I have reproduced two more figures for which the Mathematica code was given [(1) and (2)], and I have written to Dropbox Support, to inquire if they can restore the broken links.
[Most likely the files are still there, but Dropbox removed support for public links in 2017. See this message.]
UPDATE: Dropbox customer support answered: "As I do appreciate ...
I couldn't find the images, but the Mathematica notebook he posted still seems to be accessible via the Wayback Machine!
I've put a copy temporarily at https://tqft.net/Buoyancy.nb. If someone wants to do the remaining steps, and then let me know that I can take the file down, that would be great.
The "teapot" error is one of the various responses we return if something looks very suspicious at the http/form level - most likely because of an XSRF check failure. On mathoverflow, this is usually from bots that spend their entire life trying to edit one post (seriously, it is always the same post - I have no idea why, there's nothing particularly unusual ...
This MathJax tutorial contains instructions for commutative diagrams.
That should be enough for basic drawings of this type.
You might also want to check out the MO FAQ post Best way to post graphics to MO.
This post assumes that you already have the image file.
Pretty diagrams are nice, but would advice against spending too much time polishing graphics as ...
From the formatting help page:
Images can be added primarily by using the the editor toolbar button . This brings up a special interface that allows you to upload an image online (through the imgur hosting service) through us - even from your clipboard. Alternatively, it can be input similarly to adding a link:
HTML <img src="http://example.com/img....
One way to approximate a figure caption is to add this immediately
after your image:
Figure caption here.
The br breaks to a new line. The  's tab in horizontally.
The sup's make the tex smaller (superscript). For example:
This may be a bug caused by the recent migration to CommonMark, and indeed it seems to be related to the large amount of HTML (I've encountered similar issues while trying to fix broken images across the network).
I've fixed it by adding an extra newline between
and the images. They show up now.
I suppose the problem which was suggested by Stephan Kohl, i.e. missing extension. I suggested an edit which changed the links from links like http://www.freeimagehosting.net/ta8ni to links to the actual png picture: http://www.freeimagehosting.net/newuploads/ta8ni.png . The post seems to be fine after this edit.
My personal opinion is that it would be ...
It is difficult to give some advice since it is not clear what went wrong. The OP has confirmed in the meantime that now the images are visible in the post. As you can see in the revision history, all I did was adding the missing "!".
If a picture is uploaded through the editor, the Stack Exchange software should take care of the correct syntax for the ...
This is not an answer to Joseph O'Rourke's question, but rather an apology of my own, along the same lines: Many of my old posts used images that I hosted at Photobucket, and they have now have disallowed direct linking for free accounts. Thus I have now begun moving all the images to imgur as well.
I will try to restrict myself to bumping 4 or 5 old ...
Another suggestion, in case you have qualms editing forcibly OP's post : wouldn't it be easier to make your illustration answer community wiki ? This seems like a good way to avoid unintended reputation gain.
I stumbled upon this post on Meta Stack Exchange, where various reasons why typing the math formula is preferred over including images: Why are images of text, code and mathematical expressions discouraged? (There are several rather detailed answers - I recommend to anybody interested in this topic at least having a look there.)
Let me summarize briefly at ...