[ivancho]

I have a strong mathematical background, and I found the notation completely insane. Right out of the gate in chapter 1 we get a definition that has subscript indices in the subscript index and a summation with subscripts in the superscript, and then composed in a giant function chain. Later we get to 4-level subscripts deep, invent at least 3 new infix operators, define 30 new symbols from 3 different alphabets and we're barely at page 100 out of 600. I have no idea who is supposed to follow and digest this

[chongli]

I’m not sure what specialization of math you studied, but using superscripts for indices is pretty common where you’re dealing with multi-dimensional objects. I used it in a lot of the courses in my degree.

[ivancho]

I have no problem with superscripts. Here are a couple of examples of what I am talking about:

  \left(\Psi_{L} \circ \mathcal{A}_{l_{L}, l_{L-1}}^{\theta, \sum_{k=1}^{L-1} l_{k}\left(l_{k-1}+1\right)} \circ\right. & \Psi_{L-1} \circ \mathcal{A}_{l_{L-1}, l_{L-2}}^{\theta, \sum_{k=1}^{L-2} l_{k}\left(l_{k-1}+1\right)} \circ \ldots \\
  & \left.\ldots \circ \Psi_{2} \circ \mathcal{A}_{l_{2}, l_{1}}^{\theta, l_{1}\left(l_{0}+1\right)} \circ \Psi_{1} \circ \mathcal{A}_{l_{1}, l_{0}}^{\theta, 0}\right)

and

  x_{\mathcal{L}(\Psi)+k-1} & =\mathfrak{M}_{a \mathbb{1}_{(0, L)}(\mathcal{L}(\Psi)+k-1)+\mathrm{id}_{\mathbb{R}} \mathbb{1}_{\{L\}}(\mathcal{L}(\Psi)+k-1), \mathbb{D}_{k}(\Phi)}\left(\mathcal{W}_{k, \Phi} x_{\mathcal{L}(\Psi)+k-2}+\mathcal{B}_{k, \Phi}\right)

and sure, I can figure it out, but you have to agree there are some readability issues

[tsimionescu]

They are not complaining about superscripts for indices, but about having a subscripts in those superscripts. Basically like x² but the ² has a subscript of its own. That is very dense and graphically hard to follow as notations go.