I'm not challenging this. There are a lot of things in the canon I don't know about, and it doesn't bother me that those who do answer those questions instead of me.

Also, can you please stop implying this "I don't know this therefore it's too hard, or I know this, therefore it's too easy" idea?

What I'm saying is that the relation between Orpheus and the Underworld/Gregory the Great and what the typical high school student learns in high school is more or less the same as the relation between a second fact about pi and the high school math curriculum.

Look dude, I think your idea of "high school kids interested in math" is somewhat different from what we have. I don't mean to say this is bad, but it probably just a result of your exposure to other students like you. I know that you have done a lot of math (you're the same 2006 IMO medalist, right?), and what you have been exposed to far outshines what I am exposed to (I could never get past the AIME), which in turn is probably much higher than what the average quiz bowler is exposed to. The fact that they are "common things" to you is in stark contrast with the fact that they may be profound ideas for some people out there.

It is sad that the math canon is small, but there is relatively little we are going to be able to do about it, unless we find that the average person's exposure to math increases. If we start writing hard IS set tossups that become indistinguishable from ACF Fall/EFT level tossups, I think we have come to a bad state in quiz bowl.

So I generally go by what the interested kids at my high school would know. I agree that many things would not be okay at the high school level under any circumstance. And by "common" I mean, "these are accessible things that a student interested in math would go to outside the standard high school curriculum." It seems like the literature and history canons are very far divergent from the corresponding high school curriculum, so I don't see why this is not possible for math (of course not immediately but at some point).

Yisun is putting forth the argument that all the fundamental problems with math calculation questions can be solved by asking harder calculation questions, when of course this solves none of the problems and adds a new one (dead tossups).

I believe that I've addressed all your arguments against what I claim to be the helpful effects of harder questions. If I've missed any or you disagree, feel free to challenge my position. But it's a bit hard for me to really argue against these nebulous "fundamental problems." Also, I've asked a couple times whether there are indeed buzzer races, as some have claimed, or many dead tossups. Which is it? You seem to have argued the former before, so I'm a bit confused:

Matt Weiner wrote:
Which three TJ players and two Charter players knew, and were racing to do the arithmetic on. You cannot overcome the pyramidality problem here because the one math question always comes at a discrete time, as opposed to the real quizbowl tossup which can actually be pyramidal.

I find the turn this thread has taken kind of bizarre. "You want quizbowl to look like Mathcounts" and "you don't know anything except how to do arithmetic so you just want more arithmetic in quizbowl" are used as insults in these discussions, normally. They are extreme characterizations of the pro-math position that may even be unfair ad-hominem attacks to use in many circumstances. Except, Yisun seems to unironically believe them and is loudly proclaiming them? This is bordering on satire.

So a large part of my point is that arithmetic can be kept to more or less a minimum that is equivalent to "can you remember your multiplication tables." So I fail to see how your second point is in any way accurate. And what's wrong with Mathcounts, seriously? It does have questions that involve too much computations, but that doesn't mean the entire competition revolves around it. They can more or less be taken out by making the numbers nicer.

It seems that only one side of this argument is considering such a claim (eg, Gregory the Great, Orpheus in the Underworld)? I know perfectly well how to do math..

I was worried when I brought those examples up that I would be accused of making this argument. My argument is that most high school students (independent of quiz bowl) don't know these things, yet they are part of the canon. So saying that most high school students don't know some things about math is not really an argument against its inclusion.

I guess what I'd like to see is an argument for why things currently in the canon are there besides "everyone knows them" and "they are important" (so are a lot of things), since these seem to be being used a lot against harder math.

I see this to be a problem. Lets say someone does know Catalan numbers, but they have too much pressure or whatever reason to recognize those as instant Catalan numbers instantly, or they just know the definition and can't recognize them as Catalan numbers, is it fair to penalize them because they were so supposed to subliminally recognize they are Catalan numbers? I doubt that.

I agree that such subliminality is bad and is currently a feature of many of the computation questions. In this particular case though, if they just know the definition, they should probably lose to someone who has deeper knowledge of the Catalan numbers and knows the many types of places where they come up. This is actually one of the canonical examples used to introduce Catalan numbers that someone who just learned about them would probably know.