Comment by throwaway_2494

Studies have figured out how many 'concepts' or 'chunks' of information a typical human brain can hold in working memory. The famous 7±2 is a common way this is expressed. This research has been disputed and further nuanced (I know, I know, replication crisis...), but for the sake of argument, assume that there is some cognitive limit to how much information we can hold in our heads at once.

In the beginning, calculus as invented by Newton used complex ruler and compass constructions. Newton had a high cognitive capacity, so it was understandable to Newton. It took mathematicians coming later, including Leibniz, to turn this technique into a body of work that fits more easily into the average human mind. Newton and Leibniz independently developed calculus, but Leibniz's notation and formalism in particular provided a much more compact way of expressing and manipulating the ideas of calculus.

Open up Spivak at any page and find a formula; you should probably find that it contains 7±2 'things'. Like an integral, say: the integral sign, lower and upper limits, the function inside, the variable of integration. Then the theory and the rules for transforming these expressions was created so that working with calculus becomes mostly a set of rote operations.

Now a 1st-year student can do more calculus in a week than Newton even could have done in a year.

Now imagine aliens land on the Earth which have 10x our cognitive capacity, and we ask them about their mathematics. It would probably be incomprehensible to us because it would not have gone through a cognitive bottleneck sufficiently small to force it to fit into our minds. They might be totally happy with a mathematical expression containing 700 'things.'

We now find ourselves in this situation, except the alien is an AI we created.

I believe a cognitive bottleneck needs to be maintained so that maths can still remain human maths.

EDIT: Basically, mathematical elegance is finding a representation which allows irrelevant detail to dissapear.