Unicode Math Quirks

If one follows the Unicode standard — particularly the 80 slot mathematical block from U+2100 to U+214F, for which the STIX Math glyphs are protrayed here:

a segment of unicode

then one could be led to the following tasteless usage (display enlarged):

=1
where
= n=0 1n!

Examination of this 80 slot block in the Unicode standard shows that it contains a miscellaneous assortment of special mathematical characters using various fonts, each of which was intended to have a dedicated mathematical meaning. One skeptical about this observation should take particular note of U+2118, i.e., ℘, the rather standard symbol for the Weierstrass “℘-function”, the canonical generator of the field of “even” doubly periodic meromorphic functions over the subfield of constants on a 1-dimensional complex torus — a glyph one is not likely to see in any other context.

It's unfortunate that those who later filled out the Unicode standard appear to have confused the dedicated mathematical characters with the glyphs used at an early stage to represent them. For example, the upper case gothic “R” (ℜ at U+211C) was originally intended to be a mathematical symbol for the function “real part” (of a complex number), while the upper case double-struck “R” (ℝ at U+211D) was originally intended to be N. Bourbaki's notation for the field of real numbers. In fact, the sequence of seven upper case double struck symbols in the 80 slot mathematical block of Unicode, namely, C, H, N, P, Q, R, and Z, all represent notations in the style of N. Bourbaki.

One might note omission from this list of A. Weil's notation 𝔸 —an upper case double-struck “A”— for the ring of adeles. On the other hand, given the selectivity in the 80 slot mathematical block, one might question the inclusion of of “D” (ⅅ at U+2145), apparently at the request of the designers of a computer algebra system, to denote differentiation as an operator.

It's unfortunate that when the designers of Unicode later decided to add complete blocks of double-struck, calligraphic, and gothic characters to the standard, they left blank slots in those blocks corresponding to glyphs previously introduced for the dedicated mathematical symbols in the block from U+2100 to U+214F. Inasmuch as the Unicode standard is a standard for character meanings rather than a standard for particular ways of representing characters by glyphs, this was an error. Even though and even because there is a not great deal of merit in many of the choices for special mathematical characters in the 80 slot block of dedicated mathematical symbols, the slot gaps in later glyph sequences should be filled. (Of course, there would be no point in creating problems at this stage by making gratuitous accompanying slot deletions in the 80 slot block of mathematical characters.)