Guides · 5 min read
How equations are read aloud
Reading maths aloud is a solved problem for people: lecturers do it every day. They don't spell symbols; they say what the structure is. Aethel follows the same conventions, so an equation sounds like a sentence.
Updated 6 October 2026
The conventions
- Grouping is spoken: a bracket with an operation inside becomes “the quantity …”.
- Powers and subscripts: “x²” is “x squared”, “xᵢ” is “x sub i”, “e^(−x²)” is “e to the power of negative x squared”.
- Negative and minus are different: “−b” is “negative b”, “a − b” is “a minus b”.
- Greek letters by name, with ε₀ and μ₀ read as “epsilon naught” and “mu naught”.
- Calculus in words: gradient, divergence, curl, partial derivatives and integrals with their limits.
- Probability: “P(A|B)” is “P of A given B”, and “X ∼ N(0, 1)” is “X is distributed as N of 0, 1”.
- Accents: “ŷ” is “y hat”, “x̄” is “x bar”.
Examples
x = (−b ± √(b² − 4ac)) / 2a
Aethel says
x equals the quantity negative b plus or minus the square root of the quantity b squared minus 4ac, over 2a
P(A|B) = P(B|A) P(A) / P(B)
Aethel says
P of A given B equals P of B given A, times P of A, over P of B
∇ · E = ρ / ε₀
Aethel says
the divergence of E equals rho over epsilon naught
θ ← θ − η ∇L(θ)
Aethel says
theta is updated to theta minus eta times the gradient of L of theta
Try your own on the equation demo. It runs the same speech engine as the app, in your browser, with no account.
Descriptions for figures, tables and complex formulas
When a book is imported, equations, figures and tables are detected and kept as their own excerpts. Before you listen, each can get a short spoken description of what it shows or computes, written by an AI model from the surrounding text. The printed version always stays on screen.
Limits
- Very large matrices and commutative diagrams are described, not read entry by entry.
- Notation that a PDF stores as an image can only be described, not read symbol by symbol.
- Spoken notation is most complete in English. Translated chapters keep the printed formulas.
- Unusual notation can be misread. If you hear one, use the contact form and include the book and page.
Questions
Can I hear the formula again?
Yes. Tap it to replay, or ask for an explanation or a worked example.