One of my biggest pet peeves with traditional mathematical pedagogy is the ubiquity of non-semantic names (naming things after people being the typical offense...), even when an appropriate semantic identifier of similar length is available. For example, it costs basically nothing to say "frequency decomposition" instead of "Fourier transform," or "lossless compression theorem" instead of "Shannon theorem."
Even when no such semantic identifier has been established as "canonical," it is often not hard to imagine such names for common mathematical concepts. Some examples:
- L'hopital's rule: "slope ratio rule"
- Riemann integral: "domain integral"
- Lebesgue integral: "codomain integral"
- Kalman filter: "covariance filter"
- Normal distribution: "central limit distribution"
Of course, short semantic names for complicated concepts are not perfect - but I think, all else being equal, imperfect semantic labels are still a lot better than arbitrary or meaningless labels.
Does anyone know of any modern mathematical textbooks that strongly prefer semantic names to non-semantic names? Is this something that we should ever expect to improve, or has the use of arbitrary identifiers become a sufficiently-ingrained part of mathematical culture that I should just give up hope on it ever being done differently?