How to get Beamer Math to look like Article Math

Add \usefonttheme[onlymath]{serif} to your preamble. That is,

\documentclass{beamer}% http://ctan.org/pkg/beamer
\usefonttheme[onlymath]{serif}
\begin{document}
\begin{frame}
 $x^2 + y^2 = z^2$
\end{frame}
\end{document}

For both text and math in Computer Modern, use the serif document class option. Other combination of font selection is also possible. See this link for a nicely compiled collection.

_{Older versions (prior to v3.33) supported the class option \documentclass[mathserif]{beamer}.}

Alternatively, you can include

\usefonttheme{professionalfonts}

inside the

mode<presentation>{...} 

environment.

As @egreg commented, @Werner's answer might incur conflicts. Actually, Beamer supports for different fonts through the \documentclass.

In your case:

\documentclass[mathserif]{beamer}
...

for all other combinations and styles along with the outputs please refer to this comprehensive document.