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I'm using MathJax to display equations in Blogger.

Is there any way to use the amsthm package in Blogger through MathJax?

What are the other options for formatting theorem, definitions, proofs in Blogger?

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You need to use the "Edit HTML" (under Template) link and add the relevant stylesheets to enable the MathJax feature in your blog. Add the link to the script using the <script> tag and you should be able to get it running using Javascript.

With that, you should create/edit posts using the necessary HTML code to make sure the math equations appear just as you want it to be.

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