Triangle of Power

Bad/Confusing/Complex notation can absolutely ruin a learner's attempt to grok a piece of math, it's not a trivial issue at all, and it comes up in all levels of math. But good notation doesn't necessarily mean easy understanding. It's just like language. If I speak a different language, forget about communication in any deep way. But even if I'm speaking the same language, it's still not guaranteed we can communicate well or at all. Absence of shared language guarantees the impossibility of communication, but it's presence guarantees nothing. The author is correct about one thing : Notation is incredibly under-appreciated and under-discussed by mathematicians, although it has immense power to shape thinking. Some visionaries like Charles Babbage, Kenneth Iverson or Stephan Wolfram might talk about it every 50 year or so, but that's it. It's mind boggling how the primary tool of communication is just developed ad-hoc on a whim with only minimal explanation and formalization. >But is there some book or dictionary that lays this out in a novel way What do you mean by "this"? is it specifically the overbars-and-underbars notation used in the article? as far as I know, that's the first time I encountered it. But the idea that exponentials, logarithms and roots all basically say the same thing and that notations should reflect that is discussed a lot, 3blue1brown has a very well known video that explains it in a visual way. [this video]

> Mathematics is by far the biggest and longest running open source project on this planet and we are absolutely able to traverse it by centuries or millenia. This works across languages and cultures. This goes against what I understand about mathematics. I've tried to break it into a few sections. Open source: Things in mathematics once defined, tend not to change, even when changing would be beneficial. Open source software tends to be a bit more malleable, but even long running things that can't change for fear of breaking things like POSIX or the X Window System end up getting alternatives that the industry slowly turns towards. But mathematics just stays stuck. Multiple subfields will end up using the same glyph to mean two different things and when those subfields intersect it gets very bad very fast. Even small quality-of-life fixes never end up getting accepted into use. Here's a great example by 3Blue1Brown: [this video] Another example (if you're interested in going down a bit of a rabbit hole) is the history of vector algebra vs quarternions. We ended up going with vector algebra, then learned that quarternions were actually better, but we continued to teach / and be taught vector algebra. > we are absolutely able to traverse it by centuries or millenia Well, this seems easy to disprove since knowledge does get lost and things keep getting rediscovered. For example, Calculus was rediscovered multiple times: - Archimedes (at least part of it with his method of exhaustion