The varkappa and the varpi are just calligraphy versions of the regular letters κ & π, so I would avoid them. Also, the ς is just the form σ takes when at the end of a word, so I'd avoid that too.

And I don't know why anyone would use the uppercase Ξ (Xi) when the lowercase is such a nice letter: ξ.

I like ξ! Have been using it in my paper. When presenting it, people have different ideas about how to pronounce it. Some say it like x-i, some say khi, and some try hard to say xi. I like the x-i version as it is similar to its latex notation \xi.

It seems okay to use both uppercase and lowercase versions at the same time. For example Ξ is a set and ξ is an element of the set.

Generally agree, but should be supplemented with influence of hand-written math.

> Xi -- seems like a good one!

This one is fine to typeset, but is slow to write by hand because it has three disconnected strokes. (You have to pick up your pen twice.) People don't want to use it to do actual hand calculations, and so rarely use it in papers (both because they aren't used to it and, perhaps, because they know their readers won't want to write it by hand).

> Pi -- good one, I have seen this used for sets. In context there is rarely any confusion with product notation.

I think the rarity is indeed because of risk of confusion with product notation. Note that capital sigma is also very rarely used (15th), and my guess is that many of its appearances come from people mistakenly using it for a summation rather than \sum, e.g., \Sigma_{n=1}^N.

When typeset, the size of the summation symbol is pretty obviously bigger than the variable Sigma, but in handwriting it's not as clear. It's true that subscript/superscript notation for the variable being summed over (and that variable's limits) tends to disambiguate, but very often in handwritten math people just write a quick squiggle for the summation sign without bothering to write down the summed variable because it's obvious from context.

So overall, I think the rarely used Greek letters are rarely used for pretty good reasons! I'd say Upsilon is the most unfairly ignored. It's rendered like a Y in some fonts, but not the one that TeX uses for math, and it's easy to draw quite distinctly by hand.

Probably not widely known in the Latin-writing world, but capital xi has a handwriting variant that looks like two z's joined vertically at the hip; that's where the lowercase variant comes from.

Varsigma is also a bad idea because it is just a sigma, only used at the end of words. So it seems bad taste to use it as if it were its own letter.

Yes, I thought 'oh this has been done carefully' when I read the bit about considering `\var` uh.. variants, but I was surprised that that consideration wasn't grouping them together - counting sigma with 'var sigma' for example.

Are they ever treated as different? Here's a whole lot of \vartheta on Wikipedia for 'theta function', for example: https://en.wikipedia.org/wiki/Theta_function#Jacobi_theta_fu...

I always thought it was just like having both a 'double-storey' and 'single-storey' 'a' available in the same font.

We should also not forget that a lot of maths is spoken (in classes and seminars) so there the distinction between, say, \theta and \vartheta would be lost was they are pronounced the same...

Indeed. I once who had a lecturer who used p, rho, and "curly p" as different symbols -- the latter was the Cauchy Principal Part. Suffice to say my (handwritten) notes were full of little arrows saying "pee", "rho" and "squiggle".