Well, I think there is some confusion here.
The verse environment is used to compose small pieces of poetry, for a whole volume there are packages that give better results.
\begin{verse}
No milk today, my love has gone away \\
The bottle stands for lorn, a symbol of the dawn \\
No milk today, it seems a common sight \\
But people passing by don't know the reason why \\
\par \rightline{written by \emph{Graham Gouldman}, recorded by \emph{Herman's Hermits}}
\end{verse}
Meanwhile the quote environment is suited for make a longer quote than a small one you can emphasize with \emph{}. Most of the times the quote shouldn't be longer than a paragraph. If it is, then is better to use the quotation environment.
So far we have not touched anything concerning mathematics. When what you want is to insert text inside the mathematical environment of LaTeX nor verse or quote are good choices.
The simplest but not the best option is to insert the text using the commands \textup, \textit, \textsl, \textsc, \textmd, \textbf, \textrm, \textsf and \texttt, you should be careful with the spacing:
\[ a = b q + r\] even if \[0 \leq r < b \]
\[ a = b q + r \textrm{ even if } 0 \leq r < b \]
\[ a = b q + r \textrm{even if} 0 \leq r < b \]
Another possibility is to use the commands \mathit, \mathbf, \mathrm, \mathsf and \mathtt affecting only the family, the series and shape of the characters, without modifying the body or spacing. Its major drawback, however, is that LaTeX also ignores spaces in the text included with these commands
\[ a = b q + r \mathrm{even if} 0 \leq r < b \]
\[ a = b q + r \mathrm{\ even if\ } 0 \leq r < b \]
\[ a = b q + r \mathrm{ even if } 0 \leq r < b \]
Fortunately there exists the amsmath package that simplifies our lives with the command \text that makes it easy to insert text inside an equation:
\[ f_{[x_{i-1},x_i]} \text{ is monotonic,}\quad i = 1,\dots,c+1 \]
And also another command \intertext suited for adding text in the middle of a bunch of equations:
\begin{align}
A_1&=N_0(\lambda;\Omega’)-\phi(\lambda;\Omega’),\\
A_2&=\phi(\lambda;\Omega’)-\phi(\lambda;\Omega),\\
\intertext{and}
A_3&=\mathcal{N}(\lambda;\omega).
\end{align}
If you want to display text in the middle of maths, these are the best choices in my own experience. But for a presentation it depends what you want or need. Most of the times, for epigraphs you can use minipage or parbox environment or something like the epigraph package.