\begin{problem} analogue to \begin{proof}

The following provides a MWE:

\documentclass{article}
\usepackage{amsmath}

\newtheorem{problem}{Problem}

\begin{document}
\begin{problem}
    This is a new problem.
\end{problem}
\end{document}

enter image description here

To further customize the look of the problem environment, we can resort to the amsthm package and the \newtheoremstyle command. A MWE is given below:

\documentclass{article}
\usepackage{amsmath,amsthm}
\newtheoremstyle{problemstyle}  % <name>
        {3pt}                                               % <space above>
        {3pt}                                               % <space below>
        {\normalfont}                               % <body font>
        {}                                                  % <indent amount}
        {\bfseries\itshape}                 % <theorem head font>
        {\normalfont\bfseries:}         % <punctuation after theorem head>
        {.5em}                                          % <space after theorem head>
        {}                                                  % <theorem head spec (can be left empty, meaning `normal')>
\theoremstyle{problemstyle}

\newtheorem{problem}{Problem}[section] % Comment out [section] to remove section number dependence

\begin{document}
\section{Simple Problems}
\begin{problem}[Analytic]
    Prove that $2+2 = 4$.
\end{problem}
\end{document}

enter image description here


Also mine suggestion, as azetina suggested:

\documentclass{article}

\usepackage{amsthm}

\theoremstyle{remark}
\newtheorem{problem}{Problem}

\begin{document}

\begin{problem}
Prove that $2+2 = 4$.
\end{problem}

\end{document}

enter image description here

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