In Authorea Beta you have a number of ways to insert mathematical notation.

1. Inline equations using the visual math editor
If you are writing rich text, you can click on the math symbol in the toolbar.

In the popup window, you can input basic mathematical symbols to compose simple formulae using a visual, easy to use, environment. You can also inspect the TeX source straight from the visual editor by clicking the tab at the top of the editor.

2. Equations in a LaTeX block
If you want to write more complex math, insert a LaTeX snippet in your document To insert a LaTeX block, click on Insert -> LaTeX:

In the LaTeX block, you can insert an inline formula by typing the equation inside $..$ . For example, type: An inline equation is $e=mc^2$.

To obtain a numbered formula, you need to use the {equation} environment. For example, type:

\label{eq:sedov}
R(t)= A \left(\frac{E_0}{\rho_0}\right)^{1/5}t^{2/5}

Click outside of the LaTeX block (or on another block in the document) to render the LaTeX equation:

If you label it with an eq: label, you will then be able to reference it using the reference tool.
3. Equations in Markdown blocks
You can input LaTeX equations in Markdown blocks, both inline and as a separate line using the $$..$$ and $..$ syntax. For example, type in a Markdown block:
Equation inline $$x=2$$ and one more equation $e=mc^2$