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I am always reluctant to move comments to chat, if they contain MathJax, because the chat interface doesn't support it. All math expressions are displayed as plain text, with the \$ delimiters, and no attempt to render what's in between.

Some users will move comments to chat "on my behalf", the reasons for which I understand. I know what chat is for, and I know what comments are for. But the consequence is that all the math becomes illegible, and further comments in chat can't employ MathJax either.

Is there any way to overcome this, or is there a chance that SE developers will enable MathJax rendering in chat?

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SE is unlikely to ever enable MathJax in chat, as that was suggested and declined on main meta years ago. Former SE employee Shog9 explained why SE declined this feature request. You can look at the "Related" questions on the linked question to see duplicate questions that had the same outcome.

The linked question and related questions indicate various solutions to render MathJax in chat for you, but those solutions will only work for you -- there's no way to ensure that your MathJax content is displayed properly to other users.

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One thing to know is that comments are treated like post-it notes and they can be thrown away by SE. Their attitude is that relevant information should be posted in an answer, and not in comments. So it might be good to simply post the information in an answer, I know it's not always possible.

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