How to make a mathematical text more concise?
In writing a summary of a thesis, I would actually go about this the opposite way.  Don't start with 175 pages and try to cut it down to 20.  Instead, start from 0 and try to write a document that will be useful to a reader who wants to know whether to pick up the entire thesis.

I would probably do something like this:


Background description that explains why your problem is interesting.  2-3 pages maximum.
General description of what your algorithm achieves, why it is useful, and how it improves on the previous state of the art.  Don't try to explain the details of how the algorithm works.  Consider including a brief illustrative example if space permits at all; that will be very helpful to the reader who wants to know what the heck you are doing.
If space remains, state main theorem(s), preceded by any definitions needed for them to make sense.  If necessary, gloss over the less interesting parts of those theorems.  E.g. a complicated set of conditions can be encapsulated in "under mild assumptions" (assuming they are mild), a complicated formula could be replaced by "there exists a constant".
If space still remains, consider including a very high-level overview of your methods.  Specifically mention any parts that you think are especially interesting or novel.


This isn't my field, but I gather that in computer science it is pretty common to publish results first as relatively short conference papers, and then to give more complete details in follow-up papers in journals.  You might try reading such conference papers (and compare them with their extended versions) to see what details people focus on.  Writing this summary will also be good practice for eventually producing page-limited papers based on your work.