Math Symbol Frequencies

Summary

Previous post June 4, 2025 at 5:54 PM by Dr. Drang I checked out a copy of Raúl Rojas’s The Language of Mathematics: The Stories behind the Symbols at my local library this morning. As the subtitle says, it covers the history and eventual standardization of many many mathematical symbols. The book is several years old, but the English translation (by Eduardo Aparicio from the original Spanish) is new. I first read about it in this Scientific American article (that’s an Apple News link). The book has nine chapters on different aspects of mathematics, and each chapter has several short sections covering one or two symbols. Rojas says in the introduction that the sections are more or less self-contained, so you can skip around to the symbols that most interest you. At least for now, I’m starting at the beginning and reading sequentially. An early section that brought me up short was “How Do We Use Mathematical Symbols?” It includes this table, which shows the frequencies of the most-used symbols (20 identifiers and 20 operators) from a set of arXiv math papers and engineering textbooks. I had never before seen anyone do this. It’s obviously modeled on the character and word frequency tables that are pretty common and which form the basis for dissociated press and similar computer diversions.1 The tables were built to help with the development of mathematical handwriting recognition software. Software like Apple’s newish Math Notes, but this frequency analysis was done 20 years ago. I started going through the table, trying to explain to myself why the symbols were in this order, when I ran into some questionable entries, which I’ve highlighted. First, there are two as in the first column. While I can understand a being a popular symbol, there’s no reason for it to be there twice. More curious were the boxes in the last pair of columns. One of them has an overbar, so that could mean any symbol with an overbar (although that should be an identifier, not an operator), but...