# Handwritten sigma in mathematics

A year and a bit ago, I spent a semester studying mathematics in Moscow. Much to my surprise, rather than using the standard glyph "σ" to denote the Greek letter sigma, people invariably wrote a backwards delta "δ" (that's to say, with the top tail pointing to the left rather than to the right).

Does anybody have any insight as to the origins of this practice? I have been unable to discover anything about it. My best guess is that the tail of the regular "σ" somehow got curved upwards and then back over time.

Edit: I've attached an illustration of what I meant by "backwards" delta. The glyphs for "Russian sigma" and "Greek delta" are distinguishable: they're mirror images of each other. Moreover, I observed this peculiar style of σ from several faculty at the university.

In my personal experience (I studied in Moscow in applied maths) I've seen people writing both versions of sigma, but "Russian" one really was more common. And also there is a rather common scenario, when the lecturer first writes sigma with short tail, then someone asks, what letter it is (or the writer notices himself, that it is not clear enough), and then he prolongs the tail upwards to emphasize it. As @Matt pointed out, Russian mathematician don't have a special course of Greek calligraphy, that's why everybody writes according to his/her own standards. Personally for me, "Russian" version is distinguishable even when it is written very poorly, with distorted proportions, while Greek one is less resistant to such transformations. Maybe, this is the reason.

Mathematicians (at least in Russia) do not specially learn and/or practice Greek calligraphy, except while handwriting math formulas. So the quality of average handwriting may be somewhere between bad and ugly. But I'm rather surprised to hear that you found "sigma" and "delta" not differing at all. That could only be due to someone's personal mistakes.

P.S. I'm graduated in math in Russia.

UPD. I've never seen this "Russian sigma" scripting before. Actual writings may, of course, differ, yet, anyway, they are certainly way closer to "Greek sigma" pattern. I.e. normally it's about drawing "o"-clockwise, and adding some kind of "curly tail" pointing to the right.

• He wrote that the two symbols are distinguishable, not indistinguishable. Maybe this was a later edit from an earlier post that you read.
– KCd
Mar 5 '16 at 1:09
• Probably, it depends on the university... and on personal habits, of course. I've seen people writing it like you say, clockwise, but many people write it beginning from the tail, in opposite direction. At our department the second variant is more popular.
– Lara
Mar 5 '16 at 16:30

You are probably seeing some local quirk of the speakers. I searched online for Russian math videos where I thought it most likely I'd see a lowercase sigma: in analytic number theory for the real part of a complex variable s and in statistics for variance. If you look at 24:05 of https://www.youtube.com/watch?v=oAN6cp2W4ME (a lecture in Ukraine) and 40:52 of https://www.youtube.com/watch?v=JLlprGzDbzc (not a lecture in Ukraine, but note the background colors) you'll see the letter written closer to the way you are used to, with no backward sweep at the top. Look also at Russian videos teaching people how to draw Greek letters, e.g., 7:49 of https://www.youtube.com/watch?v=rReE5ycWII8

Cheers from Moscow mathematician school. I quote our professor - "Never mind, what kind of sign you are using - it could be a greek or even ancient egyptian hieroglyph- the main thing is a clear pre definition of any sign you use". So, I think there are no common rules here.

• Well, there are standard international rule of what symbols to use where. I'd say that for the OP's question, it's just a matter of the handwriting style. It is really sigma and not delta. Mar 6 '16 at 17:07