For mathematics
An arXiv paper or a textbook reads in one column, in your type size, and the formulas stay where they were: subscripts as subscripts, numbered equations on their own line, and the ones the PDF draws as vector drawings that scale with the text. The AI answers citing the passage, and when the answer carries a formula, it typesets it. No account, no install, no upload.
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Green and Tao · arXiv math/0404188 · p. 7
If A is a finite non-empty set (for us A is usually just ZN) and f : A → R is a function, we write E(f) := E(f(x)|x ∈ A) for the average value of f, that is to say
E(f) := 1|A| ∑x∈A f(x).
Here, as is usual, we write |A| for the cardi-
nality of the set <i>A</i>. More generally, if <i>P</i>(<i>x</i>) is any statement concerning an element of <i>A</i> which is true for at least one <i>x</i> ∈ <i>A</i>, we define the conditional expectation. Let <i>m</i><sub>0</sub>, <i>t</i><sub>0</sub> and <i>L</i><sub>0</sub> be small positive integer parameters.
7
What you see above: page 7 of an arXiv paper (Green and Tao, 2004), as it comes out of the converter. The centred equation stays on its own line, and in the text the subscripts are real subscripts, selectable and searchable. In a book with drawn formulas (OpenStax) each formula is rebuilt as a vector drawing in its slot. The text is trimmed to fit; nothing else is.
The original page is still there. Switch whenever you want.
What it is for
Every source carries its formulas differently, and the reader does with each the best that can be done.
Try it: press a marker in the answer.
What do dx and the integral sign mean?
According to the book, d merely means "a little bit of": dx is a little bit of x, and those little bits may be considered indefinitely small. The integral sign is merely a long S, "the sum of": ∫dx is the sum of all the little bits of x, which is the whole of x.
"These dreadful symbols are: (1) d which merely means 'a little bit of.' Thus dx means a little bit of x; or du means a little bit of u. [...] But you will find that these little bits (or elements) may be considered to be indefinitely small."
"(2) ∫ which is merely a long S, and may be called (if you like) 'the sum of.' Thus ∫dx means the sum of all the little bits of x; or ∫dt means the sum of all the little bits of t."
The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning of the two principal symbols that are used in calculating. These dreadful symbols are: (1) d which merely means "a little bit of." Thus dx means a little bit of x; or du means a little bit of u. (2) ∫ which is merely a long S, and may be called (if you like) "the sum of." Thus ∫dx means the sum of all the little bits of x.
What it does not do
With this audience, overpromising is expensive. This is what Marginalia is not and what it does not do well yet with formulas.
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What it is tested with
The converter is tested with these openly licensed documents, and with formulas it is checked by hand where they land and how they look.
If your PDF comes from another layout and comes out wrong, send it: every new layout goes into the tests.
Questions
It depends on how the PDF carries them. If they are text (LaTeX), yes: indices, italics and equations on their line. If they are drawn, they are rebuilt as vector drawings in place, which look right at any size but are not text.
As in any PDF reader, not usefully: a formula as text loses its structure, and a drawn one cannot be selected. What you can do is tap it and ask the AI to write it out in LaTeX.
Typeset with KaTeX, the same engine Wikipedia uses: fractions, roots, sums and matrices as in a book, not in plain text.
Yes; they are the layout used to test drawn formulas. The two-column exercise pages do not come out right yet; the rest does.
No. It stays in the browser's private storage. When you ask, your question travels with the passages needed and, if you point at a formula, its image. Nothing else.
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No account and nothing to install. Calculus Made Easy opens at once; a PDF with formulas converts once and stays saved. If you read often, it installs as an app.