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Comment by CaptainNegative | Hacker News Reader

The article goes into significantly more depth than is quoted above, building motivation first by describing the approach initially taken by Tao (as I understand it, analyzing the combinatorial expansion of a particular graph on the integers) followed by giving an overview of the new approach (analyzing the spectral expansion of the difference between Tao's graph and a simplification thereof) and why the simplification was reasonable. Obviously the overwhelming majority of the gory details were spared, but given the content I thought the author did a good job giving a high level picture accessible to a relatively general audience.

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Quanta is one of the most consistently high quality publications operating today, for my money. Their Joy of X podcast with Steven Strogatz is highly recommended for anyone interested in math.

Just to be clear - I love the article and want more.

I’d actually refer the interested reader at that point to just try reading the actual paper past that point. It’s probably not going to be easy or even all that legible at first, but it’s where to start. Backfill with outside sources from there.

But, to support GPs suggestion: Wouldn't it be nice if there was something that would help hold the hand of an educated-but-not-expert reader when reading the actual paper.

"just read the source" isn't the answer to a lack of documentation :) (usually)

It’d be nice but I don’t know what you’re asking for would look like exactly.

Academic papers usually have an introduction just past the abstract and may be the closest to what’s requested here. This is supposed to get the reader prepared for the meat of the paper. In a lot of math papers, it acts as a 101 prepper/refresher for the core concepts used in the paper.

There’s also the wolfram site for math. It’s been a while, but it functions something like an encyclopedia of all math topics. I’ve used it to quickly backfill a reference many, many times.

Reading an article or proof is not exactly analogous to “reading the source” as both articles and proofs are meant to be written to be read by a human with an agreed upon background and lead them logically to the conclusion(s) of the article. Articles and even proofs can be intimidating, I get that, but they are surmountable with a suitable time investment.

I think maybe Wikipedia is better here than Wolfram's site, it has entries for Ramanujan graphs and expander graphs for example.

The paper does actually seem readable, especially at the beginning, but it's dense and long. Somewhere between the article and the paper in terms of complexity and technicality would definitely be interesting to me, although I realise it's a lot of work to produce something like that.

Interestingly the paper acknowledges collaborators who have helped via MathOverflow. I wonder if a collaborative site for explaining maths papers in more detail could be viable. After all, even xkcd.com has explainxkcd.com. Like you, I am not sure what this would like, but it would be fun to find out.

It kind of sounds like they think they found a kernel of knowledge which could form the body of something like a for-loop or inductive step of an induction proof of the larger problem.

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