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Math Version of Goodreads.com?
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Interesting idea. Since you're the one posing it, what do you think it should be? What is it you're looking for? Why do you think you can't get that at Goodreads? Have you searched for math centric groups at Goodreads?

If you expand the discussion beyond books, math.stackexchange.com is a site that gets lots of traffic and where you can get good answers to most of your math questions. Very different feel from Goodreads, though. It's first and foremost a math site, not a social networking site.
I think the best approach to get a large audience, would be to emphasize math and logic puzzles and games.
So, instead of a "library" of books, it would be a collection of puzzles, games, books, images that specialize in math and logic and related fields. People could post their puzzles, and others could post suggested answers and spoilers. The puzzles could be subjectively rated by level of difficulty. People could upload images generated with math-based designs.
People could also post math-based and logic-based paradoxes, interesting derivations or proofs of theorems, interesting applications of math to everyday problems, ... the sky is the limit!
So, instead of a "library" of books, it would be a collection of puzzles, games, books, images that specialize in math and logic and related fields. People could post their puzzles, and others could post suggested answers and spoilers. The puzzles could be subjectively rated by level of difficulty. People could upload images generated with math-based designs.
People could also post math-based and logic-based paradoxes, interesting derivations or proofs of theorems, interesting applications of math to everyday problems, ... the sky is the limit!
Pramod wrote: "yeah I also searched for group's regarding math's.. but there is no such a group"
I found several math-centric groups:
https://www.goodreads.com/group/show/...
https://www.goodreads.com/group/show/...
https://www.goodreads.com/group/show/...
Some of these are more active than others, but you could help to reactivate a group by joining it and posting suggestions.
I found several math-centric groups:
https://www.goodreads.com/group/show/...
https://www.goodreads.com/group/show/...
https://www.goodreads.com/group/show/...
Some of these are more active than others, but you could help to reactivate a group by joining it and posting suggestions.

My idea of what a math version of Goodreads is pretty much like what David said--there would be math puzzles, math theorems, math strategies, and math-related images that everyone can discuss and maybe even "rate." Maybe they could describe their thoughts and experience with the stuff previously listed, like how Goodreaders discuss their thoughts and experiences with books, reading, and/or writing. I think recreational mathematics in particular might be more appealing to such a website, since as Dana observed, a regular math website may not have a lot of traffic.
I have actually never intentionally searched for math-centric groups on Goodreads. (The idea never crossed my mind lol) I clicked through the links of the groups Betsy sent; maybe I might join a group. :)
I have seen websites dedicated to recreational mathematics. They are not like the math version of Goodreads I have been thinking about, but I thought you all might be interested in looking at them:
https://mindyourdecisions.com/blog/
https://puzzlersworld.com/puzzles/mat...
https://solveme.edc.org/
The puzzles for the third link might seem basic to some people, but I think you can create your own puzzles and make them as hard as you want.
Should there be a website like Goodreads.com, except math-themed instead of book-themed, and if so, what do you think such a website would be like, or should be like?