\documentclass{article}

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\newenvironment{solution}{\renewcommand{\proofname}{Solution}\begin{proof}}{\end{proof}}

%for font.  see https://tex.stackexchange.com/a/272756
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\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Math 4803}
\rhead{Term Paper Peer Review}


\begin{document}
\title{Title of paper:\underline{\hspace{15em}}}
\author{Author(s) of paper:\underline{\hspace{20em}}}
\date{Referee number:\underline{\hspace{5em}}}
\maketitle
\vspace{5em}

\subsection*{My favorite thing in the paper}
In \textbf{complete sentences}, identify the thing you liked best: a nice theorem or proof, a helpful explanation, etc.\\
\vspace{10em}

\subsection*{Numerical ratings}
Rate each of the following aspects of the paper on a scale of 1 to 5, where
\begin{itemize}[itemsep=0em]
	\item 1 = "strongly disagree"
	\item 2 = "disagree"
	\item 3 = "neutral"
	\item 4 = "agree"
	\item 5 = "strongly agree"
\end{itemize}

\begin{center}
\bgroup
\def\arraystretch{1.2}
\begin{tabular}{|l|c|c|c|c|c|}
\hline
 & 1 & 2 & 3 & 4 & 5 \\
\hline
There is a coherent main topic for the paper & & & & & \\
\hline
The paper is directed to the correct audience (Math 4803 students) & & & & & \\
\hline
The paper presents at least one substantial proof or computation & & & & & \\
\hline
The paper is free of serious mathematical errors & & & & & \\
\hline
New ideas are well-motivated & & & & & \\
\hline
The presentation is in a logical order & & & & & \\
\hline
The mathematical notation is consistent & & & & & \\
\hline
The abstract gives a good summary of the paper & & & & & \\
\hline
Adequate references are provided & & & & & \\
\hline
The paper was carefully proofread & & & & & \\
\hline
\end{tabular}
\egroup
\end{center}

\subsection*{Explanation of ratings}
For the three lowest-rated items above, explain your numerical rating.  This explanation should be \textbf{helpful} and \textbf{constructive}, and not mean-spirited.
\vspace{12em}

\subsection*{Suggested improvements}
Give three concrete suggestions for improvement.  For instance, these could be ways of improving any low ratings you gave above.
\vspace{18em}

\subsection*{Questions}
What questions do you have about the paper?  For instance, "where did these ideas come from?" or "can you give an example of..." are good questions.

\end{document}