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Comment by vertbhrtn | Hacker News Reader

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.

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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.

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.

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.

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.

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