I think for something like HN to be broadly interesting it needs volume and variety, because people’s interests are a long tail phenomena. I imagine that is probably true for maths too.
No, not at all. Each maths researcher will understand (and care about) only a fraction of these. Maths research (like most subjects) is broken into highly specialised subfields, and experts in one often cannot readily understand research in others.
New research papers are the cutting edge of the field, pushing out the boundary between known maths and unknown maths, and this boundary is huge. Things there are understood by very few people, at first just those who developed them, and the prerequisites for understanding any individual area of new maths are substantial. Known maths is also huge, far too big for any one person to understand it all.
Source: have maths PhD.
Academics as a whole doesn't really tackle the issue of taking knowledge and bedding it down into digestible form. Individually a lot of people do great work, but as a body they don't seem to see as that as their role. So far the solution is to throw clever people at academic papers and assume they will sort out something comprehensible as they go.
It always struck me as a very hard, very high-value problem. How do we measure ease-of-learning in a systemic way? Can we cheaply and reliably rate one explanation of a topic as superior to another of the same material?
I think we need to stop conflating maths and abstraction with genius and general intelligence: it's too important to be politicised. I also think we should assume that any healthy adult can learn to do maths well by virtue of nothing other than having a human brain. If the normal healthy adult does not do maths well then that should be treated as a pedagogical problem rather than a reason to stratify society.
I think that maths in many ways can be treated analogously to language, and I think what we need to do is express maths in a way better suited for normal human language faculties. I very much like the artificial language Lojban as an architecture ingraining combinatorial and first-order logic into regular self-expression. Imagine speaking Lojban your whole childhood and having this rich vat of lived logical analogies to draw on when learning.
Effecting minds in this way and focusing on median improvements in the functionality of the majority is in my opinion has many many times more potential than any sort of elite screening or stratifying programme.
To use Neural Networks as a poor analogy. Given identical training data and different random starting weights you end up with different end results. Thus, even with identical potential at conception people would end up with different strengths naturally.
Better training clearly shifts the median, but when you start talking about populations of extreme outliers from a billon+ people that’s going to be meaningful. Especially as differences compound over time.
Currently their is a trickledown effect where useful techniques end up shifting the landscape. RSA encryption pushing little bits of what would otherwise be abstract number theory into a few high school classrooms etc.
Academic papers aren’t meant as a static store of knowledge in digestible form for outsiders. They are an ongoing conversation between experts. In his way they do assume h reader has done the work to follow along.
Eventually the good bits mostly get worked into digestible form, usually by the mechanism of seminars first, then in courses.
One can argue that there isn’t enough incentive to go past working up a seminar, and especially produce generally approachable material which is a lot of work and typically doesn’t pay at all.
The issue of the approachability of papers is similar. There is currently negative incentive for this. Some people are naturally better at it, but mostly if you are spending extra time on this it won’t help your (academic) career at all, and it might hurt.
We already use a subjective measure for rating explanations. It's called elegance. Academics tend to prefer shorter, more elegant proofs in my experience. It just takes a long time to get there. If you want to understand the latest research, you have to be a specialist in that subject area. Even the elegant proofs can require years of study before you have enough background knowledge to understand the concepts needed to make it digestible.