Most people suck at explaining. So the fact that most scientists suck at explaining is like... yeah, that's what naturally happens, unless you actively reward good explanations.

The perfect case would be if someone is great at research and also great at explaining. But great skills are rare, and specific combinations of great skills are even more rare. So you will have a scientist or two who are great explainers at the same time, but then you have a lot of scientists who are great at research but suck at explaining, and also a lot of people who are great at explaining but suck at research. How does academia reward them?

The ones with both skills will get the highest rewards: they will invent lots of cool stuff and describe it clearly, so they will get many citations. But there are only a few such people per generation. The ones who are good researchers but suck at explanation can still invent something and publish the type of paper you complain about; and they will get a (smaller) reward for doing so. The ones who are good at explaining but suck at research... will probably be fired.

There are a few things that a person whose only skill is explaining could do in academia. They wouldn't get a reward for explaining someone else's paper clearly, but they could get a reward for writing a meta-review that would explain multiple papers clearly. In theory, their scientific contribution would be in comparing the papers, but in practice, hopefully even people who only needed one of the papers would cite them as a reward for making it easier to understand. -- I don't know if this would actually be sufficient to survive academically.

People who are good at explaining can also make money by writing popular textbooks. Question is, whether there is a sufficient demand for a popular textbook explaining some obscure math.

> They wouldn't get a reward for explaining someone else's paper clearly, but they could get a reward for writing a meta-review that would explain multiple papers clearly.

I see tremendous value for such work, and I think it is one of the biggest current bottlenecks in the sciences. We've got the cutting edge stuff happening in papers, and we've got 5-10 year old knowledge that makes it into textbooks, but in the middle there is nothing. Everyone is working on their own to catch up. We're talking thousands of grad students independently banding their heard agains the same problems...

If there were more "review journals" things would drastically improve. Maybe NSF could provide some funding for such efforts? Not sure what the metrics would be for this---not citations, we'd nee more like views or upvotes like on HN. The other option would be for grad students to self-organize into "reading clubs" on different subjects and share notes.

Explainers-first shouldn't be fired if they make up a small percentage, because they do a wonderful job without the bulk of resources.

I'm not sure if explainers-first are the minority, though. After all, it's much easier to review than to create. And we do want new research.

Firstly, let's not fall for a false dichotomy. There is likely a simple equilibrium of review and creativity that must be maintained for an optimally healthy scientific community. Obviously, the old style of numerous-journals + publish-or-perish mentality was unhealthy implementations of a scientific system.

But, I would move away from papers entirely. They hold no redeeming values over alternatives like a git repository published publicly with an "issues" forum e.g., GitHub, etc. This needs to absolutely become the new standard, and we need to get rid of papers and journals, both physically and digitally, in their entirety. They have zero redeeming factors at this point in time except to boost the ego of the published. Quality control can easily be decentralized and available to everyone using something like GitHub. We know this because that is literally what the security and trust of open-source software is predicated on: putting everything in the open.

Modern math papers also love cryptic symbolism. I've been doing some research and been reading papers on a certain topic from 50s to these days. The difference in math presentation is startling: a paper from 50s really tries to explain things, e.g. it uses simple partial derivatives and some simplifications because that's just enough for the paper; on the other hand a paper from 2020 describes the very same math as a cryptic sequence of triangles and dots, and the reader really need to be familiar with the context to understand what this compressed formula expands into. I believe the main motivation behind this is the desire to look sophisticated, so anyone reading the author's paper would be impressed at a glance with the complexity of the math.

Like ∇^2 u = Δu = f? It's not really cryptic, it's taught in multivariable. And it's not done to look sophisticated, it's so that you can instantly recognize that it's Laplace, or Poisson, etc.

If I tell you B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k do you instantly see what operator is applied? That's why you just write B = ∇×A.

People presenting ideas in shorter notation is not showing a lack of progress - usually it's the opposite. In old optimization papers people would write out the entire normal equations, entry by entry. Not really insightful at all, compared to A'Ax = A'b.

That's a trivial triangle. Modern papers go far beyond that and invent some partial diff operators, like "F.∇" which means "do the grad first, then dot product", use uncommon context-depenedent subscript and superscript indices that can mean fairly arbitrary things and so on. But my complaint is mostly about the use of unnecessary and terse formalism where a short full form is replaced by a 40% shorter form just to use a uber generic high order operator to look fancy and refer to couple mysterious (and useless in the context) theorems or other papers. This is when I have to read other similar papers and see wtf that cryptic equation really means (and often it means some mundane thing). Programmers have the same kind of mental problem: in order to look sophisticated, they intentionally use more cryptic and terse solutions to impress "less initiated" and to hide the fact that what they are doing isn't that complex.

This seems to be presenting a false dichotomy. B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k and B = ∇×A are not the only ways, out of all possible strings, to encode that information. This is the power of modern programming languages. They are mathematics with much better syntax.

Can you point us to that specific pair of papers? I have never seen a debauchery of triangles of dots used to write a pde.

But that sounds like bad exposition. What benefit would any author get from purposely obfuscating what they're trying to share?

Every author has their own motivations, but I will echo what the parent has expressed that often, if not the majority of the time, authors are making their papers far more difficult to read than they need be.

To that, I'll add anecdote. Some years back, I had a fight with a coauthor on a paper who wanted to remove the majority of the substeps within a proof. He believed that it was condescending to include such material and that any interested reader should be able to derive it for themselves. And, in fact, he asked a colleague in the room at the time who agreed with him. I stated flatly that as the primary author that I could not understand nor complete these proofs without these steps, so the material stays. I contend that at least in this one particular case a combination of exclusivity and arrogance led to an attempt at obfuscation.

Remember, publishing isn't just about sharing knowledge. It's also a way to posture, advertise, build a brand, and get grant money. Beyond that, mathematicians are still people with all the imperfections that implies.

Could well be, and I have no definitive evidence otherwise, but sometimes it's hard to imagine anyone being that bad at exposition. Some "benefits" might be seeming smarter and more knowledgeable than they are, making it harder to exactly replicate their methods (most relevant in applied areas), or citations by intimidation ("I don't understand this, but it seems impressive and relevant, so I better cite it.").

They all sound plausible and likely. There are people obfuscating knowledge for all the reasons you mentioned.

At the same time, it doesn't mean there's a concerted effort to obfuscate mathematics.

Explaining things is hard, because you have to create a clear picture of the audience in your mind. Then, you have to draw the lines between what they know and what you want to introduce. The curse of knowledge is a big obstacle here.