Triangle of Power

My favorite new math notation is the triangle of power: [VIDEO] I slightly modified it to avoid subscript and keep it closer to existing notation for powers: [LINK]

I opened the video in the background and immediately recognized the person: the author behind the 3Blue1Brown YouTube channel. It has a long series of video regarding various mathematical topics which are rather accessible. My favorite by far is a "proposal" for an alternate notation which makes much more sense and, if adopted, would make mathematics way less intimidating (Triangle of Power (2016), 3Blue1Brown - [VIDEO] ). I'd give him a Fields medal (or at least an honorary mention of some sort) :-]

3Blue1Brown has a YouTube video called the "Triangle of Power" which uses a clever bit of notation to unify exponents and logarithms: [VIDEO] A bit lowbrow, perhaps (you'd want Penrose notation or such things in that case).

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. [VIDEO]

A similar idea was put forth on the math stack exchange [1], which I found through this 3blue1brown video [2]. Worth a read/watch! [1] [LINK] [2] [VIDEO]

The creator of the Triangle of Power ( [VIDEO] ) and the Essence of Linear Algebra ( [LINK] ). He is now trying to focus full time on online math education.

In addition, the choice of algorithms in use for arithmetics are a bit counterproductive. Then, notation in some cases is inconsistent and weird. [VIDEO]

3Blue1Brown made a video about math notation for power/logarithms/roots: [VIDEO] It's messy to actually draw a triangle, but there are alternative notations for it.