Mathematical notation is intended to represent the essence of mathematical thought, analogously to how musical notation represents music.

“So it's really interesting that mathematics couldn't be understood as a way to systematize thought beyond the human mind. And so in a way, you, for instance, in music, you have notations for sounds and music that allow you to talk to other musicians about what they should be playing, and it's something that's just trying to capture the essence of the music in this notation.”

“And mathematicians were trying to find a notation for the essence of when you have mathematical thoughts. And they expanded this beyond the human mind because you can write down things in mathematics that are larger than what you can fit in your own imagination.”