One thing I've always struggled with Math is keeping track of symbols I don't know the name of yet.<p>Googling for "Math squiggle that looks like a cursive P" is not a very elegant or convenient way of learning new symbol names.<p>I wish every proof or equation came with a little table that gave the English pronunciation and some context for each symbol used.<p>It would make it a lot easier to look up tutorials & ask questions.
I must confess that I have an irrational fondness for the use of weird symbols in math and technical documents, whether it's for a homework assignment in school or a white-paper for work.<p>My unit tests are literally full of hieroglyphics. My favorite design doc to this day is one where I sprinkled Sumerian cuneiform throughout the text, e.g. 𒀭𒄑𒉋𒂵𒎌 and 𒂗𒆠𒄭 (Gilgamesh and Enkidu) instead of Alice and Bob.
I left college with a math degree and a profound antipathy for weird cursive symbols. The one that nearly killed me was the Greek "xi". I couldn't pronounce it, and I couldn't write it with any fluency, and in some of the classes I took it was <i>everywhere</i>.
<p><pre><code> >>> import unicodedata
>>> unicodedata.name('℘')
'SCRIPT CAPITAL P'
>>> ord('℘')
8472
</code></pre>
<a href="https://en.wikipedia.org/wiki/Letterlike_Symbols" rel="nofollow">https://en.wikipedia.org/wiki/Letterlike_Symbols</a><p>Good enough for me.<p>Notably, this is distinct from ("MATHEMATICAL SCRIPT CAPITAL P").<p>> Books were printed in Fraktur, where the p looks quite normal, i.e., quite different from a handwritten Sütterlin p which could explain, why it hasn't been replaced in the publication of Amandus Schwarz.<p>Indeed. ("MATHEMATICAL FRAKTUR CAPITAL P") is also separate (but also, Unicode considers these mathematical symbols to exist separately from "text written in Fraktur script". So you get separate characters allocated for these symbols, but they're not intended to be suitable for printing in Fraktur - which is supposedly a presentation (i.e. typeface selection) issue.<p>Personally I'm not convinced that mathematical symbols derived from Latin or Greek (or other) scripts really have any claim to being separate "characters". Surely that's what variation selectors are for?
Strangely, the most comfortable I've felt with symbols was when learning quantum computing. At the time, there was no established standard (perhaps it has a standard now), but the symbols were used more intuitively than any other math class I've taken.
In the same Unicode block is "2129 ℩ TURNED GREEK SMALL LETTER IOTA" with explanation "unique element fulfilling a description (logic)".<p>That seems a ridiculous choice for a symbol — turning one of the most symmetrical letters upside down!<p>Background: <a href="https://philosophy.stackexchange.com/questions/51563/what-is-the-symbol-in-formal-logic" rel="nofollow">https://philosophy.stackexchange.com/questions/51563/what-is...</a>
There is an old convention in physics - from the time when Germany was world-leading in physics - to write vector-valued variables in Fraktur. Using cursive (old German cursive is weird) seems related, though AFAIU the "vectorness" of the ℘ function is just the two components of a complex number.
To me \wp looks like a plain cursive p. Had I never seen it referred to as a special character I would have thought it was a lower-case p. There are many "styles" of cursive writing. But it's nice to have specific styles of these letters for use in mathematics.
One thing I like about programming languages is that they usually constrain themselves to strings of ASCII characters, instead of using lots of more or less inscrutable symbols like mathematics does. For example, where a mathematician writes "Σ", a programmer simply writes "sum".
So this letter ℘ is distinct from another unicode symbol (that I can't copy-paste here?), which we often use for "power set" in math; it's given by U+1D4AB.
If you click the link to the wikipedia page on Sütterlin[0] that is mentioned in one of the answers, there's a link to <i>another</i> wiki page about the Antiqua-Fraktur dispute[1]. Apparently 19th and early 20th century Germany had a whole nationalistic debate about which handwriting script should be used, with the nazis ending it by preferring (somewhat surprisingly, to me) the <i>international</i> choice of the Latin alphabet.<p>Combine that with Göttingen being the capital of the maths world at the time [2], and I wouldn't be surprised if that dispute had some (now mostly forgotten) influences on funny maths squiggles in general.<p>Tangentially, the original question feels somewhat asked in bad faith imo, calling many names "bad" with unearned authority, and implicitly seeking popular votes to support their position. Also sentences like:<p>> <i>BTW Abramowitz & Stegun uses P. Wow. See p 629.</i><p>It's great if you're passionate about maths, but clutching pearls over the use of "P" instead of "℘" is a bit much (reminds me of the "π vs τ" debate and how upset that seems to make some mathematicians. Meanwhile Euler, who came up with using "π" as a circle constant, wasn't consistent about what value he gave it at all[3] - he'd just pick whatever circumference-to-radius ratio worked best for his proof at hand).<p>It's pretty clear that "℘" essentially originated as a Fraktur-based glyph that most Germans of the time would intuitively read as the equivalent of "P" in Antiqua. The letter "P" is pronounced "Pe" in German. No mathematician would have been confused by Abramowitz & Stegun's notation, just like writing "R" instead of "ℝ" won't confuse anyone either.<p>Also Milton Abramowitz was a Jewish man. He might have felt a certain way about using letters associated with German nationalism, but that's just me speculating.<p>[0] <a href="https://en.wikipedia.org/wiki/S%C3%BCtterlin" rel="nofollow">https://en.wikipedia.org/wiki/S%C3%BCtterlin</a><p>[1] <a href="https://en.wikipedia.org/wiki/Antiqua%E2%80%93Fraktur_dispute" rel="nofollow">https://en.wikipedia.org/wiki/Antiqua%E2%80%93Fraktur_disput...</a><p>[2] <a href="https://theconversation.com/how-one-german-city-developed-and-then-lost-generations-of-math-geniuses-106750" rel="nofollow">https://theconversation.com/how-one-german-city-developed-an...</a><p>[3] <a href="https://www.youtube.com/watch?v=bcPTiiiYDs8" rel="nofollow">https://www.youtube.com/watch?v=bcPTiiiYDs8</a>