For mathematics
Read math books and papers on your phone, with the formulas where they belong. Ask the AI with the equation in front of you.
An arXiv paper or a PDF textbook reads in one column, without zooming and with the formulas where they belong. The AI cites the passages it relies on, and any formulas in its answer come out typeset.
The symbols
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.
A PDF that finally reads well on your phone.
No zooming, no dragging from side to side, no words cut in half.
Green and Tao · arXiv math/0404188 · p. 7
3. Pseudorandom measures
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. In the text, subscripts are real subscripts and variables are in italics, and all of it can be selected and searched as text. The centred equation stays on its own line, as a crop of the original page. In a book with drawn formulas (such as OpenStax), each formula is rebuilt as a vector drawing in its slot. We shortened the text to fit here; nothing else was changed. The original page is still there: switch views whenever you want.
Reading math papers, textbooks and lecture notes on your phone
Each kind of document carries its formulas differently. This is what you get in each case.
An arXiv paper
Formulas inside the text are text: indices come out as subscripts and superscripts and variables in italics, and you can select and search them. Centred equations come as a crop of the page, in place and with their number. You can ask about a specific lemma or definition, and the answer cites the passages it relies on.
A textbook
Some textbooks, such as OpenStax, draw the formulas instead of setting them as text. They are rebuilt as vector drawings in their slot, crisp at any size and in all three themes (light, sepia and dark). They cannot be selected, but with an account you can tap one and ask the AI about it: it reads it from the image.
A book in EPUB
An EPUB with formulas as images, such as those from Project Gutenberg, reads as is: the text fits your screen and the font size you choose, and the formulas stay where they belong. With an account, you can tap one and ask about it. And when the AI answers with a formula, it comes out typeset, with fractions, roots and sums, not as plain text.
What a PDF reader with AI does not do with mathematics
This is what Marginalia does not do, or does not do well yet, with formulas.
A drawn formula is not text
If the PDF carries it as strokes (as OpenStax books do), there is no text to recover: it looks right and scales, but it cannot be selected or searched, and the AI only reads it if you tap it to ask about it, which needs an account. Turning those strokes into text takes formula recognition, and that is not here today.
It does not check calculations or proofs
The AI explains with the book in front of it and can work through a step, but it is not a computer algebra system: it can get a calculation wrong. That is why every answer carries its citations, and one tap takes you to the passage to check it.
Two-column exercise pages
The exercise pages of some textbooks run in two numbered columns, and in the text view they can come out interleaved. For those pages, the original is still there.
Centred equations in a paper
Equations on their own line (numbered ones, ones with fractions or sums) come as a crop of the page, not as text. They read the same, but they cannot be selected or searched, and what the AI gets from them is the text the PDF carries, which for an equation is usually jumbled.
Privacy of lecture notes or a manuscript
The file, never
The PDF or EPUB is stored in the browser's private storage and is not uploaded to any server. The file of an unpublished manuscript or of your course notes stays on your device.
When you ask, the question and the passage
Your question travels with the fragments of the document needed to answer it, and, if you tap a formula or a figure to ask about it, its image.
With an account, the text and your notes too
With an account, the book's text passes through the server to prepare the AI's search, without being stored. What is stored in your account is where you are, your highlights and notes, and your conversations, so you can continue on another device. You need to open the file once in each new browser, because it is not uploaded.
Tested with arXiv, OpenStax and Project Gutenberg
These are the documents, all openly available, used to test how formulas come out.
Green and Tao (arXiv)
"The primes contain arbitrarily long arithmetic progressions": 56 pages of LaTeX with about 300 centred equations.
Calculus Volume 1 (OpenStax)
791 pages (Spanish edition) with drawn formulas, rebuilt as vector drawings.
Attention Is All You Need (arXiv)
Numbered equations and formulas inside the text. Compared with the reference text, 96% comes out in the original reading order.
Calculus Made Easy (Gutenberg)
EPUB with formulas as vector images: the sample on this page.
If one of your PDFs comes out wrong in the text view, tell us which one or where it comes from, and its layout can go into the tests:
Before you open your first book.
Do formulas look right when a PDF is turned into text?
Can I copy a formula?
How do formulas look in the AI's answers?
Does it work with OpenStax books?
Is my document uploaded anywhere?
How much does it cost for a student?
Open a paper, a textbook or your lecture notes
No account and nothing to install. Calculus Made Easy is one tap away; a PDF with formulas is converted the first time you open it, and the conversion stays saved in the browser. If you read often, you can install it as an app.
Free, no account. The file never leaves your browser.