I say everything I'm about to say as a person who is more certain than not that you have something valuable to contribute through this sequence, and who eagerly awaits more.

All of your posts in this sequence have purportedly been written to motivate your main thesis, but it's not clear to me what that is. I think you should stop motivating and very clearly reveal your Big Secret. What can I do right now to improve my mathematical ability? That's what I want to know.

Consider these points:

• Eliezer tried to explain his metaethics the first time and failed, but it was okay because he was able to write his epistemology sequence after that and clarify. His posts pretty much always motivate people to continue reading because they usually have such high insight density and people know that they do; but your posts in this sequence, as far as I can tell, have just been anecdotes, quotes, nonstandard definitions, references detailing your nonstandard definitions, and promises of elucidation in future posts, and in your case, there isn't common knowledge of high insight density to make people trust you even when they don't understand where you're going. Your second post had less karma than your first post, and I predict that this post will have even less. I think that people are getting antsy. If no one understands your Big Secret and it turns out that all of this motivation really was necessary, then you can just do what Eliezer did and try again.

• It seems to me that you're getting strawmanned a lot. I want to argue against those things but I don't have a real man to point to, and if you wrote a clear thesis statement, then I would. Maybe someone would say that I'm defending a side rather than seeking the truth if I want to argue against another position when I have no clear position, but I think that amounts to claiming that your predicate's extension is empty rather than that it's vague. There are things that people have claimed about your posts that I can't consider an accurate statement of your (vague) position no matter how charitable my interpretation. The most obvious is that you're claiming that innate ability is irrelevant; you've explicitly claimed the opposite. Other possibilities in order of increasing plausibility include:

  • (Almost) anyone can be a famous mathematician.
  • (Almost) anyone can do mathematical research.
  • (Almost) anyone can be what an average person considers 'good at math.'
  • Current mathematical pedagogy sucks.

You've explicitly stated the fourth item, and it's the one I'm most sympathetic to, and it would be useful to me and many others if this were elucidated regardless of whether or not it means I can be a famous mathematician. If you're claiming more than one of the above, then maybe you could just refine your points about that particular point into public form, and substantiate your more radical assertions afterwards. I really want to see what you have to say about pedagogical techniques more than anything else. I want to be better at math. I'm open to the possibility that I'm misinterpreting everyone's attitudes about this and I'm the only one who wants to know what you have to say about that more than anything else.

I also think it's weird that I see a lot of people throwing around 'good at math' and 'bad at math' as if those terms mean the same thing to everyone. Some people mean Calculus III, some people mean Fields Medal or thereabouts, and some people mean somewhere in between. Whether someone is good or bad will depend on what people mean. It also surprises me because that's an amateur mistake here. It also doesn't help when you quote modest mathematicians but describe people who are characterized as 'bad at math' in your anecdotes. It makes it too easy to assume that you're claiming those people are secret Grothendiecks, and I don't think you are. If you are, then I want to know.